## Orbital Velocity Formula

The speed at which one body revolves around another is known as orbital velocity. Objects in orbit are those that travel in a uniform circular motion around the Earth. The distance between the object and the Earth’s centre determines the orbit’s velocity.

The velocity at which a body revolves around another body is known as orbital velocity. In the fields of astronomy and physics, it is commonly used to launch satellites into orbit and ensure that they remain in orbit. The inertia of the moving body causes it to keep moving in a straight line while the force of gravity pulls it down. As a result, the path traced will be a balance of these two forces, forming an elliptical path.

It relates the mass of a given planet to the gravitational constant and sweeps through the recipe given.

## Formula

Let’s take a closer look at its formula.

The orbital velocity of any rotating object can be calculated using the formula,

Where,

G is the gravitational constant.

M is the mass of the body

R is the orbital radius.

## Transverse Orbital Velocity

Because of the law of conservation of angular momentum, or Kepler’s second law, the transverse orbital velocity is proportional to the distance to the central body. The line from the core to the body sweeps a constant area of the orbital plane as a body moves around its orbit in a fixed amount of time, regardless of which part of its orbit the body marks during that period of time.

## Solved Examples

**Q1. A satellite launch is planned to study Jupiter. Calculate its orbital velocity around Jupiter.**

Jupiter’s radius R = 70.5 106 m, its mass M = 1.5 1027 kg, and its gravitational constant G = 6.67 10^{-11} m^{3}/s^{2} kg are given.

**Solution:** By substituting the orbital velocity formula parameters, we obtain

√GM / R = Vorbit

= √6.673×10^{-11 }× 1.5 ×10^{27} / 70.5×10^{6}

= √10.0095 x 10^{16} / 70.5 x 10^{6}

= √0.141 x 10^{10}

3.754 x 10^{9} m/s.

**Q2. Determine the orbital velocity of the Earth if its radius R = 6.5 106 m, mass M = 5.5 1024 kg, and gravitational constant G = 6.67 10 ^{-11} m^{3}/s^{2} kg.**

**Solution:**

R = 6.5 × 10^{6} m

M = 5.5 × 10^{24} kg

G = 6.6 × 10^{-11} m^{3}/s^{2} kg

The orbital velocity formula is as follows:

√GM / R = Vorbit

= √6.67 ×10^{-11} × 5.5×10^{24} / 6.5 ×10^{6}

= √36.68 x 10^{13 }/ 6.5 x 10^{6}

= 7.5 km/s