Circular Orbit Velocity Calculator

Calculator Input

Input Mode

Central Mass

Mass Unit

Orbital Radius

Radius or Altitude Unit

Altitude Above Surface

Central Body Radius

Body Radius Unit

Output Distance Unit

Graph Sample Points

Example Data Table

Scenario	Central Mass	Orbital Radius	Velocity	Orbital Period
Low Earth Orbit	5.97219e24 kg	6771 km	7.672 km/s	92.41 min
Geostationary Orbit	5.97219e24 kg	42164 km	3.075 km/s	23.93 h
Low Lunar Orbit	7.34767309e22 kg	1837 km	1.633 km/s	1.96 h
Near Solar Orbit	1.98847e30 kg	149600000 km	29.785 km/s	365.21 days

Formula Used

The circular orbit velocity formula is:

v = √(GM / r)

v = circular orbit velocity
G = gravitational constant
M = mass of the central body
r = orbital radius from the center of mass

Related formulas used in this calculator:

T = 2π √(r³ / GM) for orbital period
a = GM / r² for gravitational acceleration
v_e = √(2GM / r) for escape velocity
ω = v / r for angular velocity
ε = -GM / 2r for specific orbital energy

How to Use This Calculator

Select whether you want to enter total orbital radius or altitude plus body radius.
Enter the central body mass and choose the matching mass unit.
Enter orbital radius directly, or enter altitude and body radius.
Choose your preferred output distance unit.
Set the number of graph sample points if needed.
Press Calculate to display the result above the form.
Review velocity, period, acceleration, and escape velocity outputs.
Use the CSV or PDF buttons to save your results.

About This Circular Orbit Velocity Calculator

A circular orbit velocity calculator helps estimate the speed needed for a stable circular path around a central body. It is useful in physics education, astronomy, aerospace planning, and orbital analysis. By combining central mass and orbital radius, the calculator returns speed, period, acceleration, and related orbital values.

This version supports direct radius entry and altitude-based entry. That makes it easier to model satellites, lunar probes, or objects orbiting stars. Unit conversion options reduce manual work and help compare scenarios clearly. The included chart shows how required speed changes when orbital radius changes around your selected case.

Circular motion is a simplified orbital model, yet it remains very practical. Many near-circular satellite paths use this relationship for quick estimation. The downloadable result tools also help with reporting, teaching, and verification. Use the example table and formula notes to validate your inputs before deeper analysis.

FAQs

1. What does this calculator measure?

It calculates circular orbit velocity from central mass and orbital radius. It also returns period, acceleration, angular velocity, escape velocity, and specific orbital energy for the same orbit.

2. What is orbital radius here?

Orbital radius is the distance from the central body's center to the orbiting object. It is not just altitude unless the body's radius is added first.

3. Can I use altitude instead of radius?

Yes. Choose the altitude mode, enter altitude above the surface, and add the central body radius. The calculator then converts both into total orbital radius.

4. Why is circular velocity lower than escape velocity?

Circular velocity keeps the object bound in a closed orbit. Escape velocity is higher because it gives enough kinetic energy to leave the gravitational field without returning.

5. Is this valid for elliptical orbits?

This tool is designed for circular or near-circular cases. Elliptical orbits need position-dependent analysis because orbital speed changes across the path.

6. Which units can I use?

You can enter mass in kilograms, grams, Earth masses, Moon masses, or solar masses. Distance inputs support meters, kilometers, miles, and feet.

7. What does the Plotly graph show?

The graph plots circular orbit velocity against orbital radius near your selected case. It helps visualize how required orbital speed falls as radius increases.

8. Who can use this calculator?

Students, teachers, researchers, and engineers can use it for quick physics estimates. It is especially useful when comparing orbit scenarios and checking manual calculations.