Orbital Velocity Calculator

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.

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

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.

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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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.