Chapter 14, Problem 24A

A satellite can orbit at 5 km above the moon, but not at 5 km above Earth. Why?

To determine

To Explain: A satellite can orbit around 5 km above the moon but not 5 km above the earth.

Explanation of Solution

Introduction:

Satellite is the body in space which can revolve around the planet. Satellite may be natural or artificial. Around 2218 artificial satellite are orbiting around earth. Moon is the only natural satellite which moves around the earth.The satellite remains in its orbit because of the gravitational force due to planetwhich acts on it.

Momentum of rocket gained by the satellite keeps satellite in motion. When satellite moves over thousands of miles, force due to gravity still acts on it. When satellite moves in an orbit, gravity pulls it towards its center. The momentum of the satellite keepsit in motion. So, when satellite move in stationary orbit around the planet, the force due to gravity balances the momentum of the satellite. If the momentum of the satellite encounters the force due to gravity, satellite follow the straight-line path.

Orbital velocity of the satellite depends upon the distance of the satellite from the planet. Less be the distance; more be the velocity and vice-versa. The value of the acceleration to gravity decides the distance over which satellite can safely orbit. The acceleration due to gravity for earth and moon is $9.8{\text{ m/s}}^{\text{2}}$ and $1.625{\text{ m/s}}^{\text{2}}$ respectively. Gravitational pull of the earth is more than the moon’s gravitational pull. Satellite requires more orbital velocity to move around the earth. Since due to the atmosphere around the earth, air resistance opposes the motion of the satellite. Due to very low gravitational field of moon, there is no atmosphere around the moon. For moving the satellite around the moon,there is noair drag due to absence of atmosphere. So, satellite can be move safely around the moon 5 km above. Since most of the earth’s atmosphere is up to 16 km from the earth, a satellite cannot orbit around the earth 5 km above.

Conclusion:

Therefore, due to earth’s strong gravitational pull as well as presence atmosphere around the earth, satellite cannot orbit around earth 5 km above.