Astro-Physics

Orbital Speed Calculator

The physics of staying up. Calculate the exact velocity required for a stable circular orbit at any altitude above the Earths surface.

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The Formula

v = √(GM / r)
G: Gravitational Constant
M: Mass of Earth
r: Radius (Alt + 6,371km)

Satellite Altitudes

LEO (ISS)400 km
MEO (GPS)20,200 km
GEO35,786 km

The Physics of Orbital Velocity

Achieving orbit is not about being "above" the atmosphere—it is about moving sideways so fast that as you fall toward Earth, you miss it. This horizontal velocity is known as Orbital Speed.

How Speed Changes with Altitude

Gravity follows an inverse-square law. The further you are from the center of the Earth, the weaker the gravitational pull. Consequently, satellites at high altitudes (like Geostationary satellites) move much slower than those in Low Earth Orbit (LEO). While the ISS orbits every 90 minutes, a GPS satellite takes about 12 hours, and a GEO satellite takes exactly 24 hours.

Circular Orbit Formula

For a perfect circular orbit, the centripetal force required to keep the satellite in its path must exactly equal the gravitational force exerted by the central body. The formula is:

v = sqrt(G * M / r)

Where G is the gravitational constant ($6.674 \times 10^{-11} m^3 kg^{-1} s^{-2}$), M is the mass of the planet, and r is the distance from the center of the planet (Altitude + Planetary Radius).

Orbital Benchmarks Table

Orbit Type Altitude Required Speed
Low Earth (LEO) 200 - 2,000 km 7.8 - 6.9 km/s
Medium Earth (MEO) ~20,000 km ~3.9 km/s
Geostationary (GEO) 35,786 km 3.07 km/s

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Frequently Asked Questions

What is the speed of the International Space Station (ISS)?

The ISS orbits Earth at an average altitude of 400 km with an orbital speed of approximately 7.66 km/s (roughly 27,600 km/h).

Does orbital speed depend on the mass of the satellite?

No. For a circular orbit, the speed depends only on the mass of the central body (like Earth) and the distance from the center. A feather and a space station would orbit at the same speed if neglected air resistance.

What happens if a satellite slows down?

If a satellite slows down, Earths gravity pulls it into a lower, elliptical orbit. If it slows down too much, it will re-enter the atmosphere.