Created By : awnish

Reviewed By : Phani Ponnapalli

Last Updated : Apr 10, 2023

Make use of the free Orbital Velocity Calculator tool to find the orbital speed of a satellite, eccentricity, and other orbital parameters. This calculator takes semi-major axis, semi minor axis, start mass, satellite mass, period and distane details to give the eccentricity, orbital energy, radius, and speed of the planets easily.

Choose a Calculation:
Semi-major axis
Semi-minor axis

Choose a Calculation:
standard gravitational parameter (μ)
Semi-major axis (a)

Choose a Calculation:
standard gravitational parameter (μ)
Semi-major axis (a)
r

### How to Calculate Orbital Velocity?

Have a look at the steps to calculate the orbital velocity of a satellite effortlessly.

• Obtain the required orbital parameters from the question.
• Divide 2 by the distance between the satellite and satellite.
• Get inverse of the semi-major axis of the elliptical orbit and subtract one from another.
• Multiply the result by the gravitational parameter.
• Apply square root to the result to check the orbital speed.

### Orbital Velocity Formula | What is Elliptical Orbit?

The elliptical orbit is a Kepler orbit with an eccentricity between one and zero. The parameters are the semi-major axis and semi-minor axis. The eccentricity characterizes the shape of the orbit.

Its formula is e = √(1 - b²/a²)

Where,

e is the eccentricity

a is the semi-major axis

b is the semi-minor axis

Periapsis: It is the lowest possible distance between the satellite (planet) and a star.

Apoapsis: It is the highest possible distance between the satellite and a star.

This periapsis and apoapsis can be calculated after knowing the semi-major axis, semi-minor axis details

ra + rp = 2a and ra x rp = b2

Where,

ra is the apoapsis

rp is the periapsis

Vis-viva Equation or Orbital Velocity Equation:

This Vis-viva equation is used to determine the speed of a satellite in an elliptical orbit and periapsis and apoapsis. The formula of orbital velocity is as follows:

v² = μ(2/r - 1/a)

Where,

v is the relative satellite speed

μ is the standard gravitational parameter μ = G(M + m)

G is the gravitational constant and it is 6.674 x 10-11 N-m²/kg²

M is the mass of the star

m is the mass of the satellite

r is the distance between the star and the satellite

a is the semi-major axis of the elliptical orbit

### Kepler Laws | Orbital Radius of Earth

The Kepler laws of planetary motion are helpful to find the orbital period of a satellite.

Kepler First Law: Every planet of the solar system moves around the sun in an elliptical orbit.

Kepler Second Law: At equal intervals, a line segment between a planet and sun sweeps the equal areas.

Kepler Third Law: Obtain the orbital period by comparing the gravitational force and centripetal force.

T² = 4π²a³/μ

Planet Data Table:

The following are the eccentricity and mass of all the planets.

Planet Semi-major Axis (astronomical units) Eccentricity Earth's masses
Mercury 0.387 0.2056 0.0553
Pluto 39.482 0.2488 0.0021
Earth 1 0.0167 1
Saturn 9.537 0.0542 95.159
Mars 1.524 0.0934 0.107
Jupiter 5.203 0.0484 317.83
Venus 0.723 0.0068 0.815
Uranus 19.191 0.0472 14.536
Neptune 30.069 0.0086 17.147

Example

Question: A satellite launch is made for the study of Jupitar. Find its velocity so that its orbit around the Jupitar.

Solution:

Given that

Radius of the Jupitar R = 70.5 x 106 m

Mass of the jupitar M = 1.5 x 1027 kg

Vorbit = √(GM/R)

= √(6.67408 x 10-11 x 105 x 1027 / 70.5 x 106)

= √(10.0095 x 1016/70.5 x 106)

= 3.75 x 104 m/s

Therefore, the orbital velocity of satellite is 3.75 x 104 m/s.

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### Frequently Asked Questions on Orbital Velocity Calculator

1. What is the orbital velocity and its formula?

The orbital velocity is the velocity at which a body revolves around the other body. Objects that revolve in the uniform circular motion around the earth are called to be in orbit. The orbital velocity formula is Vorbit = √(GM/R). Here G is the gravitational constant, m is the mass of the body at the centre and r is the radius of the orbit.

2. How to calculate the orbital velocity?

The orbital velocity of an object can be calculated by multiplying the gravitational constant with the mass and dividing it by the radius. The square root of the result is the orbital velocity.

3. Is escape velocity greater than orbital velocity?

The escape velocity is always greater than the orbital velocity. Because the escape velocity formula has 2 times the object and orbital velocity has one time mass of the object.

4. What is the orbital velocity of earth and satellite?

Earth orbital velocity is 29.78 km/s. The orbital velocity of a satellite is 17,000 meters per hour.