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Orbital period calculator

Period depends only on the semi-major axis and the mass of what you are orbiting, not on the mass of the satellite.

m3/s2
Orbital period
92.414minutes
≈ Rounded Orbital period
Period
1:32:25
Orbital speed
7672.60
Orbits per day
15.5820
Escape speed at that radius
10 850.69
Orbital radius
6 771 000.0
Angular rate
0.001 133 16 rad/s
Show the working
  1. Gravitational parameter of the primary = 398 600 000 000 000
  2. Radius of the primary = 6371
  3. Orbit altitude = 400
  4. Orbital radius = 6371 * 1000 + 400 * 1000 = 6 771 000
  5. Orbital speed = sqrt(398 600 000 000 000 / 6 771 000) = 7672.6
  6. Period = 2 * pi * sqrt(6 771 000^3 / 398 600 000 000 000) = 5544.86
  7. Orbital period = 5544.86 / 60 = 92.4143
  8. Orbits per day = 5544.86 > 0 ? 86400 / 5544.86 : 0 = 15.582
  9. Escape speed at that radius = 7672.6 * sqrt(2) = 10 850.7
  10. Angular rate = 6 771 000 > 0 ? 7672.6 / 6 771 000 : 0 = 0.001 133 16

Values are shown to six significant figures here; the arithmetic itself runs on exact fractions and is only rounded where a number is printed.

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    The formula

    • T = 2 pi sqrt(a^3 / GM)
    • v = sqrt(GM / a)

    The International Space Station at 400 km orbits in about 92.6 minutes, which this reproduces.

    Geostationary orbit is where the period equals the sidereal day of 23 h 56 m 4 s: 35 786 km above the equator.

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