Calculating Orbital Speed and Period for a Satellite in Circular Orbit

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To calculate the orbital speed of a satellite in a circular orbit, the mass of the satellite is not needed as it cancels out in the equations. The relevant formula for orbital speed is v^2 = GM/r, where G is the gravitational constant, M is the mass of the Earth, and r is the distance from the Earth's center to the satellite. For the period of revolution, T = (2πr)/v can be used once the speed is determined. The gravitational force acting on the satellite can be calculated using F = GmM/r^2. Understanding these relationships is crucial for solving the problem accurately.
mizzy
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Homework Statement


A satellite of mass 600kg is in a circular orbit about the Earth at a height above the Earth equal to the Earth's mean radius. Find:
a) the satellite's orbital speed
b) the period of its revolution
c) graviational force acting on it


Homework Equations


a) v^2 = GM/r

b) T = (2pie) r/ v

c) F = GmM/r^2


The Attempt at a Solution


for part a, is the satellites orbital speed dependent on the mass of the earth? Do I use mass of earth? or the satellite?
 
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mizzy said:

The Attempt at a Solution


for part a, is the satellites orbital speed dependent on the mass of the earth? Do I use mass of earth? or the satellite?

Part a) you are equating the centripetal force on the satellite, so the mass of the satellite cancels out. The rest look correct.
 
ok. thanks.
 
The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?

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