An yi wannan darasi da wani Local Solar System ma'aikacin ƙungiyar Foundation kuma za'a iya inganta shi da mai duba da ya dace. Shin kana da kwarewa a cikin wannan batutuwa? Suggest an edit
Newton's Cannon
Open full pageMẽne ne wannan? Isaac Newton ya yi tunanin wani makami a kan dutse mai tsayi wanda zai fito daga sama. Ka yi wuta da kwallon kadan kuma ta fadi ƙasa. Ka yi wuta da shi, da sauri, kuma ƙasa ta karkata daga ƙarƙashinsa kamar yadda take fãɗuwa, sabõda haka bã za ta iya fãɗuwa ba. Wannan wata tafiya ce.
Yadda ake amfani da shi: Ka ƙayyade gudun farawa da slider ko maɓallin gudu, sa'an nan ka danna Shotgun. Zaɓuɓɓukan farko na iya zama a kan fuskar kwamfyuta don ka iya kwatanta su.
Yaya wannan yake?
- Your shot
- Jirgin sama na jiragen ruwa, kusan 900 km/h (0.25 km/s)
- Bullet, a kan 1 km/s
- Orbit speed
- Escape speed
An yi zane da dutsen ya fi tsayi fiye da duk wani na gaskiya don ka iya ganinsa. An manta da juriya ta iska.
Yi wannan
- Danna "Jet airliner" kuma ka yi wuta, sa'an nan kuma "Rifle bullet" kuma ka yi wuta.Bayani: Har ma da abubuwa masu sauri na yau da kullum ba su da sauri sosai don su iya tafiyar da wata.
- Danna "Saurin Orbit" kuma ka yi wuta.Bayani: An yi wa kwallon wani juyawa har sai ta dawo cikin bindigar. Takan faɗi duk lokacin da take faɗuwa, amma tana ci gaba da rasa ƙasa. Wannan shi ne yadda Tashar Samaniya ta Duniya ke zama a sama.
- Fire a little slower than orbit speed, then a little faster.Bayani: Mai sauri: yana juyawa ƙasa kuma ya tashi a wani ɓangaren hanya. Mai sauri: daurin yana faɗaɗawa zuwa wani tsawo mai launin shuɗi wanda ke juyawa zuwa waje kuma yana dawowa.
- Danna "Saurin gudu" da wuta, sa'an nan kuma canja duniyar zuwa wata.Bayani: A cikin gudun gudu, kwallon tana tafiya kuma ba ta dawo ba. A kan wata, da ƙarfin jujjuyawarta mai rauni, gudun orbit ɗinta yana kusa da 1.6 km/s kawai.
The ideas behind it
Me ya sa bawul din da ke tafiyar hawainiya bai fadi ba?
Yana faruwa, duk lokacin. Fuskar ƙasa tana canzawa zuwa ƙasa da mita 5 ga kowace kilomita 8 da kake tafiya, kuma duk abin da aka jefa yana faruwa da mita 5 a cikin minti na farko. Saboda haka kwallo mai motsi a gefen da kilomitara 8 a kowane sakan yana faruwa da mita 5 a kowane sakan yayin da ƙasa ke faruwa da mita 5. Ba ta taba kusantar ƙasa ba.
Me ya sa wannan dutse mai tsayi?
A kan ƙasa, dutsen nan yana da tsayin kilomita 510 (8% na radius din ƙasa), mafi girma fiye da inda Tashar sararin samaniya ta duniya take tashi (kimanin kilomita 400), don haka kwallon tana farawa a sama da kusan dukkan hasken rana. A cikin hasken rana, jujjuyawar za ta rage gudun kuma ta sanya kwallon ta zafi sosai kafin ta kai ga sauri mai tafiyar wata. Wannan shi ne dalilin da ya sa manyan rokets ke tashi daga sama farko kuma su kara gudu zuwa gefe.
Maɗaukaki: masu duniyar da girmansu daga NASA/JPL (bodies.json); hanyoyin sune daidaitattun orbits na jiki biyu. Saurin yau da kullum suna da siffofi masu kyau: jiragen sama na jirgin ruwa suna tafiya a cikin kusan 900 km/h, kuma bular bindigar ta bar bututun a cikin kusan 0.7 zuwa 1.2 km/s, kusan 1 km/s ga mai sauri.
Wannan ya sa duk wani abu yana da karfin jujjuyawar da yake da shi a kan sauran abubuwa.
More in the glossary →The path of something that keeps falling around a planet or star without ever hitting it, because it is moving sideways fast enough.
More in the glossary →Jirgin da kake bukatar ka tafi gefe don ka yi tafiyar hawa-hawa a wata duniyar nan mai tsayi ba tare da ka faɗi cikinta ko kuma ka gudu ba. A sama da hasken kasa ne, yana da kimanin kilomita 7.8/s.
More in the glossary →Jirgin da ake buƙata don barin wata duniyar gaske, ba tare da komawa baya ba. Daga kan ƙasa yana da kimanin kilomita 11.2 a kowane sakan, ba tare da la'akari da iska ba.
More in the glossary →Haske na canzawa da wani abu mai motsi kuma yana ragesa. Wannan kayan aiki yana hana shi; wata ƙwanƙwasa ta gaskiya da aka yi amfani da ita cikin sauri za'a iya hanata kuma a kashe ta da haske.
Jadawalin bayanai (zaɓin rubutu)
Kadan daga cikin gudun ɓoyayye: yana faduwa baya. Tsakanin gudun ɓoyayye da gudun gudu: yana orbiting. A ko sama da gudun gudu: yana fita don alheri.
| Planet name | Phonon:: MMF:: EffectFactory | Escape speed here |
|---|---|---|
| Duniya | km 7.61/d | km 10.8/d |
| Wata | km 1.62/d | km 2.29/d |
| Mars | km 3.42/d | km 4.84/d |
Ka yi jĩfa da ƙulli har ya kõma. Ka jefa shi da ƙarfi sosai kuma ba zai iya yi ba. A kan ƙasa, wannan gudu ne 11.2 kilomita a kowace sakan, kuma samun shi shine dalilin da ya sa rokets suna da girma.
Da sauri, da wani abu da aka yi wa wuta bã zai kõma ba.
Look
Ka yi ƙulli da ƙwallo zuwa sama kuma ya zo ƙasa. Ka yi gudu da shi, yana tafiya mafi girma a gabãnin ya faɗi baya. Shin akwai wani gudu da sauri kamar yadda shi ba zai iya dawowa?
Na’am! An kira shi saurin gudu (ko saurin gudu). Ka tafi da sauri kamar haka, ba tare da wani abu na hana ka tafiya ba, kuma karfin jujjuyawar ƙasa ba zai iya mayar da kai ba.
| Duniya | Escape speed from the surface |
|---|---|
| Dakata | 2.4 km/s |
| Dakata | 5.0 m/s |
| Duniya | 11.2 km/s |
| star name | 59.5 km/s |
| Dakata | 617.6 km/s |
Kuma ga watã akwai wata ãyã daga Ubangijinka. Wannan shi ne dalili guda da ya sa wata zai iya zama wurin amfani ga fitar da abubuwa a cikin sarari daga gare shi.
A cikin kayan aikin kanoni, watan an cika shi. Yi kokarin gudun ƙasa da sama na gudun gudun gudun gudun da aka nuna a cikin karantawa.
Understand
A cikin wannan yanayin, za a iya cewa makamashin da ake samu daga wutar lantarkin yana da yawa sosai. Setting kinetic energy equal to the energy needed to reach infinity:
½ v² = μ / r ⇒ v_escape = √(2μ / r)
Ka kwatanta da gudun ɓoyayye √(μ/r): gudun gudun gudu shine √2 ≈ 1.414 sau na gudun ɓoyayye a kan wannan nisan.
Abubuwan da suka fi muhimmanci biyu:
- Ba ya dogara da nauyinka. Wani dutse da jirgin sararin samaniya suna bukatar gudun guda ɗaya. Kuma lalle ne, haƙĩƙa, Allah Mai gãfara ne, Mai jin ƙai.
- Ya dogara da inda kake farawa. Idan ka wuce, r ya fi girma kuma gudu yana da sauƙi. Daga tsayin geostationary orbit, Earth’s gudun gudu ne kawai a kan 4.3 km / s.
Rockets ba sa iya kai hari da sauri fiye da 11.2 km/s a kan ƙasa. Sunã hawa da sauri, alhãli kuwa injinansu sunã ci gaba da tafiya. Jirgin gudu shi ne gudun da ake bukata ga wani abu mai ba da karfi, kamar kwanton bauna.
Master
A cikin sharuddan makamashi na musamman ε = v²/2 − μ/r, gudun yana nufin ε ≥ 0. A daidai ε = 0 hanya ce ta parabola kuma gudun yana dauke da sifar a ƙarƙashin ƙarshe. Mafi sauri fiye da wannan, hanya ita ce hyperbola kuma abu na riƙe da gudun da ya rage a gefe mai nisa, gidan gudun hyperbolic v∞:
v² = v∞² + v_escape², C₃ = v∞²
Masu shirya aikin sun ambaci farar wutar lantarki kamar C₃ (km² / s²). Ga wani canji na Mars, v∞ a lokacin da ya bar yana da kimanin 2.9 km/s, don haka C₃ ≈ 8.7 km²/s².
Wannan dangantaka tana ɓoye ɗaya daga cikin tasirin da ya fi amfani a cikin jirgin sararin samaniya, tasirin Oberth: wani zafi da aka yi zurfi a cikin wani ruwa mai nauyi, inda kake tafiya da sauri, yana siyar da v∞ fiye da irin wannan zafin da aka yi da nisa. Daga 200 km parking orbit a kusa da Earth (circular gudun 7.78 km/s, gudun gudu 11.0 km/s), samun v∞ = 2.9 km/s bukatar kawai game da 3.6 km/s na injiniya na wuta, ba 3.2 + 2.9 = 6.1 km/s. The Delta-v Map uses this for every departure from low Earth orbit.
Try it
On the Moon, fire at a speed just below the escape speed shown in the readout, then just above. Ka nũna mini hanyarsu. Sai ku yi kokarin irin wannan a kan ƙasa da Mars.
Great. kalubale ne inda koyon sticks.
Quick quiz
3 tambayoyi masu sauri. Zaɓi amsa don ka ga ko kai mai gaskiya ne.
-
Earth's escape speed from the surface is about:
- A 7.9 km/s
- B 11.2 km/s
- C 29.8 km/s
- D 617 km/s
Nuna amsa
B. 11.2 km/s
-
Escape speed is how many times the circular orbit speed at the same distance?
- A 2
- B √2 (kwanaki 1.41)
- C 1/2
- D π
Nuna amsa
B. √2 (kwanaki 1.41)
-
Shin, gudun gudu yana dogara ne da yawan abu da ake fitarwa?
- A Yes, heavier objects need more
- B Ya, abubuwa masu haske suna bukatar fiye da haka
- C No, only on the planet's mass and the starting distance
- D Only in an atmosphere
Nuna amsa
C. No, only on the planet's mass and the starting distance
Finish line
- An yi wasa da mai magana da kai
- Read the lesson
- Did the challenge
- Took the quiz
Mark the lesson complete to save it to your progress on this device.
An kammala darasi. Mai kyau!
Up next Me yasa wani orbit yana da wata faduwaWords in this lesson
Sources
- NASA JPL, Basics of Space Flight, Chapter 3: Gravity and Mechanics
- NASA NSSDCA Planetary Fact Sheet (escape velocities)
- JPL SSD: Planetary Physical Parameters
- NASA NSSDCA Sun Fact Sheet
Wannan darasi yana da lasisin CC BY-SA 4.0.