# 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.

As we learnt in

Orbital velocity when satellite is close to earth -

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

$V=\sqrt{9.8\times 6.4\times 10^{6}}$

$=7.9Km/s\; \simeq 8Km/s$

$V\rightarrow$ Orbital velocity

$g\rightarrow9.8M/s^{2}$

$R\rightarrow$ 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.

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.

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