Ubunzima beNewton

Umphumela ophakamisa i-apple ezweni ufanayo nomphumela ogcina inyanga emkhathini wayo kanye namaplanethi ajikeleze ilanga. UIsaac Newton wayecabanga ukuthi umthetho owodwa uchaza zonke lezi zinto. Lapha uzoshaya i-cannon yakhe bese uthola ukuthi kungani.

Inyanga idlula emhlabeni yonke isikhathi. Kuhlala kungekho.

Bona

Lahla ibhola bese liwela. Yithule ngakwesobunxele futhi iyawa, kodwa iwela eduze. UIsaac Newton wabuza umbuzo olula: yini uma uyithutha ngaye ngokushesha?

Ucabanga nge-cannon ephezulu komfula ophakeme kakhulu, ngaphezu kwezulu. Umlilo webhola le-cannon uqala ngokucophelela futhi lujika phezulu lushaya phansi. Umlilo osheshayo futhi uhlala eduze. Ngenxa yokuthi i-Earth iyingilazi, indawo ijikeleza eduze kwebhola. Ngejubane elifanele, indawo ijikeleza ngokushesha njengoba ibhola liwela. Ibhola lihlala liwela, kodwa alikwazi ukufinyelela. I ikwi-orbit.

Zama nge-cannon engezansi. Qala ngokucophelela, bese uhamba ngokushesha:

• Ihamba kancane kakhulu: ibuyela emuva (bomvu).
• Kulungile: ihamba yonke indlela (eluhlaza).
• Ihamba ngokushesha kakhulu: iphuma futhi ayiphindeki (yebomvu).

Leyo nayo isizathu sokuthi kungani abacwaningi belanga behamba. Azikho ngaphandle kwengcindezi. Baye, kanye nendiza yabo yendawo engaphandle, idlula emhlabeni ndawonye.

Ukuqonda

Umthetho kaNewton wesimo sezulu sisho ukuthi yonke isisindo siphakamisa yonke enye isisindo:

F = G · M · m / r²

• F yisimo, M ne m ziyizinto ezimbili ezinamandla amakhulu, r yibanga phakathi kwezifunda.
• G yisimo esiqhubekayo se-gravity: 6.674 × 10⁻¹¹ N m² kg⁻².

Iziphakamiso ezimbili zifakwe kulo:

1. Izinto ezinzima ziphakamisa ngokuqinile. Isisindo esiphindwe kabili, amandla aphindwe kabili.
2. Ibanga liyinciphisa ngokushesha. Phinda ubukhulu bese amandla ehla kuye kwengxenye. Lolu yi imithetho eshintsha-isikwere.

Kuphakathi kweplanethi, ukukhawulelwa kokwehla kwesimo ngasinye yi g = GM / r². Kumhlaba lokhu kunikeza cishe ama-9.8 m/s² ebusweni beplanethi. Kuphakame kwe-International Space Station (ibanga elingaphezu kuka-420 km), i-r inkulu ngo-7% kuphela, ngakho-ke ukunyakaza kuhlala kunamandla okungu-88%.

Ukusuka ku-orbit ejikelezayo, ukunyakaza kufanele kunikeza ngokugcwele ukucindezela okudingekayo ukubeka indlela ijikeleze:

v_circular = √(GM / r)

Ngaphakathi kweplanethi le 7.9 km/s. Ihamba ngokushesha kunebhombu le-rifle: cishe amakhilomitha angama-28,000/h.

Umphathi

Ngokuvamile asikho isikhathi lapho sisebenzisa khona i-G ne-M ngokuhlukile. Imikhiqizo yabo μ = GM, i gravity parameter, ilinganiselwa ngokuqondile futhi ngokucophelela kakhulu kusuka ekuphathweni kwezinyanga nezindiza. Kumhlaba, μ = 398,600.4355 km³ s⁻², eziwa ngezingxenye ezimbalwa ngayinye yezigidigidi, ngenkathi iG ngokwayo ibizwa ngokuthi ngama-22 amayunithi ngalinye lezigidigidi (CODATA 2018). Isisindo seplanethi esibhalwe kumathebula siyi-μ ehlukaniswe yi-G, futhi ithola ukungaqiniseki kwe-G.

Ithuluzi le-cannon lixazulula umthwalo ngokuqondile ngenkinga yezinto ezimbili. Ukuqashwa okuthe nkqo kusuka ku-radius r₀ ngejubane v kunikeza i-angle momentum h = r₀v ne-conic orbit:

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

lapho i-ν iyi-engile kusuka ku-periapsis. Uma i-v ingaphansi kwejubane lokujikeleza, indawo yokuqashwa yi-apoapsis futhi indlela ihamba ngaphakathi; uma ihamba ngaphansi kobuso, ibhola lishaya phansi. Ku-√(μ/r₀) i-orbit iyidabula (e = 0). Ku-√(2μ/r₀) ibuye ibe yiparabola (e = 1) futhi ibhola liphuma.

Umthetho kaNewton uchaza futhi ukuthi kungani i-mountain yethuluzi litholwe liphakeme kakhulu: ngokweqiniso, umoya uzoncipha noma iyiphi i-cannonball isikhathi eside ngaphambi kokuhamba kwe-orbit, ngakho-ke ama-rockets akhuphuka ngaphezulu kwengxenye enkulu yesimo sezulu ngaphambi kokukhawulela ngakwesobunxele.