A satellite is revolving round the earth in circular orbit...

A satellite is revolving round the earth in circular orbit at some height above surface of earth. It takes $5.26 \times 10^{3}$ seconds to complete a revolution while its centripetal acceleration is $9.92 \mathrm{~m} / \mathrm{s}^{2}$. Height of satellite above surface of earth is (Radius of earth $6.37 \times 10^{6} \mathrm{~m}$ ) (a) $70 \mathrm{~km}$ (b) $120 \mathrm{~km}$ (c) $170 \mathrm{~km}$ (d) $220 \mathrm{~km}$

A satellite is revolving round the earth in circular orbit at some height above surface of earth. It takes $5.26 \times 10^{3}$ seconds to complete a revolution while its centripetal acceleration is $9.92 \mathrm{~m} / \mathrm{s}^{2}$. Height of satellite above surface of earth is (Radius of earth $6.37 \times 10^{6} \mathrm{~m}$ )
(a) $70 \mathrm{~km}$
(b) $120 \mathrm{~km}$
(c) $170 \mathrm{~km}$
(d) $220 \mathrm{~km}$

Key Concepts

Circular Orbit

A circular orbit is one in which an object moves along a circular path around a central body. In such orbits, the centripetal force required to keep the object in motion is provided entirely by the gravitational attraction of the central body, establishing a balance between gravitational force and the centripetal force.

Centripetal Acceleration

Centripetal acceleration is the acceleration that keeps an object moving in a circular path, always directed toward the center of the circle. In orbital mechanics, this acceleration is attributed to the gravitational pull acting on the satellite, and it is crucial for determining the orbital radius and velocity of the satellite.

Orbital Period

The orbital period is the amount of time a satellite takes to make one complete revolution around Earth. It is fundamentally connected to the size of the orbit and the speed of the satellite, and by using it in conjunction with the centripetal acceleration, one can derive the orbital radius necessary to maintain that period.

Newton’s Law of Universal Gravitation

Newton's law of universal gravitation describes the attractive force between any two masses. In the context of satellites, this law explains how Earth's mass exerts a gravitational force that acts as the centripetal force, thereby keeping the satellite in a stable orbit.

Determination of Satellite Height

The process of determining satellite height involves calculating the orbital radius from known values like centripetal acceleration and orbital period. Once the orbital radius is obtained, subtracting Earth’s radius yields the altitude of the satellite above Earth's surface.

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