Orbital Velocity Calculator

Understanding Orbital Velocity Calculator

Orbital velocity is the speed needed to maintain a circular orbit. The ISS orbits at about 7.66 km/s at ~400 km altitude.

How to use this calculator

1. Enter the mass of the central body, usually written as \(M\).
2. Enter the orbital radius, \(r\), measured from the center of the body to the orbiting object.
3. Use the gravitational constant \(G\) if your calculator asks for it, or leave it at the default value.
4. Read the result as the circular orbital speed, \(v_o\), for that orbit.

The formula explained

The formula \(v_o = \sqrt{\frac{GM}{r}}\) computes the speed needed for a circular orbit. It shows that orbital speed increases with a larger central mass and decreases when the orbit is farther away.

• \(v_o\) = orbital velocity, the speed needed for a circular orbit
• G = gravitational constant, about \(6.674 \times 10^{-11}\,\text{N}\cdot\text{m}^2/\text{kg}^2\)
• M = mass of the central body
• r = orbital radius, the distance from the center of the central body to the orbiting object

Step by step method

1. Identify the mass \(M\) of the body being orbited and the orbital radius \(r\).
2. Substitute the values into \(v_o = \sqrt{\frac{GM}{r}}\).
3. Multiply \(G\) and \(M\), then divide by \(r\).
4. Take the square root of the result to get the orbital velocity.

Worked example

Problem. Find the orbital velocity of a satellite in a circular orbit around Earth at a radius of \(7.0 \times 10^6\,\text{m}\) from Earth's center. Use \(M = 5.97 \times 10^{24}\,\text{kg}\) and \(G = 6.674 \times 10^{-11}\,\text{N}\cdot\text{m}^2/\text{kg}^2\).

1. Substitute the values: \(v_o = \sqrt{\frac{(6.674 \times 10^{-11})(5.97 \times 10^{24})}{7.0 \times 10^6}}\).
2. Compute the value inside the square root, which is about \(5.69 \times 10^7\).
3. Take the square root: \(v_o \approx 7.55 \times 10^3\,\text{m/s}\).

Tips and common mistakes

• Make sure \(r\) is measured from the center of the planet or star, not from the surface.
• This formula is for circular orbits only, so it does not apply directly to elliptical orbits.

Frequently asked questions