Physics · Glossary

What is Geostationary orbit?

Also known as: sidereal day

Definition 27.9 High School Physics · Chapter 27 — Satellites and Planetary Motion

A satellite is geostationary when it hangs over one fixed point of the ground. Its orbit must be circular, equatorial, and of period one sidereal day, T=86164sT = 86\,164\,\mathrm{s} (23h23\,\mathrm{h} 56min56\,\mathrm{min} 4s4\,\mathrm{s}): the time the Earth takes to turn once relative to the stars. (The 24h24\,\mathrm{h} day is relative to the Sun, toward which the Earth also advances a degree a day.)

Examples

Example 27.10 (The geostationary altitude)

Kepler’s third law, read backward, dictates the radius: r=(GMT2/4π2)1/3=(3.98×1014×(86164)2/4π2)1/34.22×107mr = \left(GMT^2/4\pi^2\right)^{1/3} = \left(3.98 \times 10^{14} \times (86\,164)^2/4\pi^2\right)^{1/3} \approx 4.22 \times 10^{7}\,\mathrm{m} — an altitude h=rR3.58×107m35800kmh = r - R \approx 3.58 \times 10^{7}\,\mathrm{m} \approx 35\,800\,\mathrm{km}, traveled at v=2πr/T3.1km/sv = 2\pi r/T \approx 3.1\,\mathrm{km}/\mathrm{s}. Every relay that “hangs still” sits on this one circle over the equator — there is no other.

Example 27.11 (The navigation constellation)

Satellite-navigation systems fly some thirty satellites at r2.66×107mr \approx 2.66 \times 10^{7}\,\mathrm{m} (altitude 20200km\approx 20\,200\,\mathrm{km}), where Proposition 27.3 gives T4.32×104sT \approx 4.32 \times 10^{4}\,\mathrm{s}: half a sidereal day, so each satellite retraces its ground track daily. Your receiver compares the arrival times of their clock signals against orbits known to meters.

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