Good speed for a perfect orbit

[匿名]

2009-07-15 11:19 pm

I have no idea how to find a good speed. I'm not an advanced student and just doing some independence study. Recently I decided to learn this, so another word I'm just a pure beginning on this. So please don't make it too complicated thanks!

I'm to find a good speed so that a planet will have a perfect orbit around it's star. Here's an example:

Sun (M) 1.989110^30 KG
Earth (m) 5.973610^24 KG
G = 6.67*10^-11
r = 149,597,892 kilometers

Force between Sun and Earth
35,413,401,385,356,974,509,164,227,084.496

Circumference of orbit is 939,951,276.999 in kilometers.
Travel time is 365.26 days for a full orbit.
2,573,375.888 Kilometers per day.

If this is the information provided, how do I find a good speed. Gravitational forces from other planets are neglected. If there's a formula to do this please do tell me. It'll be appreciated.
Thanks!!!

回答 (1)

Prof. Physics

2009-07-18 9:32 pm

✔ 最佳答案

By Newton's law of gravitation,

Gravitational force, F = GMm / r2

F = (6.67 X 10-11)(1.9891 X 1030)(5.9736 X 1024) / (149 597 892 X 103)2

F = 35,413,401,385,356,974,509,164,227,084.496 N

Circumference of the orbit

= 2pir

= 2pi(149 597 892)

= 939,951,276.999 km

By F = mrw2 where w is the angular speed of Earth

35,413,401,385,356,974,509,164,227,084.496 = (5.9736 X 1024)(149,597,892 X 103)(2pi / T)2

Period, T = 365.26 days

Speed = Circumference / Period

= 939,951,276.999 / 365.26

= 2,573,375.888 km per day

參考: Physics king

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