Previous Year Question
An artificial satellite orbiting around the Earth does not fall down. This is so because the attraction of Earth
does not exist at such distance
is neutralised by the attraction of the Moon
provides the necessary speed for its steady motion
provides the necessary acceleration for its motion
Correct Answer: D
Detailed Solution
Earth’s gravitational attraction acts continuously on an artificial satellite. The satellite is actually in continuous free fall towards the Earth, but its sufficient tangential velocity makes it travel around the Earth instead of colliding with it.
Option (d) is correct.
In a circular orbit, a satellite requires centripetal acceleration to continuously change the direction of its motion.
Earth’s gravitational attraction provides this required centripetal acceleration.
Gravitational acceleration:
Centripetal acceleration required for circular motion:
For a stable circular orbit:
This gives the required orbital velocity of the satellite:
Here, M is the mass of the Earth, r is the satellite’s distance from the centre of the Earth and G is the universal gravitational constant.
Examination of the other options
Option (a) is incorrect: Earth’s gravity continues to exist at the satellite’s altitude. It decreases with increasing distance but does not disappear.
Option (b) is incorrect: The Moon’s attraction does not neutralise Earth’s attraction in an ordinary Earth orbit.
Option (c) is incorrect: Earth’s gravity does not provide the satellite’s initial tangential velocity. This velocity is imparted by the launch vehicle. In a circular orbit, gravity mainly changes the direction of velocity and provides centripetal acceleration.
Option (d) is correct: Gravity provides the necessary centripetal acceleration that keeps the satellite moving around the Earth.
Important facts directly related to an orbit
If a satellite’s tangential velocity is much lower than the required orbital velocity, its path may intersect the Earth and it may fall.
If the velocity is sufficient, the curved surface of the Earth falls away beneath the satellite as rapidly as the satellite falls towards it; therefore, the satellite continues orbiting without striking the Earth.
If the velocity reaches the local escape velocity, the satellite can escape Earth’s gravitational binding.
In low Earth orbit, a small amount of drag remains because of the extremely thin atmosphere. It can gradually reduce a satellite’s energy and altitude; therefore, some satellites require orbital corrections or reboosts.