# Orbital Velocity Calculator (v = √GM/r)

Calculate orbital velocity with v = sqrt(GM/r). Find the speed for circular orbits around Earth, Mars, Jupiter, or any body. Includes orbital period.

## What this calculates

Orbital velocity is the speed a satellite or spacecraft needs to stay in a stable circular orbit around a planet, moon, or star. The International Space Station travels at about 7,660 m/s (27,600 km/h) at 400 km altitude. This calculator finds that speed for any body and altitude, plus the time to complete one orbit.

## Inputs

- **Central Body** — options: Earth (5.972 × 10²⁴ kg), Moon (7.342 × 10²² kg), Mars (6.417 × 10²³ kg), Jupiter (1.898 × 10²⁷ kg), Sun (1.989 × 10³⁰ kg), Custom mass
- **Custom Body Mass** (kg) — min 0 — Only used when Central Body is set to Custom
- **Distance Input** — options: Altitude above surface, Orbital radius from center
- **Distance** (km) — min 0 — ISS orbits at about 400 km altitude

## Outputs

- **Orbital Velocity** (m/s) — Speed needed for a circular orbit
- **Orbital Velocity** (km/s) — Orbital velocity in km/s
- **Orbital Period** (min) — Time for one complete orbit
- **Orbital Period** (hours) — Time for one complete orbit in hours
- **Orbital Radius** (km) — Distance from center of central body

## Details

## The Orbital Velocity Formula

For a circular orbit: **v = sqrt(GM / r)**, where G is the gravitational constant (6.674 x 10 to the negative 11), M is the central body's mass, and r is the orbital radius measured from the body's center.

### Altitude vs. Orbital Radius

If you know the altitude above the surface, the calculator adds the body's radius to get the orbital radius: **r = R_body + altitude**. For the ISS at 400 km altitude above Earth (radius 6,371 km), the orbital radius is 6,771 km.

### Orbital Period

Once you have velocity, the period is: **T = 2 pi r / v**. The ISS completes one orbit in about 92 minutes, seeing 16 sunrises every day.

### Key Orbits Around Earth

| Orbit Type | Altitude | Velocity | Period |
|-----------|----------|----------|--------|
| Low Earth (ISS) | 400 km | 7,670 m/s | 92 min |
| GPS satellites | 20,200 km | 3,870 m/s | 12 hours |
| Geostationary | 35,786 km | 3,070 m/s | 24 hours |

### Why Higher Orbits Are Slower

It seems counterintuitive, but satellites farther from Earth orbit more slowly. The gravitational pull weakens with distance, so less speed is needed to balance it. Geostationary satellites at 35,786 km orbit at just 3,070 m/s, compared to 7,670 m/s for the ISS.

## Frequently Asked Questions

**Q: What is the difference between orbital velocity and escape velocity?**

A: Orbital velocity keeps you in a circular orbit, while escape velocity lets you leave the body's gravitational pull entirely. Escape velocity is exactly sqrt(2) times the orbital velocity at the same distance. For low Earth orbit, orbital velocity is about 7,670 m/s and escape velocity is about 11,200 m/s.

**Q: Why does the ISS not fall to Earth?**

A: The ISS is constantly falling toward Earth, but it moves sideways fast enough that the Earth's surface curves away beneath it at the same rate. At 7,670 m/s, it falls about 4.9 meters every second while covering 7,670 meters horizontally, perfectly matching Earth's curvature. That balance is what an orbit is.

**Q: What is geostationary orbit?**

A: Geostationary orbit is at 35,786 km altitude, where the orbital period matches Earth's 24-hour rotation. A satellite there appears to hover over the same spot on the equator. Communication and weather satellites use this orbit because ground antennas can point at a fixed location in the sky.

**Q: Can I calculate orbits around other planets?**

A: Yes. Select the central body from the dropdown or enter a custom mass. Mars orbital velocity at 200 km altitude is about 3,450 m/s. Jupiter's enormous mass means orbital velocities are much higher, around 42,000 m/s at low orbit. The formula works for any mass, including stars.

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Source: https://vastcalc.com/calculators/physics/orbital-velocity
Category: Physics
Last updated: 2026-04-08