Printable worksheet · Ages 16 to 18 · about 30 minutes
How high is a geostationary orbit?
A one-page worksheet: derive the height of a geostationary orbit from Newton's law of gravitation, then check it against a TV satellite's live height and period.
Numbers
Today's numbers come from the Satellite directory, captured when this page loaded: 12:18 UTC on 4 November 2026. Print the class set in one go so every copy matches the teacher notes. Reload for new numbers.The boxes are left blank. Pupils open the Satellite directory and copy in the numbers themselves, so answers vary a little: the teacher notes give the method and the range to accept.Live numbers are not available right now, so the boxes are blank: pupils look them up in the Satellite directory.
Orbital Radar · Space for Schools
Ages 16 to 18 · Gravitational fields
How high is a geostationary orbit?
A geostationary satellite stays above the same point on the equator, so a TV dish can point at it without moving. Work out how high it must be, then check your answer against a real TV satellite, ASTRA 2E.
Name Class Date
Today's numbers from the Satellite directory, 12:18 UTC on 4 November 2026write them in from orbitalradar.com/satellite-directory
ASTRA 2E (a TV satellite): height above the Earth
35,785 km
ASTRA 2E: time for one orbit
1,436.1 minutes
In the Satellite directory, find ASTRA 2E by its number (39285) and copy its height and period.
G = 6.67 × 10−11 N m2 kg−2 · Mass of the Earth M = 5.97 × 1024 kg · Radius of the Earth = 6.371 × 106 m · One sidereal day = 23 h 56 min 4 s = 86,164 s
A geostationary satellite goes round once every sidereal day (86,164 s), not every 24 hours. Explain why.[2]
Gravity provides the centripetal force. Show that r3 = GMT2 / 4π2, where r is the radius of the orbit.[2]
Calculate the radius of a geostationary orbit, and its height above the Earth's surface.[3]
Compare your height with ASTRA 2E's height today. Give the difference as a percentage.[2]
Calculate the speed of a satellite in geostationary orbit.[2]
Explain why every geostationary satellite must orbit above the equator.[2]
Extension A TV signal goes up to the satellite and straight back down. Estimate the shortest time this takes. (Speed of light = 3.00 × 108 m/s) [2]
Show your working on the back of this sheet.
Teacher notes and answersNot on the pupil sheet. Printed only with "Print with answers".
Teacher notes: How high is a geostationary orbit?
ASTRA 2E on today's sheet: 35,785 km high, one orbit in 1,436.1 minutes (12:18 UTC on 4 November 2026).
Pupils looked up ASTRA 2E themselves: its height is about 35,780 km and its period about 1,436 minutes.
Total 13 points, plus 2 for the extension.
Answers
A sidereal day is one turn of the Earth measured against the stars. The 24-hour solar day is about 4 minutes longer, because the Earth also moves along its orbit round the Sun and has to turn a little further to bring the Sun back to the same place. To stay over one point, the satellite must match the Earth's turn against the stars.
GMm / r2 = mω2r with ω = 2π / T, so GM / r2 = 4π2r / T2 and r3 = GMT2 / 4π2.
r3 = (6.67 × 10−11 × 5.97 × 1024 × 86,1642) / 4π2, so r = 4.21 × 107 m (about 42,150 km). Height = r − 6.371 × 106 m = 3.58 × 107 m (about 35,780 km). Accept 3.57 to 3.59 × 107 m.
The difference should be well under 1% (today ASTRA 2E is at 35,785 km). The directory lists each satellite's lowest height, and ASTRA 2E's orbit is very nearly a circle, so it is within a few kilometres of its average height.
v = 2πr / T = 2π × 4.215 × 107 / 86,164 = 3.07 × 103 m/s (about 3.1 km/s).
Gravity pulls towards the centre of the Earth, so every orbit is in a plane through the centre. Only an orbit in the plane of the equator keeps the satellite over the same point; any tilted orbit would carry it north and south of the equator each day.
Extension: 2 × 3.58 × 107 ÷ 3.00 × 108 = 0.24 s. From most places the satellite is lower in the sky and further away, so it takes a little longer: about a quarter of a second.
Watch for
Using 24 hours (86,400 s): it gives a height about 80 km too high.
Forgetting to take away the Earth's radius: r is measured from the centre of the Earth.
Curriculum
England: A level Physics, gravitational fields (geostationary orbits come from exam board specifications: check yours). Scotland: Higher Physics, Gravitation. Wales: WJEC GCSE Physics 1.5(l), Integrated Science 2.2.3 and The Sciences 3.4.3 (why a geostationary satellite stays above one spot); the calculation is A level.
How these worksheets work
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Orbital Radar · Space for Schools