A satellite moves in a circular orbit around
the Earth at a speed of 5.7 km/s.
Determine the satellite’s altitude above
the surface of the Earth. Assume the
Earth is a homogeneous sphere of radius
6370 km and mass 5.98 × 1024 kg. The
value of the universal gravitational constant
is 6.67259 × 10−11 N · m2
/kg2
.
Answer in units of km.
1
Expert's answer
2018-12-07T10:06:10-0500
The Newton’s second law states
ma=F
In our case
(mv^2)/(R+h)=G mM/(R+h)^2
So
R+h=GM/v^2
h=GM/v^2 -R=(6.67259 × 〖10〗^(-11)×5.98 × 〖10〗^24)/〖5700〗^2 -6370×〖10〗^3=5.9×〖10〗^6 m=5900 km
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