Le ncwadi yabhalwa ngu Local Solar System Iqela le-Fundamente lilungu kwaye lingaphuculwa ngumvavanyi oqeqeshiweyo. Ingaba uqeqeshiwe kulo mxholo?
I-Newton's Cannon
Vula iphepha elipheleleyoYintoni le? UIsaac Newton wacinga ukuba i-cannon kwinduli ephakamileyo kakhulu ukuba iyaphuma emkhathini. Yivulele ibhola ngokucothayo kwaye iyawa ezantsi kwakhona. Yivulele ngokukhawuleza ngokwaneleyo kwaye umhlaba ugoba kude ngaphantsi kwayo njengoko ihamba ngokukhawuleza, ngoko ayizukuba yindawo yokuwela. Eli lijikelezo.
Indlela yokusetyenziswa kwayo: Misela isixa esikhawulezayo sokuqala nge-slider okanye iqhosha lesantya, emva koko ucinezele Umlilo. Ii shots ezidlulileyo zihlala kwikhusi ukuze ukwazi ukuzithelekiswa.
Ikhawuleza kangakanani loo nto?
- Uhlaselo lwakho
- Inqwelomoya yejet, malunga ne-900 km/h (0.25 km/s)
- Ibhombu ye-rifle, malunga ne-1 km/s
- Isantya se-Orbit
- Isantya Sokuphuma
Umlambo uzotywe phezulu kakhulu kunanoma yimuphi omnye obonakalayo ukuze ukwazi ukuwubona. Ukulwa kwemoya akuhoywa.
Zama oku
- Cinizela "i-Jet airliner" kwaye uvule umlilo, emva koko "i-Rifle bullet" kwaye uvule umlilo.Isaziso: Zonke zibuyela ezantsi ngokufanayo. Nakuba izinto ezikhawulezayo kakhulu zomihla ngemihla azikho naphi na kufutshane nokukhawuleza ngokwaneleyo ukujikeleza.
- Cinizela "Isantya sokuhamba" kwaye uvule.Isaziso: Ibhola ihamba yonke indlela ijikeleze kwaye ibuyela kwi-cannon. Iyawa ixesha lonke, kodwa iyaqhubeka ilahleka emhlabani. Le yinto eyenza ukuba isiXeko seSizwe soMhlaba sihlale phezulu.
- Umlilo ohamba ngamandla aphantsi kunaleyo yesantya sokuhamba, emva koko uhamba ngokukhawuleza.Isaziso: Ecothayo: ijikeleza ezantsi kwaye iwela kwinxalenye yendlela ejikelezayo. Ikhawulezayo: umda ujika ube yi-ovale ende ejikeleza kude ngaphandle kwaye ibuyela emva.
- Nqakraza "Isantya Sokuphuma" kwaye uvule, emva koko tshintshela iplanethi kwinyanga.Isaziso: Kwisantya sokuphuma ibhola iphuma kwaye ayizukubuya. Kwinyanga, ngoxinzelelo lwayo olusezantsi, isandi se-orbit simalunga ne-1.6 km/s kuphela.
Iimbono ezimva kwayo
Kutheni ibhola ejikelezayo ingawela phantsi?
It does fall, all the time. Earth's surface curves downwards by about 5 metres for every 8 kilometres you travel, and anything dropped falls about 5 metres in its first second. So a ball moving sideways at about 8 kilometres per second falls 5 metres each second while the ground drops away by 5 metres. It never gets any closer to the ground.
Kutheni le nto intaba iphakamileyo?
Kwihlabathi lendalo iphela umlambo apha umalunga ne 510 km ubude (8% yeradius yehlabathi), ngaphezulu kwe International Space Station iqhuba ( malunga ne 400 km), ngoko ke ibhola iqala phezulu kakhulu kumoya wonke. Ezantsi elwandle, ukutsala kuyakukhawuleza kwaye kufudumeze ibhola ixesha elide phambi kokuba ifike kwisantya sokuhamba nge orbit. Le yisizathu sokuba i-rockets ezinyanzelekileyo zikhuphe ngaphandle komoya kuqala kwaye emva koko zikhawuleze ngasecaleni.
Iindawo: iindidi zeplanethi kunye nobungakanani ukusuka kwi NASA/JPL (bodies.json); iindlela ziyimijikelezo ecacileyo yezinto ezimbini. Isantya sansuku zonke siziimpawu eziqhelekileyo ezijikelezayo: iinqwelomoya ezihamba ngeejet zihamba malunga ne-900 km/h, kwaye izidumbu zerayisi zishiya isiqulathi esimalunga ne-0.7 ukuya kwi-1.2 km/s, malunga ne-1 km/s yenye ekhawulezayo.
Ukutsala okunokwenziwa yizinto zonke kwizinto zonke. Uxinzelelo lwehlabathi lutsala konke ukuya kwisiqithi saso, oko kubangela ukuba izinto ziphele.
Okuninzi kwincwadi eneenkcukacha →Indlela yento eqhubeka iwela phantsi kweplanethi okanye inkwenkwezi ngaphandle kokubetha, kuba iyahamba ngasecaleni ngokukhawuleza ngokwaneleyo.
Okuninzi kwincwadi eneenkcukacha →The speed you must go sideways to circle a planet at a given height without falling in or flying away. Just above Earth's air it is about 7.8 km/s.
Okuninzi kwincwadi eneenkcukacha →The speed needed to leave a planet for good, never falling back. From Earth's surface it is about 11.2 km/s, ignoring the air.
Okuninzi kwincwadi eneenkcukacha →Umoya otyhala into ehambayo kwaye uyicoce. Le sixhobo ayihoyi; ibhola ye cannon eyenziwe ngokukhawuleza iyakuvalwa kwaye iqhume ngumoya.
Itheyibhile yedata (umbhalo otshintshiyo)
Ecothayo kunesantya esijikelezayo: iwela umva. Iphakathi kwesantya esijikelezayo nesezantsi: ijikeleza. Kwi okanye ngaphezulu kwesantya sokuphuma: ishiya ngokulungileyo.
| Iplanethi | Isantya sojikelezo lwe-orbit apha | Isantya sokuphuma apha |
|---|---|---|
| Ihlabathi | 7.61 km/s | 10.8 km/s |
| Inyanga | 1.62 km/s | 2.29 km/s |
| I-Mars | 3.42 km/s | 4.84 km/s |
Umandla otsala i-apple phezulu ehlabathini ngumandla ofanayo ogcina iNyanga kwindlela yayo yokuhamba kunye neeplanethi ezijikeleze ilanga. Iingcamango ezikhulu zikaIsaac Newton zazi ukuba umthetho omnye uchaza zonke. Apha uya kutyhila i-cannon yakhe kwaye ufunde ukuba kutheni.
Inyanga iwela phezulu esuka kwihlabathi lonke ixesha. Ihlala ilahlekile.
Bona
Ukhupha ibhola kwaye iyawa. Uyithutha ngaphaya kwaye iyaqhubeka iwela, kodwa ihlala phantsi kude. UIsaac Newton wabuza umbuzo olula: yintoni ukuba uyityhila kwaye ngokukhawuleza?
Ucinga ukuba ibhombu liphezulu komlambo ophakamileyo ongazange ukwenzeka, ngaphezulu komoya. Umlilo webhola yentsimbi ekhawulezayo kwaye ijikeleza phantsi kwaye ibetha umhlaba. Yivule ngokukhawuleza kwaye ihlale kude. Kuba ihlabathi lijikeleze, indawo igoba kude phantsi kwebhola. Kwisantya esifanelekileyo, umphezulu ugoba kude ngokuchanekileyo njengoko ibhola iwela phantsi. Ibhola iqhubeka iwela, kodwa ayizukuhlala. I kwi orbit.
Zama ngempu ephezulu. Qala ngokucothayo, emva koko uye ngokukhawuleza:
- Icotha kakhulu: ibuyela umva (bomvu).
- Kulungile: iyahamba yonke indlela ejikelezayo (luhlaza).
- Ikhawuleza kakhulu: iphuma kwaye ayizukubuya (imfusa).
Leyo ke inokuba yinto ebangela ukuba abaqhubi benqwelomoya bahambe. Azikho ngaphandle koxinzelelo. Ziye, kunye nenqwelo-moya yabo, ziwela phantsi ejikeleze ihlabathi ndawonye.
Ukuqonda
Umthetho kaNewton woxinzelelo lwehlabathi liphela utsho ukuba yonke i-mass itsala enye i-mass:
F = G · M · m / r²
- F yimandla, M ne m zii-mases ezimbini, r umgama phakathi kwezikhululo zabo.
- I-G yi-gravity constant: 6.674 × 10⁻¹¹ N m² kg⁻².
Iimbono ezimbini zifakwe kulo:
- Izinto ezinzima zitsala ngokuxhaphakileyo. Iphindwe kabini isisindo, iphindwe kabini amandla.
- Umgama uyamnciphisa ngokukhawuleza. Phinda umgama kwaye amandla awela kwikota enye. Le yi imithetho ejikelezayo-ethe nkqo.
Kufutshane neplanethi, ukukhawulezisa kwento ehlayo yi g = GM / r². Kwihlabathi elinika malunga ne-9.8 m/s² kwinqanaba lomhlaba. At the height of the International Space Station (about 420 km), r is only 7% larger, so gravity is still about 88% as strong.
Kwindlela ejikelezayo, uxinzelelo kufuneka lubonelele ngokuchanekileyo ngoxinzelelo olufunekayo ukuqhubeka nokujika indlela:
v_circular = √(GM / r)
Ngaphaya komhlaba oku kumalunga ne7.9 km/s. Ikhawuleza kunebhombu ye-rifle: malunga ne28,000 km/h.
Umphathi
Kwimisebenzi sihlala singasebenzisi iG neM ngokuzimeleyo. Imveliso yabo μ = GM, i-gravity parameter, ilinganiselwa ngokuthe ngqo kwaye ngokuchanekileyo kakhulu ukusuka kwintshukumo yenyanga kunye nenqwelo-moya. Kwihlabathi, μ = 398,600.4355 km³ s⁻², eyaziwayo kwiinxalenye ezimbalwa kwizigidigidi, ngelixa iG ngokwayo iziwa kuphela malunga neenxalenye ezili-22 kwizigidigidi (CODATA 2018). Ubunzima behlabathi obuchazwe kwiitheyibhile ngu μ ohlukaniswe yi G, kwaye ifumana ukungaqiniseki kweG.
Isixhobo sebhombu silungisa intshukumo ngokuchanekileyo kwingxaki yezinto ezimbini. Ukuqaliswa okuthe tyaba ukusuka kumda we-r₀ ngesantya se-v kunika umthwalo ojikelezayo h = r₀v kunye nekona ye-orbit:
r( ν) = p / (1 + e cos ν), p = h² / μ, e = |p / r₀ − 1|
apho i-ν iyikona ukusuka kwindawo ejikelezayo. Ukuba i-v ingaphantsi kwesantya esijikelezayo, indawo yokuqalisa yindawo ephakamileyo kakhulu kwaye indlela ihamba phantsi; ukuba ihamba phantsi komhlaba, ibhola iyabetha umhlaba. Kwi √(μ/r₀) i orbit yidayari (e=0). Kwi √(2μ/r₀) ivela ibe yiparabola (e=1) kwaye ibhola iphuma.
Umthetho kaNewton uchaza ukuba kutheni isixhobo somlambo sizotywa phezulu ngokungabonakaliyo: kwinyaniso umoya uya kukhawuleza nayiphi na ibhola yentsimbi ixesha elide phambi kokuba iqhube kwisantya esijikelezayo, oko kukuthi kutheni ii-rockets zinyuka ngaphezulu kweyona nto ininzi yemozulu ngaphambi kokukhawuleza ngasecaleni.
Zama
Kwihlabathi, fumana isantya esicothayo sokuqala esinika umjikelo. Emva koko tshintshela kwinyanga ne Mars. Kutheni isisombululo sihlukile? Khangela ngokuchasene namaxabiso ekufundeni.
Iingxaki zikhona apho ukufunda kuqhekeka khona.
Uvavanyo olukhawulezayo
3 imibuzo ekhawulezayo. Khetha impendulo ukuze ubone ukuba ulungile na.
-
Ukuba uphindaphindo umgama phakathi kwezinto ezimbini, amandla oxinzelelo phakathi kwazo abonakala:
- A I-Double strong
- B Ingxenye enamandla
- C Ikota enamandla
- D Ayitshintshwanga
Bonisa impendulo
C. Ikota enamandla Ukutsala kulandela umthetho wesiqwenga esijikelezayo: 1/2² = 1/4.
-
Abaqhubi beenqwelomoya kwisikhululo sehlabathi esiphakathi bahamba ngenxa yokuba:
- A Akukho mthwalo wesibhakabhaka kwisithuba
- B Ziye zawela phantsi kwehlabathi kunye nesikhululo
- C Isitishi singaphandle kwemozulu yehlabathi
- D Inyanga izisa phezulu
Bonisa impendulo
B. Ziye zawela phantsi kwehlabathi kunye nesikhululo Kwinqanaba lomgangatho wesikhululo uxinzelelo lwelanga luhlala malunga ne-90% yexabiso layo lendawo.
-
Yintoni isantya sojikelezo lwe-orbital phezulu nje kwehlabathi (ukungahoyi umoya)?
- A malunga ne 0.8 km/s
- B malunga ne 7.9 km/s
- C malunga ne 11.2 km/s
- D malunga ne 30 km/s
Bonisa impendulo
B. malunga ne 7.9 km/s v = √(GM/r) = √(398,600 / 6,371) ≈ 7.9 km/s. 11.2 km/s yisantya sokuphuma.
Iilayini Ezigqibekileyo
- Idlala nge-interactive
- Funda isifundo
- Ukwenza isigqibo
- Uthathe isifundo
Phawula isifundo sencwadi eneenkcukacha egqityiweyo ukusigcina kwindlela yakho yokuqhubekeka kule sixhobo.
Isifundo sigqityiwe. Yenziwe kakuhle!
Phezulu Okulandelayo Imithetho kaKeplerAmagama kule ncwadi eneenkcukacha
IiNkqubo
- NASA JPL, Basics of Space Flight, Chapter 3: Gravity and Mechanics
- I. Newton, Philosophiae Naturalis Principia Mathematica (1687), Book III; the cannon thought experiment is in 'A Treatise of the System of the World' (1728)
- CODATA 2018 value of the Newtonian constant of gravitation (NIST)
- JPL SSD: astrodynamic parameters (GM values)
- NASA NSSDCA Planetary Fact Sheet
Eli nqaku lilayisensiwe CC BY-SA 4.0.