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sandraquah · Feb 5, 2012, 08:50 PM

A satellite is in a geosynchronous orbit around the Earth if its period of rotation is the same as that of the Earth, i.e. 24h. Such a satellite is called a geostationary satellite. Venus has a mass of 4.87x10^24kg and radius of 6.05x10^6m. The length of a day on Venus is 2.10x10^7s. For a satellite to be in a synchronous orbit around Venus, calculate:
1. the orbital radius of the satellite
2. its orbital speed
3. its orbital acceleration

the given answer:
1. 1.54x10^9m
2. 4.60x10^2m/s
3. 1.37x10^-4 m/s2

ebaines · Feb 6, 2012, 08:03 AM

You have the answers - so what do you need to know? If it's how to derive the answers, then start with force due to gravity = centripedal force for the circular orbit:

$<br /> \frac {GMm}{R^2} = mR \omega ^2 <br />$

where $\omega = 2\pi/T$

Note that m (the mass of the satellite) cancels out. Rearrange and solve for R.

Then orbital speed and radial acceleration for circular motion are found using:

$<br /> a = \frac {v^2} R = \omega ^2 R<br />$