Astronomija

Usporavaju li pada tijela?

Usporavaju li pada tijela?


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Nedavno sam vodio neke rasprave o crnim rupama i problemu pada tijela koji su zauvijek trebali doći do horizonta događaja. To je u osnovi ono što je Einstein rekao u svom radu iz 1939. godine o stacionarnom sistemu sa sfernom simetrijom koji se sastoji od mnogih gravitacijskih masa. On je rekao "lako je pokazati da i svjetlosnim zracima i materijalnim česticama treba beskrajno dugo (mjereno u" koordinatnom vremenu ") da bi dosegli točku r = μ / 2 kada potječu iz točke r> μ / 2".

Sad sam veliki obožavatelj Einsteina. Ali čini se da postoje dva problema s ovim:

  • Jedno je da je Einstein zaključio da crne rupe ne mogu nastati, ali imamo dobre dokaze da tamo postoje crne rupe. Očiti primjer je Strijelac A *. Tu postoji nešto mase Sunca mase 4.28 miliona puta, prečnika manjeg od 44 miliona kilometara, a mi to ne možemo videti. To mora biti crna rupa.

  • Drugo je pitanje što padajuća tijela ne usporavaju. Zamislite da ispustite tijelo na kotu A i ono padne na kotu B. "Sila" gravitacije odnosi se na prvi derivat gravitacijskog potencijala. Dakle, što je veća razlika u gravitacijskom vremenu dilatacije između kota A i B, to tijelo brže pada iznad B. Tada, ako spustite tijelo na koti B, ono pada na kotu C. Opet je veća razlika u gravitacijskom dilataciji vremena između kota B i C, što tijelo brže pada iznad C. U tipičnom gravitacijskom polju sila gravitacije u B je veća nego u A. Dakle, kako se tijelo spušta, ubrzanje raste, kao i brzina pada.

Zamislite svemirski brod gedanken sa kojeg smo suspendirali kabel. Imamo satove na različitim kotama, tako da možemo izmjeriti gravitacijsko dilataciju vremena na svakoj visini. Takođe možemo osloboditi ispitna tijela na svakoj nadmorskoj visini i zabilježiti očitanja sata dok prolaze pored ostalih uzvišenja:

Na kraju eksperimenta možemo umotati kabl i prenijeti snimljena mjerenja kako bismo utvrdili kako su se ponašala naša ispitna tijela. Koliko razumijem, uvijek ćemo otkriti da se vremenska dilatacija uvijek povećava kako se spuštamo, da padajuće tijelo uvijek ubrzava prema dolje i da se ubrzanje i padajuća brzina uvijek povećavaju kako se tijelo spušta. Je to tačno? Ili padajuća tijela nekako prestaju ubrzavati? I usporavaju li se pada tijela?


Prema standardnoj interpretaciji opšte relativnosti (npr. Kako je predstavljeno u "Istraživanju crnih rupa" Taylora i Wheelera, poglavlje 3, ili "Crne rupe, bijeli patuljci i neutronske zvijezde" Shapiro & Teukolsky, str. 343-345), onda da . Ali to ovisi o referentnom okviru promatrača - nema apsolutnog odgovora.

Prema promatraču daleko od crne rupe, stopa promjene radijalne koordinate s vremenom (za objekat koji je počeo radijalno padati prema unutra daleko od nerotirajuće crne rupe) data je sa $$ frac {dr} {dt} = - lijevo (1 - frac {r_s} {r} desno) lijevo ( frac {r_s} {r} desno) ^ {1/2} $$ gdje $ r_s $ je Schwarzschildov radijus i $ r $ i $ t $ su Schwarzschild koordinate.

Ako ovo nazivamo padajućom brzinom mjerenom od strane udaljenog promatrača, onda diferencijacijom možemo vidjeti da ona prolazi kroz maksimum pri $ r = 3r_s $ i to $ dr / dt rightarrow 0 $ kao $ r rightarrow r_s $.

Međutim, promatrač koji prati padajuću česticu potpuno se ne bi složio. Njima je brzina data sa $ dr / d tau $, stopa promjene od $ r $ s obzirom na vrijeme na njihovom satu. $$ frac {dr} {d tau} = - lijevo ( frac {r_s} {r} desno) ^ {1/2} $$ koja se nastavlja povećavati do i ispod horizonta događaja.

Čini se da ovo drugo priznaje mogućnost bržeg putovanja od svjetlosti, ali ne više od mene (tačno) koji kažem da ako putujete brzinom svjetlosti možete doći do zvijezde udaljene 10 svjetlosnih godina za mnogo manje od 10 godina (mjereno na vašem satu).

Konačno, mogli bismo imati gledište stacionarnih promatrača "ljuske" na fiksnim radijalnim udaljenostima (izvan horizonta događaja, jer nijedan stacionarni promatrač nije moguć ispod horizonta događaja). Izmjerili bi brzinu predmeta koji padaju pored njih $$ frac {dr _ { rm shell}} {d tau _ { rm shell}} = - lijevo ( frac {r_s} {r} desno) ^ {1/2}. $$ To znači da su izvještaji nepokretnih posmatrača (što je suština vašeg pitanja) na sve nižim visinama zaista da brzina padajućeg objekta raste kako pada.

Nema paradoksa sa ovim naizgled kontradiktornim gledištima. Mjerenja ne-lokalnih događaja i pojava ne moraju se složiti u Opštoj relativnosti, gdje čak nema ni saglasnosti oko toga što se podrazumijeva pod "sada" ili čiji koordinatni sistem u kojem referentnom okviru treba koristiti u bilo kojoj posebnoj okolnosti.


Pad u crnu rupu

Čitao sam da biste, ako biste upali u veliku crnu rupu, sa svoje točke gledišta jednostavno nastavili prema njoj i prešli horizont događaja kao ne-događaj - ne biste to ni primijetili. Tada bi vas ubrzo razdvojile plimne sile, a zatim biste se zgnječili u centru.

Također, dok padate i približavate se horizontu događaja, primijetili biste da se čini da se sve zvijezde počinju kretati sve brže i brže. To je zato što se vrijeme za vas usporava.

Pitam se kako izgledaju zvijezde nakon što prijeđete horizont događaja? Svjetlost ne može napustiti crnu rupu, ali svejedno može ući, pa biste li i dalje vidjeli zvijezde? Da li bi se brzo kretali? Ili ne biste vidjeli ništa otkako se vrijeme za vas zaustavilo? Ili nećete vidjeti ništa jer je vrijeme toliko napredovalo da su sve zvijezde izgorjele?

# 2 Supernova74

Pokušajte, javite mi što ćete naći s druge strane !?

# 3 TOMDEY

Uvjeren sam unutra nema ništa --- da je sve što "padne" u stvarnosti skrenuto bočno oko horizonta događaja. Po analogiji, poput prskanja vode iz crijeva na nepropusnu ljusku. Kao dokaz, mi vanjski promatrači nikada ne vidimo mrav ukrštanja, već samo asimptotski usporavamo u zauvijek vrisak. Dakle

nikada ne može doseći dalje od toga. i stoga je u potpunosti sporan. Tom

Priložene sličice

# 4 Gschnettler

# 5 DSOGabe

Pretpostavljam da će biti pomaknuti crveno dok ubrzavate u crnu rupu sve do trenutka kada špagetizacija sve to postavi spornim

# 6 Gschnettler

# 7 TOMDEY

To je istina samo u referentnom okviru dalekog promatrača koji miruje u odnosu na crnu rupu. Ako ste promatrali predmete koji padaju iz referentnog okvira u kojem se približavate crnoj rupi relativističkom brzinom, vidjeli biste predmete kako padaju .

Što se tiče horizonta događaja, prostorno-vremenska metrika je dobro definirana sve do neposredne blizine "singularnosti" u središtu crne rupe, tako da bi objekti i dalje padali prema centru unutar horizonta događaja.

Sama singularnost je matematička singularnost, koja se naziva koordinatna singularnost. Kao fizički objekt, vjerovatno ne postoji u smislu da je bezdimenzionalna točka, jer bi gotovo sigurno bio podložan kvantnim efektima, ali za sada nemamo izvodljivu teoriju koja bi objedinila QM s GR.

Ne, ne bi. Nemoguće je izvana vidjeti nešto što prelazi horizont. Jedini način da vidite kako nešto upada je da vi upadnete, ostavljajući moj izvorni argument potpuno netaknutim.


Usporavaju li pada tijela? - Astronomija

Najnoviji eksperimenti uključuju usporavanje brzine svjetlosti do znatno ispod njene vrijednosti u vakuumu (c). Kako je to moguće?

Evo veze do članaka o jednom takvom eksperimentu.

Iako je brzina svjetlosti u vakuumu konstantna, svjetlost se usporava kada putuje kroz medij. To ne čini veliku razliku kada putujete zrakom, ali to čini razliku u mnogim drugim medijima. Na primjer, svjetlost koja prolazi kroz staklo usporava na dvije trećine brzine u vakuumu. Baš kao što se čovjeku teže kretati kroz vodu nego kroz zrak (tako ljudi plivaju sporije nego što trče), fotoni (čestice bez mase koje čine svjetlost) sporije se kreću kad prolaze kroz medij koji im je težak. Određena stanja materije usporavaju ogromnu količinu (zamislite osobu koja pokušava proći kroz rezervoar melase ili glupog kita), a koristeći ta stanja materije, naučnici mogu usporiti svjetlost do "ljudske" brzine. Nisam stručnjak za fiziku koja je u pitanju, pa evo veze koja će vam pružiti više informacija.

O autoru

Cathy Jordan

Cathy je diplomirala na Cornellu u maju 2003., a magistre obrazovanja u maju 2005. Istraživala je proučavajući obrasce vjetra na Jupiteru dok je bila na Cornellu. Sada je učiteljica 8. razreda Zemaljskih nauka u Naticku, MA.


Padaju li predmeti koji padaju jednakom brzinom (na primjer olovka i kugla za kuglanje spušteni s iste visine) ili padaju različitom brzinom? Znam da pero lebdi vrlo sporo, ali pomislio bih da bi težak predmet pao brže od lakog. Hvala na pomoći. Kladim se na ovu.

Ako nema zračnog otpora, brzina spuštanja ovisi samo o tome koliko je objekt pao, bez obzira na to koliko je težak. To znači da će dva predmeta istodobno doći do tla ako se istovremeno spuste s iste visine. Ova izjava slijedi iz zakona o očuvanju energije i eksperimentalno je demonstrirana ispuštanjem pera i olovne kugle u cijev bez zraka.

Kada otpor zraka igra ulogu, oblik predmeta postaje važan. U zraku pero i lopta ne padaju istom brzinom. U slučaju olovke i kuglice otpor zraka je mali u odnosu na silu gravitacije koja ih vuče na tlo. Stoga, ako ispustite olovku i kuglu za kuglanje, vjerojatno ne biste mogli znati tko je od njih dvojice prvi stigao do tla, osim ako ih niste ispustili s vrlo vrlo visokog tornja.
Odgovorio: dr. Michael Ewart, istraživač sa Univerziteta u Južnoj Kaliforniji

Gornji odgovor je potpuno tačan, ali, ovo je pitanje koje zbunjuje mnoge ljude i oni koji su samozatajni odgovori naših liječnika teško da su zadovoljni. Postoji jedno dobro objašnjenje koje čini sve zadovoljnima - koje ne pripada meni, već nekom poznatom naučniku, ali ne mogu se sjetiti koga (Galileo?) I mislim da bi bilo dobro imati ga ovdje.

(Argument nema nikakve veze s otporom zraka, pretpostavlja se da je odsutan. Odgovor dr. Michael Ewart već odgovara na taj dio.)

Argument ide na sljedeći način: Pretpostavimo da imamo loptu od 10 kg i kuglu od 1 kg. Pretpostavimo da lopta od 10 kg pada brže od lopte od 1 kg, jer je teža. Sada, povežimo dvije kuglice zajedno. Šta će se onda dogoditi? Hoće li kombinirani predmet sporije pasti, jer će lopta od 1 kg zadržati loptu od 10 kg? Ili će kombinacija pasti brže, jer je sada riječ o objektu od 11 kg? Budući da se oboje ne može dogoditi, jedina mogućnost je da su u prvom redu padali jednakom brzinom.

Zvuči izuzetno uvjerljivo. Ali, mislim da postoji lagana zabluda u argumentu. Ne spominje se ništa o prirodi sile koja je uključena, pa izgleda da bi trebala raditi s bilo kojom vrstom sile! Međutim, to nije sasvim tačno. Da živimo u svijetu u kojem je do 'pada' došlo zbog električnih sila, a predmeti imaju mase i trajne naboje, stvari bi bile drugačije. Stvari sa nultim nabojem ne bi pale bez obzira koje su mase. U stvari, stopa pada bila bi proporcionalna q / m, gdje je q naboj, a m masa. Kada povežete dva predmeta, 1 i 2, nabojima q 1, q 2 i m 1, m 2, kombinirani će objekt pasti brzinom (q 1 + q 2) / (m 1 + m 2). Pod pretpostavkom da q 1 / m 1 2 / m 2, ili objekt 2 padne brže od objekta jedan, kombinirani će objekt pasti srednjom brzinom (to se lako može pokazati). Ali, postoji još jedna stvar. 'Težina' predmeta je sila koja na njega djeluje. To je proporcionalno q, naboju. Budući da je za brzinu pada važno q / m, težina neće imati određenu vezu sa brzinom pada. U stvari, mogli biste imati objekt nulte mase s nabojem q, koji će padati beskrajno brzo, ili objekt beskonačne mase s nabojem q, koji uopće neće pasti, ali oni će isto 'težiti'! Dakle, u stvari, izvorni argument trebao bi se svesti na sljedeću izjavu, koja je tačnija:

Ako svi predmeti jednake težine padaju jednakom brzinom, tada će svi predmeti pasti jednakom brzinom, bez obzira na njihovu težinu.

U matematičkom smislu, ovo je ekvivalentno kazivanju da ako je q 1 = q 2, tada je m 1 = m 2 ili, q / m jednak za sve objekte, svi će pasti jednakom brzinom! Sve u svemu, ovo je prilično šuplji argument.

Vraćajući se na slučaj gravitacije .. Gravitaciona sila je

(G je konstanta, koja se naziva konstanta gravitacije, M je masa tijela koje privlači (ovdje zemlja), a m 1 je „gravitacijska masa“ objekta.)

A Newtonov zakon kretanja je

gdje je m 2 „inercijalna masa“ objekta, a a ubrzanje.

Sada, rješavajući ubrzanje, nalazimo:

Što je proporcionalno m 1 / m 2, tj. Gravitacijsku masu podijeljenu s inercijalnom masom. Ovo je naš stari 'q / m' iz električnog kućišta! Sada, ako i samo ako je m 1 / m 2 konstanta za sve objekte, (ta se konstanta može apsorbirati u G, pa se pitanje može svesti na m 1 = m 2 za sve objekte), svi će pasti u isto vrijeme stopa. Ako ovaj omjer varira, tada nećemo imati određenu vezu između brzine pada i težine.

Dakle, sve u svemu, vratili smo se na početak. Što samo poništava mase u jednadžbama, pokazujući tako da moraju padati jednakom brzinom. Jednakost dvije mase neophodna je za opću relativnost i ulazi u nju prirodno. Takođe, utvrđeno je da su dvije mase eksperimentalno jednake izuzetno dobroj preciznosti. Tačan odgovor na pitanje "zašto objekti različitih masa padaju istom brzinom?" je, "jer su gravitaciona i inercijalna masa jednake za sve objekte."

Zašto onda argument zvuči tako uvjerljivo? Budući da naše svakodnevno iskustvo i intuicija nalažu da stvari koje teže jednako padaju istom brzinom. Jednom kad to pretpostavimo, implicitno smo već pretpostavili da je gravitaciona masa jednaka inercijalnoj masi. (Vau, koje stvari radimo a da to ne primijetimo!). Ostatak argumenta slijedi lako i prirodno.
Odgovorio: Yasar Safkan, doktor fizike Kandidat, M.I.T.

'Što se tiče zakona matematike na stvarnost, oni nisu sigurni, a koliko su sigurni ne odnose se na stvarnost.'


Možda je ovo pitanje postavljeno više puta ovdje, ali jednostavno nisam uspio pretražiti ga po temi ili pojmu za pretraživanje.

Pitanje je da li svaka stvar pada prema suncu (tj. Planeti). Zašto planete ne padaju prema suncu spiralno i na kraju padaju na sunce? To je možda zbog centrifugalne sile, ali kako se ta sila održava?

Planete ne padaju na sunce jer se prebrzo kreću u tangencijalnom smjeru. Dok padaju prema suncu, tangencijalno putuju taman toliko da se nikada ne približe suncu. Oni u stvari padaju oko toga.

Tehnički, moglo bi se tvrditi da Padaju na sunce. Međutim, kao što je gore navedeno, zaista putuju prebrzo da bi to učinili spiralno. Ovo funkcionira na sljedeći način:

Objekt A povlači objekt B
Objekt B putuje dovoljno brzo da kruži
Kako objekt B putuje, povlači se prema objektu A
Dok se povlači prema objektu A, pomiče se naprijed tako da se za svaki metar koji se vuče pomiče, tako da zakrivljenost objekta A čini još uvijek jednaku udaljenost.

U osnovi, to je zato što ide dovoljno brzo do te mjere da ne može pobjeći, ali ni u jednom ne može pasti do kraja. Do trenutka kada bi objekt bio izvučen na površinu drugog, drugi je zakrivljen tako da je još uvijek iznad njega. U osnovi, samo zamahnite oprugom s priključenim tegom. Ako predmet ide dovoljno brzo, opruga se neće ispružiti, osim ako ne ide brže. Ali ako uspori, opruga će ga povući.

Nije tako sićušno. Otprilike 1/100 AU u promjeru znači da će zauzeti mali, ali ne i beznačajan dio ukupnog presjeka sistema. To je sigurno dovoljno da se osigura da, da nije sferne simetrije potencijala, sve do sada već završilo na Suncu.

Ukratko, rekavši da stvari ne padaju na Sunce samo zato što je Sunce malo u odnosu na veličinu sistema je barem nepotpuno. To nije jedini razlog.

Tehnički, moglo bi se tvrditi da Padaju na sunce. Međutim, kao što je gore navedeno, zaista putuju prebrzo da bi to učinili spiralno. Ovo funkcionira na sljedeći način:

Objekt A povlači objekt B
Objekt B putuje dovoljno brzo da kruži
Kako objekt B putuje, povlači se prema objektu A
Dok se povlači prema objektu A, pomiče se naprijed tako da se za svaki metar koji se vuče pomiče, tako da zakrivljenost objekta A čini još uvijek jednaku udaljenost.

U osnovi, to je zato što ide dovoljno brzo do te mjere da ne može pobjeći, ali ni u jednom ne može pasti do kraja. Do trenutka kada bi objekt bio izvučen na površinu drugog, drugi je zakrivljen tako da je još uvijek iznad njega. U osnovi, samo zamahnite oprugom s priključenim tegom. Ako predmet ide dovoljno brzo, opruga se neće ispružiti, osim ako ne ide brže. Ali ako uspori, opruga će ga povući.

Možete to zamisliti i ovako:

Telo planete ima određeni zamah. U svemirskom svemiru, ukoliko se ne dogodi sudar ili tijelo ne eksplodira, zamah je sačuvan.

Sada, ako planetarno tijelo počne da se vrti spiralno prema Suncu, ono bi moralo ići sve brže i brže da bi sačuvalo svoj zamah. U jednom trenutku, međutim, zamah u tangencijalnom pravcu postaje dovoljno velik da planetarno tijelo može početi bježati od gravitacije Sunca.

Tada, kako se kreće dalje, zbog promjene zakrivljenosti orbite, tangencijalna komponenta postaje manja i planetarno tijelo je ponovo zarobljeno u orbiti.

Ako želite znati više o ovome, stabilnost gibanja planete u osnovi je ono što je proslavilo Poincarea (pa, tehnički je u to unosio kaos) i dodijelilo mu nagradu Oscar za matematiku. Samo guglajte & quotthree problem sa tijelom & quot.

I ja sam imao problema sa zamišljanjem zašto zemlja ne bi trebala pasti na sunce, i još uvijek sumnjam u ove stvari.

Šta ako bi se brzina kojom se zemlja okreće oko Sunca naglo smanjila? Ili ako je zemlji data mala brzina koja ima neku komponentu u pravcu sunca?


Jednostavnije i jednostavnije

Sporo kotrljanje.

Neko me je jednom pitao hoće li cilindrični magnet koji se kotrlja na nagnutom aluminijumskom limu ometati vrtložne struje. Sigurno takve struje mora inducirati i kotrljajući magnet, ali geometrija situacije čini ih relativno neučinkovitima. Međutim, evo načina na koji se magnet za disk može polako kotrljati, koristeći aluminijumsku masku od 1 inča (standardni predmet za pohranu hardvera u dužini od 6 ili 8 stopa). Magnet diska (magnetiziran duž osi cilindra) kotrlja se s jednom stranom blizu jedne strane aluminijumske staze. (Slika 6.)

Aluminijumski kutni nosač takođe se može koristiti kao trag za sferne magnete.

Kao i kod većine mojih projekata, većina dimenzija nije kritična. Budi kreativan.


Usporavanje u svemiru

Prije trideset godina Nasa je lansirala prvi umjetni objekt koji je napustio Sunčev sistem. Pioneer 10, naš izaslanik u međuzvjezdani prostor, ide prema sazviježđu Bika, Bika. Za dva miliona godina približit će se sjajnoj zvijezdi Aldebaran - oku Bika - možda da bi je presrele neke vanzemaljske vrste koje žive na obližnjoj planeti. Sonda nosi posjetnicu čovječanstva, ploču dizajniranu da kaže vanzemaljcima gdje smo.

Radio praćenje njegovog toka, međutim, ukazuje da će trebati više vremena da stigne do zvijezda nego što su naučnici izračunali. Još važnije, njegovo anomalno kretanje može dovesti u pitanje naše temeljno razumijevanje sila prirode. "Nismo ni pomislili da će Pioneer 10 - prvobitno zamišljen kao 21-mjesečna misija na Jupiter - preživjeti 30 godina i dalje isporučivati ​​iznenađenja u 2002", kaže dr. Larry Lasher, šef projektnog tima Pioneer-a u Istraživačkom centru Nasa Ames u Kaliforniji .

Pioneer 10 eksplodirao je s rta Canaveral u martu 1972. Vratio je naše prve Jupiterove slike iz blizine krajem naredne godine. Na njegovom tragu bila je vruća sestrinska sonda Pioneer 11, koja je takođe posjetila Saturn. Dve sonde Voyager krenule su sledeće, poslane 1977. godine da pregledaju ove planete. Voyager 2 je također poslao naše jedine detaljne poglede na Uran (1986.) i Neptun (1989.). U međuvremenu su dva pionira ostavila planete iza sebe. Što se tiče udaljenosti od sunca, Voyager I ih je pretekao 1998. godine, ali Pioniri su prvi od naših artefakata koji su napustili Sunčev sistem.

Pioneer 10 ima još jednu vezu sa vanzemaljcima. Razni projekti koji traže znakove vanzemaljske inteligencije koriste radio teleskope za traženje signala koji dolaze iz drugih zvjezdanih sistema. Oni će vjerovatno biti slabi, i naravno ne znamo u kakvoj bi formi mogli biti. Treba testirati algoritme koji se koriste za ispitivanje podataka, pokušavajući prepoznati umjetne signale među kosmičkim šumovima.

To se postiže pomoću radio signala sa Pioneer-a 10. Trenutno je 80 puta dalje od Sunca od Zemlje - udaljeno oko 7,3 milijarde milja, više nego dvostruko više od Plutona. Njegov radioizotopski termoelektrični generator (RTG) smanjio je snagu sa 165 vati pri lansiranju na samo osam vata sada - otprilike jednako kao ručna baklja. RTG Pioneer-a 11 prošao je gore, raspadao se tako da je morao biti zatvoren 1995. Otkrivanje slabog signala sa Pioneer-a 10 stoga predstavlja izazov. Misija je službeno završila sa 25. godišnjicom 1997. godine, ali praćenje se nastavlja.

Praćenje svemirskih letjelica putem radija vrlo je precizno, što ga čini optimalnim načinom sondiranja složenog trodimenzionalnog gravitacijskog polja u i oko Sunčevog sistema. Praćenje Voyagera 2 dok je prolazio Uran i Neptun 1980-ih omogućilo je astronomima da izvode mase tih planeta sa mnogo većom preciznošću nego što je moguće iz zemaljskih promatranja njihovih mjeseci. Pioneer 10 je možda antikvitet, ali još uvijek nam pruža jedinstvene podatke.

A to praćenje je donijelo iznenađenja. Pioneer 10 usporava brže nego što se očekivalo samo na osnovu gravitacione privlačnosti sunca i planeta. Učinak je sićušan - samo oko jedan dio u 10 milijardi od toga zahvaljujući Zemljinoj gravitaciji koja trenutno djeluje na vas - ali definitivno je tu.

Ovo je zagonetka. Efekat se najbolje pokazuje kod Pioneers-a - Pioneer 11 je pokazao isti trend prije isključivanja - jer su stabilizirani. U osnovi, cijela svemirska letjelica djeluje poput žiroskopa, vrteći se jednom u 14 sekundi, a to pomaže u održavanju orijentacije.

Druge svemirske sonde, poput Voyagera, koriste troosovinsku stabilizaciju. Ne vrte se: mali potisnici oko svojih eksterijera kontroliraju svoju orijentaciju. Ali povremene ubrizgavanja goriva koje se koriste da ih usmjere na pravi način također ubrzavaju letjelicu u cjelini, prikrivajući sva sitna iskrivljenja koja bi inače mogla biti očita.

Vrtljivi Pioniri ne trpe takvu zbrku. Ipak, pokreti Voyagera u skladu su sa usporavanjem koje se najbolje vidi u podacima Pioneer-a 10. To vrijedi i za Uliks, koji je proletio pored Jupitera početkom devedesetih i iskoristio svoju gravitaciju da bi satelit prebacio na putanju preuzimajući ga nad sunčevim polovima. Isti se efekat vidi i u drugim svemirskim sondama. Pa šta se dešava?

Objašnjenja se mogu podijeliti u tri tabora. Treće u nizu je najlakše iznijeti: naše znanje iz fizike je nepotpuno ili pogrešno. To jest, gravitacija se ne ponaša onako kako mi mislimo (poput zakona obrnutog kvadrata koji ne radi na vrlo velikim udaljenostima), ili možda postoji nepoznata "peta sila" koja prati slabe i jake nuklearne sile, elektromagnetizam i gravitaciju . To bi potkopalo sve kosmološke teorije. Takvom se tumačenju treba oduprijeti.

Glavni osumnjičeni uključivao bi anomalije svemirskih letjelica. Stvari koje se razmatraju pod ovim naslovom uključuju isparavanje gasa sa satelita, pritisak koji nameće sunčeva svjetlost i sunčev vjetar, toplotno zračenje svemirske letjelice, interakcije s međuplanetarnim magnetskim poljem itd. Slično tome, traženi su problemi u primljenim podacima, na primjer zbog klimavanja Zemlje.

Druga klasa objašnjenja pokriva poremećaje sondi koje su nametnute neviđenim masama: tijela Sunčevog sistema poput velikih asteroida u vanjskom Sunčevom sistemu koji tek treba uočiti lako je modelirati na osnovu trenutnih saznanja. Takođe postoji mogućnost kozmološke tamne materije u okolini Sunčevog sistema.

Pokazalo se da nijedno od objašnjenja za Pioneer 10 anomalije ne djeluje. "Nije pronađeno normalno fizičko objašnjenje za ovo čudno usporavanje," kaže član tima za dinamičku analizu, dr. Michael Martin Nieto iz Nacionalne laboratorije Los Alamos u Novom Meksiku. "Moramo dodatno testirati, recimo s novom svemirskom letjelicom_ Tada bismo zaista mogli riješiti problem." U međuvremenu, nedoumica ostaje.

Pioneer 10 je slavu pronašao na mnogo načina. U filmu Zvjezdane staze V: Posljednja granica, inat je prikazan kapetanom klingonske flote koji ga minira u sitne komade. 1974. godine, ubrzo nakon što je poslao slike Jupitera, američka pošta izdala je marku na kojoj je prikazan Pioneer 10. Četvrt stoljeća kasnije ponovo je izabrana kao prikladna tema za poštansku marku, kao jedna od ikona sedamdesetih . Ali istraživači svemira još uvijek ga nisu lizali.

· Duncan Steel predaje svemir i astronomiju na Univerzitetu Salford


Usporavaju li pada tijela? - Astronomija

Za naš Univerzum prostor je prevelik da bismo mogli koristiti geometrijske testove, poput mjerenja uglova trokuta. Jednostavno ne možemo nacrtati dovoljno velike trokute. Ali mogli bismo brojati galaksije, što će nam reći kako se površina kruga mijenja s radijusom. Da biste to učinili, gledate sve galaksije u krugu na određenoj udaljenosti. Ako se broj galaksija mijenja između krugova na različitim udaljenostima, možda ćete moći shvatiti jeste li u pozitivnom ili negativnom prostoru, za razliku od ravnog. To bi u principu funkcioniralo, ali postoji toliko komplicirajućih čimbenika (poput nejednolike raspodjele galaksija, tj. Jata i zidova), kao i činjenice da Univerzum nije statičan, već se mijenja s vremenom i gledajući unatrag određena udaljenost je ista kao i gledanje unazad određenog vremena. Dakle, iako bi to funkcionisalo u principu, neće raditi u praksi.

Ali, razmislite o čemu govorimo. Zakrivljenost prostora. Lokalno, prostor se zakrivljuje kao odgovor na masu, pa ima smisla misliti da bi gustina mase u Svemiru odredila univerzalnu zakrivljenost.

Ako je gustina Svemira velika, Svemir je pozitivno zakrivljen.

Ako je gustina Svemira mala, Svemir je negativno zakrivljen.

Ako je gustina Svemira tačna, Svemir je ravan.

„Upravo tačna“ gustina naziva se „kritična gustina“ i iznosi oko 10 -26 kg / m 3, što je oko 10 atoma vodonika po metru u kockama.

Astronomi definiraju parametar za razgovor o zakrivljenosti. Ovaj parametar naziva se 'omega ništa', a prikazuje ga 0.

0= (gustina struje) / (kritična gustina)

Ako 0 > 1, zakrivljenost je pozitivna.
Ako 0 = 1, zakrivljenost je nula.
Ako 0 Budućnost širenja

Gustina Univerzuma takođe utiče na budućnost širenja. Ako je Svemir 'težak', on će se neko vrijeme širiti, usporiti, a zatim kolabirati. Ako je Univerzum 'svjetlost', širit će se zauvijek. Ako je Svemir 'u pravu', on će se dugo širiti, a zatim usporiti i zaustaviti, i Svemir će zauvijek ostati na toj gustoći. Ove moguće opcije vezane su za vrijednost 0.

Ako 0 > 1, zakrivljenost je pozitivna, a Svemir će usporiti, zaustaviti se i urušiti.
Ako 0 = 1, zakrivljenost je nula, a Svemir će usporiti i zaustaviti se.
Ako 0 Doba svemira

Starost svemira je 1 / H SAMO ako se svemir širio istom brzinom cijelo vrijeme.

Ako svemir usporava (što je treba zbog gravitacije koja uvlači stvari i usporava širenje --- razmislite o interakciji jata / lokalne grupe Djevica, tada je 1 / H gornja granica--- Univerzum ne može biti starije od 1 / H.

Ako se Univerzum cijelo vrijeme ubrzava ili širi brže, tada je 1 / H a donja granica--- Univerzum mora biti mlađi od 1 / H. Ali zamisliti kako bi se to moglo dogoditi vrlo je teško i već dugo je odbačeno kao mogućnost. Razmislite. Da bi se nešto ubrzalo, to mora biti 'potisnuto' prema van. Ali svi mehanizmi koje poznajemo 'vuku se' prema unutra.

Najnoviji dokaz je da se Univerzum zapravo ubrzava. 1998. godine potvrđeni su novi podaci koji pokazuju da se Univerzum nekada širio sporije nego danas! Još niko nije uspio pomiriti ove nove dokaze s teorijom, osim što je rekao da postoji 'energija vakuuma', tako da i sam prostor ima energiju, koja odbija drugi prostor, ubrzavajući ga. Ovo je "prvo izrezano" objašnjenje i nije ga detaljno testiralo dovoljno različitih ljudi da bi odlučilo je li ispravno ili ne.


Kako nastaju planete?

Zasluge: S. Schnee i dr.

Imamo prilično dobru ideju o tome kako se planete formiraju oko zvijezda. Znamo da se prašina stvara od ostataka supernovih, da se protoplanetarni diskovi prašine formiraju oko mladih zvijezda i da se zrna prašine mogu skupiti i stvoriti kamenčiće. Takođe znamo kako veći planetoidi mogu pokretati stvaranje planeta i kako planete mogu migrirati od svog ishodišta do stabilnih orbita. Ali još uvijek postoje praznine u našem razumijevanju.

Na primjer, nismo sasvim sigurni kako od čestica veličine šljunka dolazimo do objekata veličine planetoida. Sve je povezano s količinom iskustva povlačenja objekata dok se krećete kroz protoplanetarni disk. U početku je većina zrna prašine izuzetno sitna, veličine manje od mikrometra. Budući da su tako maleni, količina otpora koji imaju od okolnog plina je minimalna. Oni su toliko sićušni da su u svom ponašanju gotovo slični plinovima. Za velike nakupine, promjera stotine metara, otpor okolnih plinova također je relativno zanemariv. Njihova masa je dovoljno velika da ih tokom 10 miliona godina planetarnog formiranja gas ne usporava mnogo. Ali između toga postoji veličina koja je dovoljno velika da vuča bude bitna, ali nedovoljno masivna da je prevlada. Ovo je na skali od oko metra. Kad nakupine dosegnu ovu veličinu, povlačenje okolnog plina uzrokovalo bi njihovo prilično brzo usporavanje. Kao rezultat, oni bi se uvili u zvijezdu prije nego što postanu mnogo veći.

Da je ovo istina, planete bi bile vrlo rijetke. But we know planets are quite common, so there must be a mechanism that prevents planetary seeds from falling into the star. There have been some ideas, such as pressure waves in the planetary disk causing pebble-sized grains to clump into larger planetoids rather quickly, but this would require gravel-sized grains to form early on, which we aren't sure could happen.

Now a new paper has found evidence of gravel-sized dust grains in the Orion Molecular Cloud. The team used radio telescope observations to determine the size of dust grains in the cloud. This technique is nothing new, but the team found filaments of dust grains that are a millimeter to a centimeter in size. This is much, much larger than typical dust grains observed. What's particularly interesting about this discovery is that the filaments are in a region where stars will likely start forming in the next 100,000 to a million years. It is possible, then, that these large grains formed within the general cloud itself. If that's the case, protoplanetary disks could have a ready-made source of large grains that could kickstart the formation of planetoids early on.

Although this is an exciting result, we should still be a bit cautious. The radio observations could be explained by things other than large dust grains (though that doesn't seem likely), so we will need further observations to confirm the result. We also aren't sure whether these grains actually formed in the molecular cloud, or if they are debris remnants from another process.


Ep. 270: Inertia

An object at rest tends to stay at rest. An object in motion tends to stay in motion. Isaac Newton dismantled the traditional idea that objects would tend to slow down over time, and described the concept of inertia: the amount an object will resist changes in its motion.

Show Notes

    • Google+: Pamela and Fraser
    • Sponsor: 8th Light — The Physics Classroom — MIT — Vanderbilt U – Wiki (water clock/inclined plane) — University of Virginia — Rice University — Northwestern U — Bucknell — UTK — GSU — UIUC — Teach Engineering

    Transcript: Inertia

    Fraser: Welcome to Astronomy Cast, our weekly facts-based journey through the Cosmos, where we help you understand not only what we know but how we know what we know. My name is Fraser Cain I’m the publisher of Universe Today, and with me is Dr. Pamela Gay, a professor at Southern Illinois University – Edwardsville. Hi, Pamela. How are you doing?

    Pamela: I’m doing well. How are you doing, Fraser?

    Fraser: Doing great. So actually, again — warping space and time — this is the second episode that we’re recording on this day, which is actually in July, moments before the announcement of the Higgs-Boson! But as we’re catching up shows…so we’re actually only a couple of episodes behind. We will be caught up this week, I think.

    Pamela: Maybe Wednesday, maybe Friday we can record?

    Fraser: Yeah, we will be caught up, and then we will…I won’t say that we’ll never fall behind because we absolutely will because that’s just the reality. Now, we had a couple of people who posted sad reviews in iTunes because Astronomy Cast was a little bit late, and they took away some stars from us, so we’re really sorry for all of you who felt that us being late detracted from the Astronomy Cast experience. We understand that keeping this show coming out on a very regular basis is really important to you, and it’s important to us, and we will absolutely focus our energy on getting this show out as regularly as we can. Now, if you do love Astronomy Cast, or you know feel like you need to give an honest review, the iTunes reviews are a great place to do that. So you can just do a search for Astronomy Cast on iTunes and give us a review — be honest! But it’s great those reviews are wonderful, and we really appreciate them so…

    Pamela: And we do read them and take them to heart.

    Fraser: We absolutely do, and in fact the funny thing is because I’m in Canada, I see a tiny version of the number of reviews and I only thought we had a few reviews, and then I was able to switch my country to pretend like I was in the U. S., and there were like thousands or 1500 reviews or something like that. It was quite overwhelming to see all of these at the same time. The other thing that is really important to know is Google Plus (Google), recorded a documentary about the virtual star parties that we do, which is really cool. So they actually flew a team of film makers out to all across north America to our friends in North Carolina, and in your house, Pamela, and my house here on Vancouver Island, and down in Los Angeles to meet with Gary, and they recorded this really moving documentary about the star parties that we do, and it’s on YouTube, and you can get it from…you know, I’m sure we’ll put it into the show notes, but if you haven’t seen this, it is unbelievable it is really cool, and I highly recommend that everybody watch it. It is really neat, and if you want, remember we always do our virtual star parties every Sunday night from when it gets dark on the west coast for about an hour/hour-and-a-half, and we bring in a live view of telescopes, so we’re trying to use all of the different media in the appropriate ways so people can appreciate astronomy as much as we do. Alright! Well, let’s get recording.
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    Fraser: So an object at rest tends to stay at rest. An object in motion tends to stay in motion. Isaac Newtown dismantled the traditional idea that objects would tend to slow down over time, and describe the concept of inertia, the amount an object will resist changes to its motion: inertia. Alright, Pamela, so then I think this is where we really kind of need to go back in history and get an idea. The traditional, the ancient Greeks, the medieval scientists (if you can call them that)…what did they think about the way motion worked?

    Pamela: Well, the initial ideas go all the way back to Aristotle, and he thought that an object in motion would, over time, just stop, and he explained the motion of things like projectiles through the air as the median that they were flying through, so in this case the air was providing that extra something that was needed to keep them in motion while they flew. Now, this…

    Fraser: Whoa! Whoops! I didn’t understand that. Hold on. Šta? The air was…

    Pamela: The air was somehow going, “Keep moving, keep moving, keep moving,” and so his idea was if you were able to create a vacuum, objects wouldn’t move through vacuums, which is a really weird concept.

    Fraser: So the air provided a way to propel objects forward?

    Pamela: It kept them in motion somehow.

    Fraser: It kept them in motion — somehow, but not accelerating. They would still slow down.

    Pamela: Well, and that was the crazy thing was an object falling through air is clearly accelerating. A projectile goes up, arcs, and then accelerates back down, so somehow the air was responsible for all of this craziness.

    Fraser: Oh! So in other words…

    Fraser: No, I understand. So in other words, you go and you take an object up to the top of a cliff, and you drop it, the air is going to be accelerating it towards the ground until it runs out of air and hits the ground.

    Pamela: And so there’s something clearly funky going on…the idea that in a vacuum things aren’t moving. People who started thinking about the idea of a Sun-centered solar system had a [gag sound] reaction to this, and so it was actually Galileo who initially started doing the hard experimental work to overturn this idea. Now, he wasn’t the first one. So we had well before that we had Lucretius (Titus Lucretius Carus), who was working in the last century B. C., who was trying to say the default state of stuff isn’t to be at a dead stop, which was Aristotle’s idea, that if you left anything in motion it would come to an eventual stop. He decided that this probably didn’t make sense. John Philoponus and said the idea of the median keeping things going…there were issues with it, and that void probably wouldn’t limit motion.

    Fraser: Was this the impetus theory? Was this the…

    Pamela: Well, the impetus theory is all tied into it, and the impetus theory finally came out in the 14th century B. C., and this was an idea that air is somehow pushing, and that when you give something energy — when you push it, when you accelerate it — you’re giving it an impetus, and then that can get dissipated in to the surrounding…well, this is where friction comes in, but they didn’t have friction yet. Galileo’s the one who really came up with a solution for this, and one of the big problems they had was they didn’t have clocks, and Aristotle’s thinking…and Aristotle did not believe in experimentation Aristotle believed in thinking, and that a true understanding of the Universe could come from thinking.

    Fraser: This is one of those Classic examples, right, where you had these ancient scientists, you know ancient Greeks who would argue about the number of teeth that a horse had, right, and somebody would go out and say, “Well, I’ll just count them,” and they were like, “No! Don’t do that!”

    Pamela: And what’s funny is sometimes it seems like there’s very little difference between particle physics today and regular physics back then. [laughing] Sorry.

    Fraser: Zing! Zing! You think people missed that? That was Pamela zinging the particle physicists. Send any letters to Pamela Gay, [email protected]

    Pamela: So you had all these people philosophizing about how things move, and they actually believed that acceleration of a falling object was a linear process, so you go a distance, you accelerate an amount, you go twice that distance, you accelerate twice as much. And the reality is that it’s a square relationship. So your acceleration: go one unit of time, you go one unit of distance go two units of time, it’s going to be, so…let me actually do one and two units of distance: two units of time, four units of distance (that does the math a little bit easier), and so you have this square relationship going on, and you have to have a clock to figure that out. And it was Galileo who didn’t solve the clock problem, but figured out a circumvention of it with what’s called the water clock. If you have a very large surface area on a container, the rate at which the water level falls for small amounts is fairly linear over time, so you’re getting a constant stream of fluid coming out, so every beat of the clock is a set of volume of water coming out. So what he did was he built this drum of water that had a system with water coming out the bottom that he could turn on and off, and he would very carefully weigh the amount of water that came out after a ball had gone a certain distance. And the one thing, the one miscalculation that’s in this is an object that’s rolling has slightly different physics than an object that is sliding down, but it’s such a small correction that it didn’t affect the physics in this course.

    Fraser: Right, but this was a way that Galileo could slow down time. Essentially, he could make an object fall as quickly or as slowly as he needed to be able…

    Pamela: …using an inclined plane.

    Fraser: …using an inclined plane, right, so that he could say, “Well, it’s too fast for me to measure this stuff just dropping it, so let’s use an inclined plane then I can measure this stuff in a much more slow…” you know, everything unfolds in slow time. Brilliant! Absolutely brilliant! Do you do that experiment with your physics students?

    Pamela: I don’t do it at SIUE. When I was at Harvard we did this, and we did everything to stay similar to what he did while not killing ourselves. So what he did is he actually used a many-meters-long inclined plane made out of a carved groove, he lined it with parchment to decrease the friction absolutely as much as possible, he created the water clock, he marked off the distances going down the inclined plane, measured how long it took it to go one unit of distance, to go two units of distance, and so on all the way down. Well, what we did because, well, wood weighs a lot is we used PVC pipe because that starts out nice and parchment-smooth, and so we had things going down a half-tube of PVC pipe that students used grease pencils to mark. And we did build our own water clocks using surgical hosing, and those big old buckets that you get when you’re tarring your driveway.

    Fraser: So then, what is the relation to inertia, though? How does this play into the story that we’re telling?

    Pamela: Well, what he figured out, as he decreased friction as much as possible, is that when you send something going down the inclined plane, it would just keep going down the other side if it was flat, but if he ended up with two back-to-back inclined planes, and decreased the friction as much as possible, it would go up to basically the same starting height. So he was able to take how much potential energy — and he didn’t have these concepts, it took Newton to get to gravity, but he could start it off at the top, it would accelerate down, and then it would decelerate up, and as he lowered the plane, it went further and further and further, and so he was able to say whatever was needed to go up that incline precipitated the motion, but if there was no force, if there was no “something” acting on the object, it would keep going forever. And he actually…in writing about this, trying to explain the concept of friction, he had some great discourses where he was basically…he had different characters arguing over what friction was, and this is where the little demons argument comes in where there were people basically saying there were little demons out there stopping things, and getting them to stop moving, and that when you smooth something off, you’re clearing the demons off, and things like that.

    Fraser: Smoothing things off to clear the demons off.

    Pamela: It’s a brilliant…if you ever have a chance to read the discourses that Galileo wrote, they’re brilliant, and you can instantly see why he got himself in so much trouble with the Pope.

    Fraser: -Da. If people haven’t read these, they absolutely should. I’m sure it’s all available open-source out there somewhere.

    Pamela: It should be. There’s a great source of Galileo-related everything at Rice University.

    Fraser: And he wrote in a very accessible style, and he was clearly poking fun at the people who disagreed with him, who also happened to be very powerful people who were able to put him in jail, but that’s a whole separate show that we’ve already done on Galileo. So Galileo gets to the point that he’s created this, he’s figured out that there is some kind of inherent motion that is accumulated by the object rolling down the hill, which it then dissipates again as it goes back up — so how did this sort of carry the concept of inertia forward?

    Pamela: So we went from an “Aristotilian” view of the Universe, in which an object in motion comes to a stop to a way of looking at it of: an object in motion will stay in motion unless friction, or something else, acts on it to eventually…when Newton came along, the idea of: we finally started to get friction, we finally started to get gravity, we finally started to get all of these things mathematically described, and it became: an object in motion stayed in motion unless acted upon by an external force. So suddenly, everything got quantified, and here you have: things stay in motion in straight lines unless they’re worked on by an external force as well, and this was one those things that folks really struggled with because with Galileo’s view of: they keep going in a straight line — but why do the planets keep orbiting? That was a serious challenge that Newton had to figure out how to address, and that’s where gravity became such an important part of understanding inertia, basically.

    Fraser: Right, and so if Aristotle had really just thought a bit, and looked up and noticed that the planets are flying though space…of course, he didn’t know that there was no air up there, right? They thought it was like some kind of ether, I guess.

    Pamela: Well, and he had them embedded on spheres.

    Fraser: On spheres…OK. Never mind. Vidiš? He never would have figured it out, but the point being that you’ve got the situation where you’ve got these objects, they’re moving, and yet they’re going in a circle. Why don’t they stop? Why don’t they spiral outward? Why don’t they spiral inward? What’s going on, right?

    Pamela: And this is where we had to understand that the force of gravity connects two points at their center of mass. And if my microphone here is the planet Earth, and this rock is the Moon, then what’s happening is if the Moon had no velocity, gravity would pull it straight into the Earth, and that would be a very bad thing, but because the Moon has a velocity that’s trying to carry it forward, the force of gravity is constantly pulling it in, causing it to constantly arc inward, but it has enough velocity so that it never actually hits the Earth. So it’s trying to go straight, gravity is trying to pull it down, and the result is an almost circular motion.

    Fraser: Right, so you’ve got this situation where you’ve got these planets that are moving, that nothing is slowing them down, they’re not spiraling outward, they’re not spiraling inward — what is the force? Why are they kept going in this circular orbit around the Earth? And this is this concept of gravity and inertia, so…

    Pamela: And so this is where, for a while, there were actually people thinking that inertia wasn’t just an object in motion stayed in motion in the same way, but an object in motion could either stay in motion in a curve or in a straight line. Well, today we now know that an object in motion will stay in motion with the same vectoral motion that it had to begin with unless acted upon by an outside force. And a vector defines both its speed and its direction.

    Fraser: But in the case of the planets, of course, they’re orbiting in a circular vector? I mean they’ve got multiple forces pulling on them, right?

    Pamela: No, that’s…so the thing is vectors are straight lines, but then you can define them across…well, a vector’s something that has multiple characteristics. So velocity is something that only has a speed and a direction. The planets are actually accelerating, which means their exact velocity is constantly changing because that direction is constantly changing. Now, if an orbit’s a perfect circle, then its speed is constant at all times, but its velocity is constantly changing as that direction changes.

    Fraser: Tačno. Tačno. OK, so then where did Newton’s main discovery come in?

    Pamela: Well, the story, as frequently told, is he was sitting under a tree and saw an apple fall, and saw the Moon in the sky, and had this epiphany that a falling apple and a falling moon are the exact the same thing except the moon is missing the planet. And the analogy that often gets used is if you had a cannon, you put the cannon on a hill, when you fire the cannon ball, if you have it with sufficiently low velocity, it lands on your foot (assuming you’re standing right in front of the cannon). If you hit it with larger force, it goes a larger distance. If you hit it with larger and larger force, it goes a larger and larger distance, and it always arcs down to the planet, though, as it falls because gravity’s constantly trying to pull that cannon ball back to Earth. Well, if you use enough force to fire that cannon ball, it’s going to gain sufficient velocity that Earth’s pull only succeeds in bringing it around so that you hit the butt of the cannon. Now, if you hit it with even more force, you can actually start to hit escape velocities, and this is what we do with rockets, in which case the force of gravity is insufficient to change the initial velocity sufficiently to get the cannon ball to return to the planet.

    Fraser: So then, I mean, he also…he really famously coined that phrase, right, that “a body in motion tends to stay in motion, and an object at rest tends to stay at rest.”

    Pamela: “…unless acted upon by an external force.”

    Fraser: “…unless acted upon by an external force.” Tačno. Upravo. So how did this sort of change people’s understanding of the objects moving around them?

    Pamela: Well, it was a sudden epiphany that everything is connected by forces, and that when we see something happen, one of two things has to be true: there’s either a force acting on the system, or we’re looking at a system that’s undergoing acceleration, and this is where we start to get into inertial and non-inertial frames of reference. So if you’re in an accelerating car, that’s a non-inertial frame of reference, so that when you look at the hanging dice hanging from your 1970s vintage automobile’s rear view mirror, you’ll see the dice don’t hang straight down toward the center of mass of the planet Earth. As you’re accelerating, they will actually sway backwards, and that’s because it’s an accelerating frame of reference. An inertial frame of reference is one in which there’s no acceleration taking place.

    Fraser: And this is why as you go around a corner, you feel pushed up against the side of the car, right, because you tend to want to stay in the motion that you were going, which in this case, you wanting to move straight forward, but the car is now exerting an external force on you, on your left shoulder, that is pushing you around the corner with it, and so your body is pushing back against the side of the car, and that’s what you feel.

    Pamela: Well, this is where crazy frictional forces come into play because as your car whips around that corner, as little kids in the backseat always know because you try to purposely smush each other into the door…

    Fraser: Wheeee! Yeah, yeah…

    Pamela: …you feel like you’re getting forced to the outside of the car, but the actual force is towards the center of the circle. So this is why when you have a ball on a string, the ball stays on the end of the string. It’s because the force is going toward the center of the circle. Now, there’s a sudden, “Wait! Hold on, but the kids are flying outwards!” No, the kids are simply trying to go in a straight line, and the car is getting in the way of that straight line, and so you’re experiencing this frictional force on your butt. Your body’s trying to keep going straight forward, and as the car curves, you’re getting caught by friction, basically, and that’s: you want to go in a straight line, you’re failing to go in a straight line, the car’s preventing you from going in a straight line, you feel like you’re getting flung outwards. The reality is the real force is towards the center of the circle.

    Fraser: Now, this is all fine and good, and you know, completely changed everyone’s thinking about the Universe, and the motion, and physics, and you know, how things [missing audio], and all these great technological advances (Thanks, Isaac Newton!), but this was all sort of thrown out the window again when Einstein came along.

    Pamela: Well, it wasn’t so much thrown out the window as it was changed. So as we’re trying to figure out frames of reference, as we’re trying to figure out what is an inertial frame, suddenly, in a relativistic situation, things started to become much more curious. So suddenly, when you’re looking at your frame of reference, you realize everyone has their own frame of reference, you start to realize everything’s in motion, you start to realize there is no such thing as a truly inertial frame of reference. I mean we can pretend that we have a non-accelerating frame of reference. If you’re standing next to a railroad train, and a railroad train goes by, and you see someone drop a ball in the window, relative to the moving train that ball falls straight down relative to you, you’ll see it starts falling here it lands over here because the whole window moved sideways. So within the train, it seems to be a non-accelerating inertial frame of reference. You can go back and forth between the two frames of reference, but you’re on the surface of a planet going in a circle, which means you’re actually constantly changing velocity as you stay adhered to the surface of the planet. But over small distances, we’re able to make these assumptions, but when we start looking at larger and larger distances, we start having to worry about things like Coriolis force, we start having to worry about the effects of the fact that the planet is rotating underneath you, and all of these things start to come together and life gets more and more complicated. Now, add to that the effects of time contraction, add to that all of the relativistic effects, and suddenly defining inertial frames is a nightmare because they don’t totally really exist, and every observer is their own observer.

    Fraser: And that’s where the headaches start to set in.

    Fraser: Yeah, but of course, the predictions made by Einstein perfectly match the measurements that are made in space to a level of accuracy that Newton could have only dreamed about, and so…

    Pamela: And one of the beauties of all of this was this realization that whenever we’re dealing with things, the proper way to think of them isn’t: an object of a given mass moving at a given velocity, it’s to think of it as an object with a set amount of momentum because it’s the momentum that things carry with them that has the true impact (just to be unintentionally punny). And so the example I use in class a lot is you can imagine a three-year-old and a Sumo wrestler on roller skates. If that three-year-old starts going as fast as it can skating toward the Sumo wrestler, it’s carrying a set amount of momentum that it’s going to impact into that Sumo wrestler, who, assuming no friction, no inelastic parts of the collision, they’re going to bounce off each other, and the Sumo wrestler’s going to be basically unaffected, and the three-year-old is going to go flying off in the opposite direction. Now, if you instead have two Sumo wrestlers doing this, you’re going to end up with, perhaps if you get a second equal-mass Sumo wrestler coming along and hitting at the same velocity as that small child was, well that big other Sumo wrestler’s now going to take all that velocity and start going in the same direction, and that first dude will stop cold just like a pool ball will.

    Fraser: Yeah, talk about that pool ball example, right, which is a wonderful example of this transfer of inertia. You have a ball sitting on the table…

    Pamela: Transfer of momentum.

    Fraser: Transfer of momentum, sorry…and you shoot your cue ball at that ball, your cue ball (in a perfect world) stops perfectly, and now that second ball is moving.

    Pamela: And the key to achieving that perfect world is to have the two centers of mass completely line up so that when it hits, all of its force goes straight into an impulse on the other one, and all of the momentum gets cleanly transferred. Now, the reality is that most of the time when you hit pool balls together, it’s not that perfect center of mass, and you end up hitting slightly off-center, and so this is where you hit it and it veers off. And if you get good, you can actually hit something with a glancing blow and cause it to go off at close to a right angle.

    Fraser: That was really cool. Alright, well, I think we made our way through this episode of inertia. So once again, thank you very much, Pamela, and we will see you next week.

    Pamela: We’ll see you next week, and hopefully the internets will be with us.

    This transcript is not an exact match to the audio file. It has been edited for clarity.


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