### Orbital Velocity Calculator:

Orbital speed of a body is the speed with which it moves around another body. Objects moving around the earth in uniform circular motion are said to be in an orbit. The speed of this orbit depends on the distance between the object and the center of the Earth.

This speed is usually associated with artificial satellites because they can orbit any particular planet. The orbital velocity formula is used to calculate the orbital velocity of an object if its mass and radius are known. The velocity required to achieve balance between the gravitational force of the body and the inertia of motion of the body is called orbital velocity. The speed of a satellite’s orbit around the Earth is determined by its height above the Earth. The faster the orbital speed required, the closer to Earth it is.

For example, If the muzzle velocity of a cannon fired from a hilltop increases, the projectile will travel further. If the velocity is high enough the bullet will never hit the ground.

The Earth’s surface can be imagined bending away from the projectile or satellite at the same rate as it falls toward it.

The greater the orbital velocity for a given height or distance, the greater the body’s center of gravity. If air resistance near the Earth’s surface can be neglected, the orbital speed is about eight kilometers (five miles) per second.

The weaker the gravitational force, the farther a satellite is from the center of gravity, the lower the speed it must orbit. See also Definition of escape velocity.

### Orbital Velocity Formula:

Orbital velocity formula is V_{orbit (km/s)} in kilometer per second is equal to the root of the gravitational constant √G_{(m3 kg-1 s-1) }in meter^{3} per kilogram^{-1} per second^{-1} and multiply the mass of the body at centre M_{(kg)} in kilogram and divided by the radius of the rabit R_{(m)} in meter.Hence the orbital velocity formula can be written as

V_{orbit (km/s)} =√G_{(m3 kg-1 s-1)} *M_{(kg)} /R_{(m)}

It is given by where

G = gravitational constant in m^{3} kg^{-1} s^{-2}

M= mss of the body at centre in kg

R= radius of the orbit in m

### Example:1

Calculate the orbital velocity of the earth so that the satellite revolves around the earth if the radius of earth R =8.9 *10^{6}m, the mass of the earth M =6.9872*10^{24} kg and gravitational constant G =6.67408 *10^{-11}m^{3} kg^{-1}s^{-2}

### Answer:

R =8.9 *10^{6}m

M =6.9872*10^{24} kg

G =6.67408 *10^{-11}m^{3} kg^{-1}s^{-2}

The orbital velocity formula is given by

V_{orbit } =√G *M /R

_{=}√6.67408 *10^{-11} *6.9872*10^{24} /8.9 *10^{6}

=21594705 /8.9 *10^{6}

=2.42637 *10^{12} km/s

### Example:2

Calculate the orbital velocity of the earth so that the satellite revolves around the earth if the radius of earth R =12.4 *10^{6}m, the mass of the earth M =342*10^{24} kg and gravitational constant G =6.67408 *10^{-11}m^{3} kg^{-1}s^{-2}

### Answer:

R =12.4 *10^{6}m

M =3.42*10^{24} kg

G =6.67408 *10^{-11}m^{3} kg^{-1}s^{-2}

The orbital velocity formula is given by

V_{orbit } =√G *M /R

_{=}√6.67408 *10^{-11} *3.42*10^{24} /12.4 *10^{6}

=151080 /12.4 *10^{6}

=1.218392*10^{12} km/s