Obtain the expression for the orbital speed of a satellite revolving around the earth at a height h from its surface
Answers
Answer:
Consider a satellite of mass m revolving round the Earth at a, height 'h' above the surface of the Earth.
Let M be the mass and R be the radius of the Earth.
The satellite is moving with velocity V and the radius of the circular orbit is r=R+h. Centripetal force = Gravitational force
∴
r
Mv
c
2
=
r
2
GMm
∴v
c
2
=
r
GM
∴v
c
=
R+h
GM
This is the expression for critical velocity of a satellite moving in a circular orbit around the Earth,
We know that,
g
h
=
(R+h)
2
GM
GM=g
h
(R+h)
2
Substituting in equation (1), we get
∴v
c
=
R+h
g
h
(R+h)
2
∴v
c
=
g
h
(R+h)
where g
h
is the acceleration due to gravity at a height above the surface of the Earth.
Consider a satellite of mass m revolving round the Earth at a, height 'h' above the surface of the Earth.
Let M be the mass and R be the radius of the Earth.
The satellite is moving with velocity V and the radius of the circular orbit is r=R+h. Centripetal force = Gravitational force
∴
r
Mv
c
2
=
r
2
GMm
∴v
c
2
=
r
GM
∴v
c
=
R+h
GM
This is the expression for critical velocity of a satellite moving in a circular orbit around the Earth,
We know that,
g
h
=
(R+h)
2
GM
GM=g
h
(R+h)
2
Substituting in equation (1), we get
∴v
c
=
R+h
g
h
(R+h)
2
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∴v
c
=
g
h
(R+h)
where g
h
is the acceleration due to gravity at a height above the surface of the Earth.