Orbital Velocity

Orbital Velocity

We saw that there are natural satellites moving around the planets. There will be gravitational force between the planet and satellites. Nowadays many artificial satellites are launched into the Earth’s orbit. The first artificial satellite Sputnik was launched in 1956. India launched its first satellite Aryabhatta on April 19, 1975. Artificial satellites are made to revolve in an orbit at a height of few hundred kilometres. At this altitude, the friction due to air is negligible. The satellite is carried by a rocket to the desired height and released horizontally with a high velocity, so that it remains moving in a nearly circular orbit.

The horizontal velocity that has to be imparted to a satellite at the determined height so that it makes a circular orbit around the planet is called orbital velocity.

The orbital velocity of the satellite depends on its altitude above Earth. Nearer the object to the Earth, the faster is the required orbital velocity. At an altitude of 200 kilometres, the required orbital velocity is little more than 27,400 kph. That orbital speed and distance permit the satellite to make one revolution in 24 hours. Since Earth also rotates once in 24 hours, a satellite stays in a fixed position relative to a point on Earth’s surface. Because the satellite stays over the same spot all the time, this kind of orbit is called ‘geostationary’. Orbital velocity can be calculated using the following formula.

G= Gravitational constant (6.673 × 10^–11Nm²kg^-2)

M = Mass of the Earth (5.972 × 10²⁴ kg)

R = Radius of the Earth (6371 km)

h    = Height of the satellite from the surface of the Earth.

Example

Can you calculate the orbital velocity of a satellite orbiting at an altitude of 500 km?

Data: G = 6.673 × 10^–11 SI units;

M = 5.972 × 10²⁴ kg;

R = 6371000 m;

h = 500000 m.

Solution:

v = √ (  [6.67 × 10^–11 × 5.972 × 10²⁴ ] / (6371000 + 500000) )

Ans: v = 7613 ms^-1 or 7.613 kms^-1