Geostationary Satelite Problem

AI Thread Summary
To place a satellite in a geostationary orbit around Venus, its orbital period must match Venus's rotation period of 2802 hours. The relevant equations involve calculating the orbital velocity using v = 2πr/T, where T is the period converted to appropriate units. Additionally, the gravitational force must equal the centripetal force, leading to a second equation that relates velocity and radius. By solving these two equations, the required distance from the center of Venus for the satellite can be determined. This approach combines gravitational dynamics with orbital mechanics to achieve a stable orbit.
Jtappan
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Homework Statement



Venus has a mass of about 4.87 1024 kg. The length of a day on Venus is 2802 hrs. Your task is to put a satellite into a circular orbit around Venus so that it stays above one spot on the surface, orbiting Venus once each Venus day. At what distance from the center of the planet should you place the satellite?
_____ m



Homework Equations



v = 2(pie)r/T where T = the period ? that is one equation

The Attempt at a Solution



Do you use the period of venus to calculate the acceleration and speed of the planet? What do you do with the mass of venus?
 
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Yes, the period gives you the rotation speed. Keep in mind that there is a relationship between rotational speed and tangential velocity.

Once you have the velocity, think about what will keep the satellite in place: Gravity.
 
what is the relationship between rotational speed and tangential velocity?
 
Jtappan said:
what is the relationship between rotational speed and tangential velocity?

The period of the orbit = 2802 hrs

v = 2(pie)r/T... here T = 2802 converted to the appropriate units...

also, equate the gravitational force to the centripetal force... that gives a second equation in terms of v and r...

2 equations with 2 unknowns, v and r. solve for r
 
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