Centrifugal Force- Finding Speed of Satellite

AI Thread Summary
To find the speed of a satellite in a stable circular orbit at a radius of 6736 km, the centripetal acceleration is inversely proportional to the square of the radius. The gravitational force equation fg = G(m1)(m2)/r^2 relates to this, where fg equals the product of mass and acceleration (m2a). Understanding that the acceleration a can be expressed as a = Gm1/r^2 clarifies that as the radius increases, the acceleration decreases. This relationship is crucial for calculating the satellite's speed using the centripetal acceleration formula Ac = v^2/r. Ultimately, applying these principles allows for the determination of the satellite's orbital speed in meters per second.
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Homework Statement



In order for a satellite to move in a stable circular orbit of radius 6736 km at a constant speed, its centripetal acceleration must be inversely proportional to the square of the radius r of the orbit.
What is the speed of the satellite? The universal gravitational constant is 6.67259 × 10−11 N · m2/kg2 and the mass if the Earth is 5.98 × 1024 kg.
Answer in units of m/s.

r=6736

Homework Equations


fg=G(m1)(m2)/r^2
Ac=v^2/r
Mv^2/r=Fg

The Attempt at a Solution



One thing that trips me up is "its centripetal acceleration must be inversely proportional to the square of the radius r of the orbit." What does this mean? Once i know this i can figure it out.
 
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That just means that in fg=G(m1)(m2)/r^2, fg = m2a so that a=Gm1/r^2. Gm1 is constant so a is proportional to 1/r^2.
 
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