A satellite, of mass m=1.32E3 kg, falls from rest directly tothe earth from a di

Question

A satellite, of mass m=1.32E3 kg, falls from rest directly tothe earth from a distance of R=3.00 earth radii from the center ofthe earth. (Mass of earth: 5.976*1024 kg. Radius ofearth: 6.37*106 m. G: 6.67*10 -11N*m2/kg2.)

a) What is the speed of the satellite just before it hitsearth?

b) What would the speed have been if the acceleration due togravity was a constant g=9.8 m/s2?
I will give top score for detail explained answers... Thank you,

A satellite, of mass m=1.32E3 kg, falls from rest directly tothe earth from a distance of R=3.00 earth radii from the center ofthe earth. (Mass of earth: 5.976*1024 kg. Radius ofearth: 6.37*106 m. G: 6.67*10 -11N*m2/kg2.)

a) What is the speed of the satellite just before it hitsearth?

b) What would the speed have been if the acceleration due togravity was a constant g=9.8 m/s2?
I will give top score for detail explained answers... Thank you,

Explanation / Answer

The final mechanical energy(when satelite reaches theEarth) is equal to the initial mechanical energy.          Kf+ Uf = Ki + Ui The falls initially from rest, so that Ki =0 Therefore         Kf = Ui - Uf        0.5mvf2 = Ui - Uf         0.5mvf2= (GMm / Re ) - (GMm /3Re )          vf2 = 2 ( (GM / Re ) -(GM / 3Re ) )               = (4/3)(GM / Re ) Where   G = 6.67 x10-11m3 / kg.s2                M= 5.98 x 1024 kg               Re = 6.37 x 106 m Substitute values.         0.5mvf2= (GMm / Re ) - (GMm /3Re )          vf2 = 2 ( (GM / Re ) -(GM / 3Re ) )               = (4/3)(GM / Re ) Where   G = 6.67 x10-11m3 / kg.s2                M= 5.98 x 1024 kg               Re = 6.37 x 106 m Substitute values.

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