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Mushandisi Webrowseri · Module 5

Escape velocity

Ndezvipi zvinoda kuitwa kuti nyika iite seyakaomarara? Ndiani anofanira kuenda kunoisa rocket panyika? Uye nei rocket isina kufanira kusvika pasi pevhu.

12 min

NASA/JPL/Space Science Institute

Iyi dzidzo yakanyorwa ne Local Solar System Foundation team member uye inogona kuvandudzwa nemunhu ane ruzivo. Une ruzivo rwekutaura nezvenyaya iyi here? Suggest an edit

Newton's Cannon

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Chii 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.

Kutanga
Kutenderera orbit speed pano
Escape speed pano

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
  1. 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.
  2. 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.
  3. 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.
  4. 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.
Mashoko ekuti uzive
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.

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.

Kufamba kwakakodzera pamusoro pemugwagwa
PlanetKutenderera orbit speed panoEscape speed pano
Earth7.61 km/s10.8 km/s
Moon1.62 km/s2.29 km/s
Mars3.42 km/s4.84 km/s

Twisa mutambo uye unodzokera. Throw yakasimba zvakakwana uye hazvina kuitika. Panyika, iyo speed ndeye 11.2 kilometres pasecond, uye kusvika kwacho ndiko kwakaita kuti marocketi ave nesimba rakakura.

Artemis I rocket ichibuda pazuva munguva yechiedza chakanaka.
Artemis I inotanga kubva kuKennedy Space Center, 16 November 2022. Credit: NASA/Bill Ingalls

Zvakaoma, uye chinhu chakasviba hachizodzokera.

Ona

Throw a ball pamusoro uye inosvikazve pasi. Throw zviri nyore, inoenda pamusoro pamberi kupararirazve. Pane sei kukwira kwechiedza kwakanyanya kuti hakusi kudzokerazve?

Ndinoda. Inonzi escape speed (kana escape velocity). Go kushoma kuti nekukurumidza, pasina chinhu kunonoka iwe pasi, uye gravity anogona kamwe bvisa iwezve.

WorldKubuda kwesimba kubva panzvimbo
Moon2.4 km/s
Mars5.0 km/s
Earth11.2 km/s
Jupiter59.5 km/s
Sun617.6 km/s

Kubuda kwezuva kunoitika nenguva yakati rebei kupfuura kubuda kwezuva. Izvi ndizvo zvakaita kuti mwedzi uve nzvimbo yakanakisisa yekumisikidza zvinhu munzvimbo yepasi.

Mukanzuru yeMutare, mutauro wemutauro wechirungu ndiyo mitauro inoshandiswa. Tarisa kukwira uye kudzika kwechikepe pamusoro pekubuda mumvura kwakaratidzwa nechiratidzo.

_Zvinyorwa

Kubuda kunoitika kana simba rekinetic remuviri richikwana kukwira kunze kwe “hukuru” hwekumanikidza zvachose. Kuisa kinetic energy seyakafanana neyodarika kusingaperi:

½ v² = μ / r  ⇒  v_escape = √(2μ / r)

Kuenzanisa nenguva yemuchina √(μ/r): nguva yekubuda ndeye √2 ≈ 1.414 times nguva yemuchina pamwecheteyo distance.

Mamwe mashoko akakosha:

  1. Inobva pahuwandu hwako. Chikepe chepasi nechikepe chenyika zvinoda kukwira nesimba rimwe chete. (The spaceship inodiwa zvikuru * simba *, of course.)
  2. Inoenderana nekwaunotanga. Panzvimbo dzakadzika, r ikuru uye kubuda kunokwanisika. Kubva pakureba kwegeostationary orbit, kubuda kwepasi kunosvika 4.3 km/s chete.

Rockets kamwe chete haasi kuuraya kusvika 11.2 km / s panyika. Vachikwira zvakasimba, masimba avo achiri kumanikidza. Kubuda kwesimba remhepo kunoitwa nechiedza chezuva, chisingaite sechiedza chezuva.

Munyori

Nekureva kwesimba rekuti orbital ε = v²/2 − μ/r, kubuda kunoreva ε ≥ 0. Pa ε = 0, nzira inonzi parabola uye kumhanya kunosvika pazero pasingaperi. Panguva imwecheteyo, nzira iyi inonzi hyperbola uye chigadzirwa chinochengeta mukana wekukwira wakawandisa, iyo hyperbolic excess speed v∞:

v² = v∞² + v_escape²,   C₃ = v∞²

Misheni vagadziri vanotaura kuburitsa simba seC₃ (km² / s²). Kuti uende kuMars, v∞ pakutanga ndezve 2.9 km/s, saka C₃ ≈ 8.7 km²/s².

Iyo kubatana inochengeta imwe yemhedzisiro yakakosha kwazvo mundege dzepasi, iyo Oberth effect: kuora kwakaita mukati megravity well, uko iwe wakambofamba nekukurumidza, kunotenga zvakawanda zve v∞ kupfuura kuora kwakafanana kwakaita kure. Kubva pa200 km parking orbit pamusoro penyika (circular speed 7.78 km/s, escape speed 11.0 km/s), kusvika v∞ = 2.9 km/s inodiwa chete nezve 3.6 km/s yechigadzirwa chekupisa, kwete 3.2 + 2.9 = 6.1 km/s. Delta-v Map inoshandisa izvi kune ese kubuda kubva kumahombekombe epasi.

Tarisa

Pazuva, rova nesimba rakakura kupfuura simba rekubuda rakaratidzwa mubhuku, wobva waenda pamusoro. Tsananguro:

Chidzidzo chekukurukura

3 nhanho mibvunzo. Choose mashoko kuti uone kana iwe uri zvakanaka.

  1. Kubuda kwenyika kubva panzvimbo yepasi kunosvika:

    1. A 7.9 km/s
    2. B 11.2 km/s
    3. C 29.8 km/s
    4. D 617 km/s
    Kuratidza mhinduro

    B. 11.2 km/s

  2. Kubuda speed ndezvipi nguva yakati wandei ye circular orbit speed pamwechete distance?

    1. A 2
    2. B √2 (about 1.41)
    3. C 1/2
    4. D π
    Kuratidza mhinduro

    B. √2 (about 1.41)

  3. Chii chinonzi escape speed? Inoenderana sei nesimba rechigadzirwa chiri kuburitswa?

    1. A Yeah, zvidimbu zvakaoma zvinoda zvakawanda
    2. B Yeah, lighter zvinhu zvinoda zvakawanda
    3. C Hapana, chete pamasaizi epasi uye pakutanga kwenzvimbo
    4. D Only in an atmosphere
    Kuratidza mhinduro

    C. Hapana, chete pamasaizi epasi uye pakutanga kwenzvimbo

Kusvika pakupera

  • Yakatamba neyakaenzana
  • Ona dzidziso
  • Akakunda chipingamupinyi
  • Akatora chidzidzo

. Kuchengeta kuenderera mberi kwebasa pane iyi kifaa, tinya paKunyora.

Mashoko mubhuku rino

Zvinyorwa

Iyi dzidzo ine mubhadharo CC BY-SA 4.0.

Zvigadzirwa uye zvidzidzo zvinoshandisa mamodheru akapusa ekudzidza chete. Hazvifanirwe kushandiswa kune yekufambisa, kumisikidza chiitiko kana chero chisarudzo chekushanda. Dzvanya pano kuti uwane ruzivo nezvezvinyorwa zvedzidzo