This lesson was drafted by a Local Solar System Foundation team member and could be improved by a qualified reviewer. Are you qualified in this subject?ផ្ដល់យោបល់កែសម្រួល
ប្រអប់ខ្សាច់អ័ក្ស
បើកទំព័រពេញWhat is an orbit? Throw a ball sideways and it curves down to the ground.Throw it faster and it lands farther away.Throw it fast enough and the ground curves away beneath it as quickly as it falls, so it never lands: it keeps falling around the planet and always misses.That is an orbit.Nothing holds a satellite up;it is falling all the time.
អ្វីដែលកើតឡើង:
ព្យាយាមក្នុងនេះ
ធ្លាក់ត្រឡប់ក្រោយ អូប៊ីត ជម្រះ
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កំណត់អ័ក្សឲ្យសម (ធាតុអ័ក្ស និងច្បាប់របស់ Kepler)
Astronomers describe an orbit with five numbers called orbital elements.Change them here;the height and speed above follow.
របៀបប្រើវា
- ល្បឿនចំហៀង
- This one control decides what happens.Too slow and it falls back.Fast enough and it goes round in a circle.Faster and it swings out into an ellipse.Faster than escape speed and it leaves for ever.The coloured bar under the slider shows where each begins at the chosen height.
- កម្ពស់
- Where it starts.Higher up, gravity is weaker, so a slower speed is enough to stay in orbit.
- ល្បឿនពេលវេលា
- Real orbits take hours, days or years, so time runs faster here.ពេលវេលា × 1,000 មានន័យថាវិនាទីនីមួយៗនៅលើអេក្រង់គឺ 1,000 វិនាទី (ប្រហែល 17 នាទី) ក្នុងចន្លោះ ។The planet's turning is sped up by the same amount.The numbers shown are always the real ones.
- បទដី
- The gold trail on the ground is the path directly beneath the satellite.Earth turns underneath the orbit, so each lap passes over different places.
- ព្រួញមាស
- Which way it is moving and how fast: the longer the arrow, the faster.
- មើលជុំវិញ
- Drag to turn the view, scroll or pinch to zoom.The faint grid is the plane of Earth's equator (or, around the Sun, the plane of Earth's orbit).
តារាងទិន្នន័យ (ជំនួសអត្ថបទ)
| ជំហានពេលវេលា | ចម្ងាយពីព្រះអាទិត្យបច្ចុប្បន្ន | ល្បឿនឥឡូវ |
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How fast is a spacecraft moving? Tell me how far it is from the planet and how big its orbit is, and one short equation answers the question anywhere along its path. អ្នករៀបចំផែនការបេសកកម្មប្រើវារាល់ថ្ងៃ ។
One short equation gives the speed anywhere along an orbit.
មើល
Anything in orbit is always trading height for speed, like a skateboarder on a half-pipe.
- Falling closer to the central body, it speeds up.
- Climbing away, it slows down.
In the sandbox the yellow arrow shows the speed: long arrow, fast;short arrow, slow. មើលវារីកធំឡើងដូចជារាងកាយលោតចូល ហើយខ្សោយដូចជាវាឡើងចេញ ។
ភពផែនដីធ្វើរឿងដូចគ្នា, គ្រាន់តែដោយប្រុងប្រយ័ត្នព្រោះអ័ក្សរបស់វាគឺស្ទើរតែជារង្វង់: វាផ្លាស់ទីប្រហែល 30.3 km / s នៅដើមខែមករានិងប្រហែល 29.3 km / s នៅដើមខែកក្កដា។
យល់
The vis-viva equation (“living force”, an old word for energy) gives the speed at any point:
v = √( μ · (2/r − 1/a) )
- v: ល្បឿន
- μ: the central body’s gravitational parameter (GM)
- r: current distance from the centre of the central body
- a: semi-major axis of the orbit
Check it:
- រង្វង់ (r =a): v = √(μ/a) ។ That is the circular speed from the Newton lesson.
- នៅ periapsis, r គឺតូចបំផុត ដូច្នេះ 2/r គឺធំបំផុត និង v គឺលឿនបំផុត ។
- ឆ្ងាយណាស់នៅលើផ្លូវរត់គេចខ្លួន (a → ∞): v = √(2μ/r) ។ That is the escape speed, covered in the next lesson.
ឧទាហរណ៍ធ្វើការ: ផែនដីជុំវិញព្រះអាទិត្យ, μ = 1.327 × 10¹¹ km³/s²,a= 149.6 លានគីឡូម៉ែត្រ។ នៅ aphelion r = 152.1 លានគីឡូម៉ែត្រ:
v = √(1.327 × 10¹¹ × (2/1.521 × 10⁸ − 1/1.496 × 10⁹)) ≈ 29,3 គ.ម/វិ.
មេ
Vis-viva is energy conservation in disguise. ថាមពលអ័ក្សជាក់លាក់ (ថាមពលក្នុងមួយគីឡូក្រាម) គឺ
ε = v²/2− μ/r = −μ / (2a)
Kinetic plus potential energy is constant along the orbit and depends only on a. Solve for v and you get vis-viva. Consequences:
- The sign of ε classifies the orbit: negative for ellipses, zero for a parabola, positive for a hyperbola.
- នៅចម្ងាយដែលបានផ្ដល់ណាមួយ ល្បឿនតែមួយគត់កំណត់ a. This is why a single engine burn at one point changes the size of the whole orbit, and why the next lessons can talk about delta-v budgets.
ល្បឿន Apsis តាមពីក្រោយពី vis-viva ជាមួយ r = (1 ± e):
v_ p = √(μ/a · (1+e) / (1−e)), v_ a = √(μ/a · (1−e) / (1+e))
Their product is v_p · v_a = μ/a = v_circ², so the circular speed is the geometric mean of the two, not the arithmetic mean. That answers the Try it question.
សាកល្បងវា
With the Sun as central body, set a = 1 au and e = 0.Note the speed.Now raise e to 0.6 and compare the fastest and slowest speeds with that number.Is the average of the two equal to the circular speed?
អស្ចារ្យ. ការប្រឈមមុខគឺជាកន្លែងដែលការរៀនត្រូវបានចង ។
សំណួររហ័ស
3 quick questions.Pick an answer to see if you are right.
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In the vis-viva equation, what happens to the speed as the body moves closer to the central body?
- A វាកើន
- B វាថយចុះ
- C វានៅថេរ
- D វាក្លាយជាសូន្យ
បង្ហាញចម្លើយ
A. វាកើន
-
For a circular orbit (r = a), vis-viva gives:
- A v = √(2μ/r)
- B v = √(μ/r)
- C v = μ/r
- D v = 0
បង្ហាញចម្លើយ
B. v = √(μ/r)
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Earth moves about 29.8 km/s around the Sun on average.ល្បឿននៅចំណុចប្រសព្វ?
- A 29.3 km/s
- B 30.3 km/s
- C 35 គីឡូម៉ែត្រ/ វិនាទី
- D 42 គីឡូម៉ែត្រ/ វិនាទី
បង្ហាញចម្លើយ
B. 30.3 km/s v_p = √(μ/a · (1+e)/(1−e)) with e = 0.0167 gives about 30.3 km/s ។
បន្ទាត់បញ្ចប់
- បានលេងជាមួយអន្តរកម្ម
- អានមេរៀន
- បានធ្វើការប្រកួត
- បានធ្វើការសាកល្បង
Mark the lesson complete to save it to your progress on this device.
Lesson complete.ល្អណាស់!
ឡើងលើបន្ទាប់ ល្បឿនគេចពាក្យក្នុងមេរៀននេះ
ប្រភព
- JPL SSD: astrodynamic parameters (GM of the Sun)
- NASA JPL, Basics of Space Flight, Chapter 3: Gravity and Mechanics
- NASA NSSDCA Planetary Fact Sheet (orbital velocities)
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