An artificial satellite is moving in a circular orbit around the earth with a speed equal to half the magnitude of escape velocity from the surface of the earth. R is the radius of the earth and g is acceleration due to gravity at the surface of the earth. (R= 6400 km) A) If the satellite is stopped suddenly in its orbit and allowed to fall freely onto the earth, the speed with which it hits the surface of the earth.
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Answer:
Escape velocity is given by v
es
=
R
2GM
Orbital velocity is given by v
o
=
R+h
GM
According to question, v
o
=
2
v
es
R+h
GM
=
2
1
R
2GM
\
Or R+h=2R
⟹ h=R
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