Geostationary Satelite Problem

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SUMMARY

The discussion focuses on calculating the distance from the center of Venus required for a satellite to maintain a geostationary orbit, given Venus's mass of approximately 4.87 x 1024 kg and a rotational period of 2802 hours. The key equations utilized include the orbital velocity formula, v = 2πr/T, and the relationship between gravitational force and centripetal force. Participants emphasize the importance of converting the period into appropriate units and solving the resulting equations to find the radius (r) necessary for the satellite's orbit.

PREREQUISITES
  • Understanding of gravitational force and centripetal force relationships
  • Familiarity with orbital mechanics and satellite motion
  • Knowledge of unit conversion for time periods
  • Proficiency in algebraic manipulation of equations
NEXT STEPS
  • Study the concept of geostationary orbits and their requirements
  • Learn about gravitational force calculations in celestial mechanics
  • Explore the implications of orbital velocity on satellite positioning
  • Investigate the effects of planetary mass on satellite orbits
USEFUL FOR

Aerospace engineers, astrophysicists, students studying orbital mechanics, and anyone involved in satellite deployment and positioning around celestial bodies.

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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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