Calculating C for a Freely Falling Satellite

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In summary, the conversation discusses the equation T=C(R^3/GM)^0.5 and the constant C=pi/2^(1.5) in relation to a satellite falling freely towards the Earth from a distance R, treating the Earth as a point mass M. The equation of motion of the satellite is also mentioned.
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didimimi2266
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Homework Statement



A satellite falls freely towards the Earth starting from rest at distance R, much larger than the Earth's radius.Treating the Earth as a point mass M then
T=C(R^3/GM)^0.5
where G is gravitational constant
By using equation of motion of the satellite, show that C=pi/2^(1.5)

Homework Equations



use GM/r^2=a


The Attempt at a Solution


I m not sure how the satellite falls ...why is pi in the constant C??
 
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  • #2
What's T supposed to be?
 
  • #3
ideasrule said:
What's T supposed to be?

Sorry..T is the time taken by the satellite to reach the Earth
 

FAQ: Calculating C for a Freely Falling Satellite

How do you calculate the acceleration of a freely falling satellite?

The acceleration of a freely falling satellite can be calculated using the formula a = GM/r^2, where G is the gravitational constant, M is the mass of the planet, and r is the distance between the satellite and the center of the planet.

What is the formula for calculating the velocity of a freely falling satellite?

The velocity of a freely falling satellite can be calculated using the formula v = √(GM/r), where G is the gravitational constant, M is the mass of the planet, and r is the distance between the satellite and the center of the planet.

How do you determine the time taken for a freely falling satellite to reach the surface of a planet?

The time taken for a freely falling satellite to reach the surface of a planet can be calculated using the formula t = √(2h/g), where h is the height of the satellite above the surface and g is the acceleration due to gravity on the planet.

Can the mass of the satellite affect its acceleration?

Yes, the acceleration of a freely falling satellite is directly proportional to its mass. This means that a higher mass satellite will experience a greater acceleration due to gravity compared to a lower mass satellite.

How do you calculate the orbital period of a freely falling satellite?

The orbital period of a freely falling satellite can be calculated using the formula T = 2π√(r^3/GM), where r is the distance between the satellite and the center of the planet and M is the mass of the planet.

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