Orbital periods of real spacecraft

Here is the same formula applied to objects you can follow live on SpaceTracker.live. The altitudes are typical, rounded values for a circular orbit, so real periods differ by a minute or so as orbits change. Click any name to see where that spacecraft is right now.

Object

Altitude

Orbital period

Orbits per day

Tiangong space station

390 km

92.4 min

15.59

International Space Station

420 km

93.0 min

15.49

Typical Starlink satellite

480 km

94.2 min

15.29

Hubble Space Telescope

510 km

94.8 min

15.19

Polar weather satellite (NOAA-type)

830 km

101.5 min

14.19

OneWeb satellite

1,200 km

109.4 min

13.16

GPS satellite

20,200 km

11.98 h

2.00

Geostationary orbit (GOES, TV satellites)

35,786 km

23.93 h

1.00

The Moon (average distance)

378,022 km

27.45 days

0.04

Three patterns stand out. First, everything in low Earth orbit, from Tiangong to OneWeb, circles the planet in roughly 90 to 110 minutes, which is why the ISS crew sees about 16 sunrises a day. Second, the period grows much faster than the altitude: GPS satellites are about 50 times higher than the ISS, yet their 12-hour period is only eight times longer, because the period scales with the orbit radius to the power 1.5. Third, at 35,786 km the period matches one sidereal day (23 h 56 min), so a satellite there keeps pace with Earth’s rotation and appears fixed in the sky. That is the geostationary belt used by GOES weather satellites and satellite TV.

The Moon is a useful check on the formula: using its average distance, Kepler’s law gives about 27.4 days, close to the observed sidereal month of 27.3 days. The small difference comes from the Moon’s mass, which the simple formula ignores, and from the Sun’s pull on its orbit. For satellites, the opposite effect matters: at low altitude, drag from the thin upper atmosphere slowly lowers the orbit, making the period a little shorter over time until the spacecraft re-boosts or re-enters.

How the Orbital Period Calculator works

Orbital period links the size of an orbit to the time required to complete it. Kepler’s third-law relation is one of the most useful first checks in orbital mechanics. The core relationship used here is T = 2π × √(a³ / μ), where a is semi-major axis from the central body’s centre. If you are building a complete observing or imaging setup, use the Orbital Velocity Calculator alongside this page rather than treating one number in isolation.

Figure: Kepler orbit scale (variables: central body, semi-major axis and orbital period).

Worked example and interpretation

A semi-major axis near 42,164 km around Earth gives a period close to a sidereal day, the scale used by geosynchronous orbits.

For broader physical context, the NASA/JPL Solar System Dynamics is a useful external reference.

Figure: Altitude versus radius (variables: surface, altitude and radius from centre).

When this calculator is useful

Use it to compare LEO, MEO, geosynchronous and planetary orbit scales and to understand how strongly period grows with orbital size.

When the result involves angular size, field, observing conditions or a current target, continue with Escape Velocity Calculator. For a different but related perspective, Satellite Directory can connect the formula to an actual observing, telescope or Solar System context.

Diagrams

Figure: Period growth (variables: low orbit, medium orbit and high orbit).

Assumptions, accuracy and practical limits

This is a two-body estimate. Earth oblateness, atmospheric drag, the Moon, Sun, resonances and maneuvers can shift a real orbit.

A second external cross-check is available from NASA Solar System. Not for operational or published work.

Reference table: circular orbit periods around Earth

T = 2π √(a³ ÷ μ) with μ = 398,600.4418 km³/s²
Orbit	Semi-major axis	Period
International Space Station (≈400 km)	6,771 km	92.4 min
Sun-synchronous (≈800 km)	7,171 km	100.7 min
GPS (≈20,200 km)	26,560 km	11.97 h
Geosynchronous	42,164 km	23.93 h
Moon	384,400 km	27.45 days

Notice that a ≈ 42,164 km gives almost exactly one sidereal day, which is why geostationary satellites seem to hang above one point on the equator.

Related SpaceTracker.live tools

Continue with Orbital Velocity Calculator, Escape Velocity Calculator and Satellite Directory.

Worked scenarios: using Kepler’s third law

Doubling the semi-major axis multiplies the period by 2^1.5 ≈ 2.83. A satellite at 540 km altitude (semi-major axis 6,911 km) has a period of 95.3 minutes, close to the Hubble Space Telescope’s orbit.

To get a 90-minute orbit you need a semi-major axis of about 6,653 km, which is an altitude near 282 km. A satellite whose period is exactly one sidereal day (86,164 s) needs a = 42,164 km, the geostationary radius.

Common mistakes and period lookup

Using altitude instead of semi-major axis. Add Earth’s radius (6,371 km) to the altitude.
Mixing units. μ is in km³/s², so the radius must be in kilometres, not metres.
Expecting a circle. For an elliptical orbit use the semi-major axis, not the current distance.

Circular-orbit period by altitude (Earth)
Altitude	Period
400 km	92.4 min
550 km	95.5 min
800 km	100.7 min
1,200 km	109.3 min
20,200 km	11.97 h
35,786 km	23.93 h

Frequently asked questions

Does the period depend on the satellite’s mass?

No, as long as it is much lighter than the central body. Only the semi-major axis and the central body’s gravitational parameter matter.

Is semi-major axis the same as altitude?

No. Add the central body’s radius to the altitude for a circular orbit.

Why does the ISS orbit about 16 times a day?

Its period near 92 minutes fits roughly 15.5 times into 24 hours.

Search satellites

Orbital Period Calculator: Kepler’s Third Law