Question

Two artificial satellites, one close to the surface and the other away are revolving around the earth, which one has larger speed?

Answer 1

Hint: For a satellite revolving around a massive body, gravitational force results in the generation of centripetal force due to which the satellite acquires a constant speed for a particular value of its distance from the center of the massive body. We will use the formula of orbital velocity to compare the speed of the two satellites.

Complete step by step answer:
A satellite is any object that is orbiting around the earth, sun or other massive body. A satellite is basically a projectile. We can say that a satellite is an object upon which the only force acting is the force of gravity. Once launched into the orbit, the only force which governs the motion of a satellite is the gravitational force.
The motion of an orbiting satellite can be described as by the same motion characteristics as any object in circular motion. The velocity of the satellite is directed tangent to the circular orbit at every point along its path. The acceleration of the satellite would be directed towards the center of the circle, meaning towards the central body around which satellite is orbiting. The centripetal force is supplied by the force of gravity.

Orbital velocity is the velocity at which a body revolves around another body. The objects which travel in uniform circular motion around the earth are called in orbit. The velocity by which a satellite revolves around the earth is orbital velocity. The value of orbital velocity depends upon the distance between the object and the center of the earth.
Expression for orbital velocity is given as,
${{v}_{O}}=\sqrt{\dfrac{Gm}{R+h}}$
Where,
$G$ is the gravitational constant
$m$ is the mass of the body at center
$R$ is the radius of the earth
$h$ is the height of the satellite above the surface of earth
It means that, $R+h$ is the radius of orbit of satellite
As the value of $h$ increases, the value of orbital velocity decreases. It means that the satellite revolving close to the surface of the central body has a greater speed while the one revolving at a larger distance from the surface of the central body will have a less speed.
Hence, the satellite revolving close to the surface of earth has a greater speed.

Note:
The orbital velocity of a satellite is the minimum velocity required to place or maintain a satellite in a given orbit. The value of orbital velocity does not depend upon the mass of the satellite; rather it depends upon the mass of the body at center.