an aircraft satellite revovles around the earth remaining close to the surface of the earth show that its time period is T=2π√Re/g
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The satellite is undergoing circular motion.
Centripetal force for the motion is being provided by the gravitational attraction between the satellite and the earth
Let the mass of earth be M, mass of satellite be m and radius of earth be R.
mv^2/R = GMm/R^2
Solving, v=√(GM/R)
Now time period = 2πR/v
Solving which we get
T= (2π/√GM)* R^(3/2)
Also, GM/R^2 = g
Thus, T= 2π √(R/g).
:)
Centripetal force for the motion is being provided by the gravitational attraction between the satellite and the earth
Let the mass of earth be M, mass of satellite be m and radius of earth be R.
mv^2/R = GMm/R^2
Solving, v=√(GM/R)
Now time period = 2πR/v
Solving which we get
T= (2π/√GM)* R^(3/2)
Also, GM/R^2 = g
Thus, T= 2π √(R/g).
:)
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