Kuwala kwa Newton

Kuwala kwa mwezi kumachokera ku dzuwa ndipo ndicho chida chofunikira kwambiri pakupanga ma satellites, monga momwe zimakhalira ndi ma satellite a m’madera ena. Mfundo yayikulu ya Isaac Newton inali kuti malamulo amodzi amafotokoza zonse. Mudzakhala moto kanoni ake ndi kudziwa chifukwa chake.

Mwezi umayenda mozungulira dziko lapansi nthawi zonse. Zimachititsa kuti zikhale zosatheka.

Onani

Kutulutsa mpira ndi kugwa. Kuthamanga kwa mpweya kumathamanga kwambiri, koma kumakhala kovuta kwambiri. Isaac Newton anafunsa funso lokha: kodi ngati mumawadula * mwamphamvu kwambiri *?

Kuganizira kanoni pa pamwamba pa imfa yaing’ono, pamwamba pa nyanja. M’malo mwake, mpweya wotentha umatuluka m’magazi ndipo umalowa m’thupi. Mphamvu yake imakula kwambiri ndipo imatha kuwononga zinthu zambiri. Pofuna kuteteza nyanjayi, dziko lapansi limayenda mozungulira m’mphepete mwake. Pa nthawi yoyenera, nthaka imayenda mofulumira kwambiri ngati momwe mpira umayenda. Mpira amasunga kugwa, koma si nthawi zonse malo. Ndi Kuwala.

Sankhani mfundo ya pamwambapa. Kuyambira slowly, ndiye kupita mofulumira:

• Zosatheka: imabwerera m’mbuyo (chingwe).
• Ine ndimakonda: imayenda mozungulira (chinyezi).
• M’njira yofulumira: imatuluka ndipo siyibwereranso (yachikasu).

Izi ndi chifukwa chake astronauts kuwala. Iwo si m’mbali mwa gravity. Iwo, ndi ndege zawo zakunja, akugwa padziko lonse limodzi.

Kumvetsa

M’malo mwake, malamulo a Newton a gravity amatanthauza kuti zinthu zonse zimayenda mozungulira mtunda wina.

F = G · M · m / r²

• F ndi mphamvu, M ndi m maselo awiri, r ndi kutalika pakati pa maziko awo.
• G ndi mfundo ya gravity: 6.674 × 10⁻¹¹ N m² kg⁻².

Maganizo awiri ndi packed mu izo:

1. Zinthu zoyipa zimathamanga kwambiri. Double the mass, double the force.
2. Mtunda umaichepetsa mofulumira. Kudutsa mtunda kumawononga mphamvu mpaka kukwapula. Izi ndi inverse-square malamulo.

Near a planet, the acceleration of anything falling is g = GM / r². Kuzungulira kwa dziko lapansi kumatha kufika pafupifupi 9.8 m / s² pamalo ozungulira. Pamutu wa International Space Station (makilomita 420), r ndi 7% yokha, kotero gravity imakhalabe pafupifupi 88% yolimba.

Kuti tipite ku orbit ya m’mphepete, gravity iyenera kupereka kulimba kwamphamvu kofunikira kuti tipititse patsogolo njira:

v_circular = √(GM / r)

Just above Earth’s surface this is about 7.9 km/s. M’chifupi chake ndi 28,000 km/h.

Woyang’anira

M’mawu ambiri, G ndi M sagwiritsa ntchitonso mawu osiyana. Zogulitsa zawo μ = GM, Kusintha kwa gravity, imawerengedwa moyenera ndi mosamala kwambiri kuchokera ku mgwirizano wa maola ndi ndege zakunja. Kumwamba, μ = 398,600.4355 km³ s⁻², yomwe imadziwika ndi magawo angapo pa biliyoni, pomwe G yokhayo ikudziwa kuti ndi pafupifupi 22 mayunitsi pa miliyoni (CODATA 2018). Mtundu wa G umakhala ndi maonekedwe amtundu wa G, ndipo umadziwika kuti ndi mtundu wa silika.

M’mabuku ena, lamulo la Cantor limafotokoza kuti kuwala kwa zinthu ndi kofanana ndi kuwala kwa maonekedwe a zinthu. Kutulutsidwa kwa kutalika kuchokera ku radius r₀ ndi kuthamanga v kumapatsa mphamvu ya angular h = r₀v ndi orbit conic:

r(ν) = p / (1 + e cos ν),   p = h² / μ,   e = |p / r₀ − 1|

kumene ν ndi kutalika kwa nyanja kuchokera ku periapsis. Ngati v ndi pansi pa kutalika kwa mtunda, ndiye kuti malo oyamba a mpirawo ndi apoapsis ndipo njira imangoyenda kumbuyo; ngati imakhala pansi pa kutalika kwa mtunda, mpira umangopita pansi. M’madera ena, 0 (zero) ndi gawo la mawu akuti “zero” (zero). Pa √(2μ/r₀) imakhala parabola (e = 1) ndipo bowo limatuluka.

Mfundo ya Newton imafotokozanso chifukwa chake mapiri a chidachi ndi opanda pake kwambiri: m’maganizo, mpweya ukhoza kuchepetsa kuthamanga kwa kanoni nthawi yayitali pambuyo pa mayendedwe ake, zomwe ndizofunikira kuti zipite pamwamba pa atherosphere.