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Newton's Cannon
Open full pageChii ichi? Isaac Newton akafunga nezvemugwagwa wakakwira kwazvo kuti uenderere mberi kubva mumhepo. Usati waisa mvura, bvisa bhodhoro uye richadzokera pasi. Usati waisa mvura, bvisa bhodhoro nekukurumidza sezvazvinogona uye nyika ichazvibata ichibva pasi pebhodhoro zvakaomarara sezvairi kubuda, saka hachizombomira. Izvi zvinonzi orbit.
Maitiro ekuishandisa: Seta kuvhura speed ne slider kana speed bhatani, wobva wadzima moto. Vatsva shots vanogara pascreen kuti ugone kuvaenzanisa navo.
Chii chinonzi speed?
- Kubuda kwako
- Jet ndege, pamusoro 900 km / h (0.25 km / s)
- Rifle bullet, pamusoro 1 km / s
- Orbit speed
- Kubuda-munzira
Mugwagwa unoratidzwa semugwagwa wakakwira kupfuura chero mumwe wacho, saka unogona kuona kuti ndeupi.
Tarisa izvi
- Tinya "Jet ndege" uye moto, wobva wasarudza "Rifle bullet" uye moto.Nharaunda: Vaviri vacho vanodzokera pasi zvakaenzana. Kunyangwe zvinhu zvinofamba nekukurumidza kwazvo mazuva ese hazvina kunyatsosvika pakutenderera.
- Tinya "Orbit speed" uye moto.Nharaunda: Bhora rinofamba nenguva yose uye rinovakazve kukanzura. Rinokwira nguva dzose, asi rinotoramba risina kusvika pasi. Izvi ndizvo zvinoita kuti International Space Station igare ichimira.
- Fire a little slower than orbit speed, then a little faster.Nharaunda: Kuomarara: inokurumidza kutenderera uye inokwira pasi. Kuomarara: inofamba nekumhanya kwakanyanya. Kuomarara: inoramba ichienda pasi, asi ichidzokera kumashure.
- Tinya "Escape speed" uye moto, wobva wachinja nyika kuenda kuMweya.Nharaunda: At escape speed the ball leaves and never comes back. On the Moon, with its weaker gravity, orbit speed is only about 1.6 km/s.
Maitiro ari kutevera
Nei mutambo webhola uchifamba mumigwagwa usina kusvikira wadzikiswa?
Zvinenge zvakaoma kumbofunga kuti mvura inobuda muvhu inobva kupi? Asi zvinoitika, nguva dzose. Panzvimbo yenyika inotenderera pasi ne5 metres pamakore 8 iwe uchifamba, uye chero chinhu chinobuda chinobuda ne5 metres munguva yekutanga. Saka bhodhoro rinofamba kumashure ne8 kilometres per second rinobuda ne5 metres pamwedzi, asi nyika ichibva yasvika pasi ne5 metres.
Nei ichi chiri chikepe chakakura?
Panyika, mahombekombe aya ane 510 km (8% yemativi epasi) uye ari pamusoro penzvimbo iyo International Space Station inofamba (inenge 400 km), saka bhodhi rinotanga richikwira pasi pemhepo. Mumhepo, kumanikidza kunowedzera uye rinopisa bhodhi kwenguva yakareba usati wasvika pasimba rekumhanya kweorbit.
Izvo: marudzi eplaneti uye madiki kubva ku NASA/JPL (bodies.json); nzira dziri zvakajeka zviviri-zvisikwa orbits. Zvimwe zvinoitika zuva nezuva ndezvekutenderera zviratidzo: ndege dzendege dzinofamba pa900 km / h, uye mabhureki emaruva anobuda mubhazi pa0.7 kusvika 1.2 km / s, pamusoro pe1 km / s kune imwe nhanho.
Kunyangwe zvinhu zvese zviri pasi penyika zvinofamba zvakaenzana, kuoma kwepasi kunobata zvinhu zvese zvichienda kumashure.
More in the glossary →Nzira yechimwe chinhu chinoramba chichidonha pamusoro peplaneti kana chiratidzo pasina kumbobvira chacho, nekuti chiri kufamba pasi zvakaomarara.
More in the glossary →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.
More in the glossary →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.
More in the glossary →Mvura inomanikidza zvinhu zvinofamba uye ichizvidzikisa. Iyi kiyi haisi kunyatsonzwisisa izvi; kana mvura yakanga iri mumidziyo yakaiswa zvakasimba, ichava nesimba rekuparadza zvinhu zvichadzokera kumashure.
Data tafura (text alternative)
Panguva ino, iyo mhepo inogara ichifamba nesimba rayo. Kana iri pasi pesimba rekunze, inoda kudzokera kumashure. Kana iri pakati pesimba rekunze nesimba rekubuda, inotanga kutenderera. Kana iri pamusoro pesimba rekunze, inodzoka kwairi.
| Planet | Kutenderera orbit speed pano | Escape speed pano |
|---|---|---|
| Earth | 7.61 km/s | 10.8 km/s |
| Moon | 1.62 km/s | 2.29 km/s |
| Mars | 3.42 km/s | 4.84 km/s |
Chisimba chinobata maapples kunyika ndechimwe chimiro chesimba rinoita kuti mwedzi ugare munzira yake uyewo zvinhu zvinofamba pasi pezuva. Isaac Newton’s great idea yaive kuti imwe mitemo inotiudza zvese. Pano iwe uchaparadza chipfuva chake uye uone nei.
Mwezi unoenda kunyika nguva dzose. Asi zvinoramba zvisina kuitika.
Ona
Kusiya mutambo uye inosvika. Twisa pasi uye ichiri kudonha, asi inosvika kumashure. Isaac Newton akabvunza mibvunzo mishoma: chii kana ukazvikanda really nekukurumidza?
Kufunga kana kanzuru iri pamusoro pemugwagwa, pamusoro pemhepo. Fire a cannonball slowly and it curves down and hits the ground. Fire zviri nyore uye inosvika kure. Nekuti nyika iri mufananidzo, nzvimbo inokura pasi pebhora. Panguva yakakodzera, nzvimbo inofamba zvakajeka sezvinoita mhepo kana kuti sezvakaitika pakutanga. The ball keeps falling, but never lands. Inowanikwa muOrbit.
Tarisa nechipfuva pamusoro. Kutanga zvakaoma, wobva waenda nekukurumidza:
- Mune simba rakawanda: inodzokera kumashure (yekumusoro).
- Just right: inoenda yose nzira (yechiedza).
- Mumwe nguva yakareba: inobuda uye haizodzokere (yemavara emaruva).
Izvi ndizvowo zvinokonzera kuti vafambi vemunyika vagare pasi. Hazvisiri kunze kwegravity. Va, uye zvikepe zvepasi ravo, vari kudonha pamusoro penyika pamwe chete.
_Zvinyorwa
Newton’s Law of Universal Gravity inoti: “Zvinoitika kuti muviri wese unobatawo mumwe nemumwe.”
F = G · M · m / r²
- F ndiyo simba, M uye m zviuru zviviri, r ndechekudzika pakati pezvipatara zvavo.
- G is the gravitational constant: 6.674 × 10⁻¹¹ N m² kg⁻².
Mazana maviri epfungwa dzakagadzirwa muzvinyorwa izvi:
- Zvimwe zvinhu zvinorema zvinotora zvakaoma. Double the mass, double the force.
- Maawa anowedzera simba rayo. Kana uchiwedzera maawa maviri, simba rinodzikira kusvika pachikamu chegumi. Chii chinonzi inverse-square law?
Panzvimbo yepasi, kukwirisa kwezvinhu zvinodonha ndeg g = GM / r². Kuti nyika inopa pamusoro 9,8 m / s² panzvimbo. Pamusoro peInternational Space Station (maererano ne420 km), r idiki chete 7%, saka gravity iri zvakare pamusoro pe88% seyakasimba.
Kuti zvive neorbit yakatenderera, gravity inofanira kupa zvakakwana kutambanudza kunodarika nzira:
v_circular = √(GM / r)
Pamusoro pepasi rose, inosvika 7.9 km/s. Inofamba nekukurumidza kupfuura muchina wemupumburu: 28,000 km/h.
Munyori
Mumitauro yechinyakare, tinowanzoshandisa G neM zvakasiyana. Kugadzirwa kwavo μ = GM, iyo gravity parameter, inoongororwa zvakananga uye zviri nyore kubva kune kutenderera kwezuva nendege dzepasi. Kune nyika, μ = 398,600.4355 km³ s⁻², inozivikanwa kune mamwe marudzi ezviuru zvemadhora, asi G pachayo inozivikanwa chete kune 22 marudzi emamiriyoni (CODATA 2018). Kuwanda kwenyika kwakanyorwa mumifananidzo ndekwe μ yakaparadzwa ne G, uye inotora kusinganzwisisike kweG.
Iyo cannon tool inogadzirisa motion zvakajeka kune imwe nyaya ine mabody maviri. Kutanga kwehorizontal kubva pa radius r₀ nespeed v kunopa angular momentum h = r₀v uye conic orbit:
r(ν) = p / (1 + e cos ν), p = h² / μ, e = |p / r₀ − 1|
uko ν inzvimbo kubva ku periapsis. Kana v iri pasi pekutenderera kwesimba, iyo yekumisikidza nzvimbo ndeye apoapsis uye nzira inodzika mukati; kana ichikwira pasi penzvimbo, bhandi rinobata pasi. Pa√(μ/r₀) orbiti inonzi circle (e = 0). Pa√(2μ/r₀) inowanzove parabola (e = 1) uye bhandi rinobuda.
Chirevo cheNewton chinotsanangurawo kuti nei mugwagwa wechigadzirwa uchiratidzika kunge uri mukuru kwazvo: mune chokwadi, mhepo ichaita kuti michina yemudziyo iite zvishoma nezvishoma nguva yakareba usati wasvika pakutenderera, izvo zvinoita kuti marockets aende pamusoro pekunze kwepasi pevhu usati waenda kumashure.
Tarisa
Panyika, tsvaga iyo yakanyanya kuoma kumhanya kwechiedza ichi kuti chikwanise kuenda muobiti. Saka chinja kuita Kurume kana kuti Mars. Nei mhinduro iri yakasiyana? Ona kuti ndeipi inowirirana nezvinotaurwa mubhuku.
Great. Zvipingamupinyi ndezvekuti kudzidza kunoramba kuripo.
Chidzidzo chekukurukura
3 nhanho mibvunzo. Choose mashoko kuti uone kana iwe uri zvakanaka.
-
Kana ukawedzera nezvikamu zviviri makiromita pakati pezvimwe zvinhu, simba rekuti dzive dzakaomarara rinova:
- A Two Times Stronger
- B Half as strong
- C A quarter as strong
- D Hachisi chinhu
Kuratidza mhinduro
C. A quarter as strong Kuomarara kunoteverwa nechirevo chekuzvimiririra kwekwaka: 1/2² = 1/4.
-
Astronauts paInternational Space Station vanofamba nekuda kwezvikonzero zvinotevera:
- A Hapana kuomarara munzvimbo
- B Vachaenda kutenderera panyika pamwe chete nendege yepasi.
- C Iyo stations iri kunze kweatmosphere yenyika
- D The Moon pulls them up
Kuratidza mhinduro
B. Vachaenda kutenderera panyika pamwe chete nendege yepasi. Panzvimbo yepamusoro pechitima, gravity ichiri pamusoro pe90% yeiyo surface value.
-
Chii chinonzi circular orbit speed pamusoro pepasi (kusiya kunze kwemhepo)?
- A Maererano ne 0.8 km/s
- B Maererano ne 7.9 km/s
- C Maererano ne 11.2 km/s
- D Maererano ne30 km/s
Kuratidza mhinduro
B. Maererano ne 7.9 km/s v = √(GM/r) = √(398,600 / 6,371) ≈ 7.9 km/s. 11.2 km/s ndiyo nguva yekubuda.
Kusvika pakupera
- Yakatamba neyakaenzana
- Ona dzidziso
- Akakunda chipingamupinyi
- Akatora chidzidzo
. Kuchengeta kuenderera mberi kwebasa pane iyi kifaa, tinya paKunyora.
Chidzidzo chakapera. Yakanaka!
Kumusoro Maitiro eKeplerMashoko mubhuku rino
Zvinyorwa
- 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
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