A satellite S is moving in an elliptical orbit around the earth. The mass of the satellite is very small compared to the mass of the earth. Then,

  • Option 1)

    the total mechanical energy of S varies periodically with time.

  • Option 2)

    the linear momentum of S remains constant in magnitude.

  • Option 3)

    the acceleration of S is always directed towards the centre of the earth.

  • Option 4)

    the angular momentum of S about the centre of the earth changes in direction, but its magnitude remains constant.

 

Answers (1)

As we learnt in

Orbital velocity when satellite is close to earth -

V=sqrt{frac{GM}{R}}=sqrt{gR}

V=sqrt{9.8	imes 6.4	imes 10^{6}}

=7.9Km/s; simeq 8Km/s

V
ightarrow Orbital velocity

g
ightarrow9.8M/s^{2}

R
ightarrow Radius of Earth 

- wherein

As  h=0 and  GM=gR^{2}

 

 

 

The motion of satellite is due to force applied by the earth on satellite and hence its acceleration is always towards centre of the earth . Angular momentum and total energy of satellite is conserved. Linear momentum is not constant.


Option 1)

the total mechanical energy of S varies periodically with time.

This is incorrect answer

Option 2)

the linear momentum of S remains constant in magnitude.

This is incorrect answer

Option 3)

the acceleration of S is always directed towards the centre of the earth.

This is correct answer

Option 4)

the angular momentum of S about the centre of the earth changes in direction, but its magnitude remains constant.

This is incorrect answer

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