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24 February, 04:11

Find the speed of a satellite in a circular orbit around the earth with a radius 4.03 times the mean radius of the earth. (radius of earth = 6.37*103 km, mass of earth = 5.98*1024 kg, g = 6.67*10-11 nm2/kg2.)

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  1. 24 February, 06:00
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    We will equate the earth's grav force to the centrip force acting on the satellite

    GMm/r^2=mv^2/r

    where M is the mass of the earth, v the speed of the satellite, r the distance from the center of the Earth, m the mass of the satellite, and G the newtonian grav cst

    this gives us:

    v^2=GM/r

    v=sqrt[GM/r] =

    sqrt[6.67x10^ (-11) (6x10^24) / (3.67xR) ] =

    4137.5 m/s

    (where R is the radius of the Earth=

    6.37x10^6m)
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