Geostationary satellites
Key idea: A geostationary satellite orbits above the Equator in Earth's rotation direction, with the same period as Earth's rotation. It therefore stays above one ground position.
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Guided lessons · coming soon
Guided lesson
Guided steps
- Read why all four orbit conditions are needed.
- Explain why the matching period is not enough.
- Check the proposed orbit one condition at a time.
- Use the latitude observations to find what must change.
- Explain why a westward orbit moves across the sky.
- Connect the fixed period with the fixed orbital radius.
- Follow the orbital radius, height and speed calculation.
- Explain why a heavier satellite cannot use a lower orbit.
- Read how a fixed view helps communication and weather monitoring.
- Explain why more longitudes do not give overhead polar images.
- Review orbit conditions and centre-to-surface height.
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ContinueA satellite dish on a roof points at one spot in the sky and never moves, yet the satellite it receives from is travelling at about 3 km s⁻¹. The satellite goes round the Earth at exactly the rate the Earth turns, so from the ground it seems to hang still. Only one orbit can do this.
Conditions for a geostationary orbit
A geostationary satellite stays above the same point on the Equator, so it appears fixed in the sky. It is not at rest: it moves in a circle round the Earth, and gravity provides its centripetal force. To stay above one point, its orbit must meet four conditions.
| Condition | Why it is needed |
|---|---|
| Circular | The radius and angular velocity stay constant. |
| In the plane of the Equator | The satellite does not drift north and south of the Equator. |
| In the same direction as the Earth’s rotation | The satellite and the ground turn the same way, west to east. |
| Period equal to the Earth’s rotation period | The satellite and the ground have the same angular velocity. |
The Earth’s rotation period relative to the stars is 23 h 56 min, a little less than 24 hours, because the length of a day is also affected by the Earth’s motion round the Sun. In calculations, use the period you are given.
The circular orbit is drawn as an ellipse because it is seen in perspective. The sizes of the Earth and the orbit are not to scale.
Check your understanding 1 A polar orbit
A satellite in a polar orbit, passing over both poles, has the same period as the Earth’s rotation. Is it geostationary?
Show answer
No. It passes over different latitudes, so it does not stay above one point. The right period is not enough on its own.
Worked example 1
A 12-hour orbit
Problem
A satellite moves eastwards in a circular orbit in the plane of the Equator, with a period of 12 hours. Does it stay above one point on the ground?
Show full solution
Shape, plane and direction
Method
Check the first three conditions.Reason
Each one is necessary.Working
Answer
The orbit is circular, equatorial and eastwards, so these three are met.
Period
Method
Compare the angular velocities.Reason
The satellite stays above one point only if it turns at the same rate as the ground.Working
Answer
Approximating the Earth’s rotation period as 24 hours, in 12 hours the satellite goes round once while the Earth turns half way. Its angular velocity is twice the Earth’s, so it moves across the sky. It is not geostationary.
Guided practice 2
An orbit inferred from observations
Problem
A satellite moves eastwards in a circular orbit with the same period as the Earth’s rotation. Observations show it passes above the Equator twice per orbit and reaches latitudes of 15° north and 15° south. An engineer proposes changing only its period to make it geostationary. Explain why that cannot fix the problem, and identify what must change.
Test each condition
Hints
Hint 1
latitude
Could any change in timing make this orbital path stay over the Equator?
Show full solution
The failed condition
Method
Infer the orbital plane from the changing latitude.Reason
Changing the period does not change which latitudes the path passes over.Working
Answer
The north–south motion shows that the orbital plane is tilted to the Equator. The plane must change to the equatorial plane; the period already has the required value. Changing only the period would leave the latitude variation, so the satellite would still not remain above one point.
Check your understanding 2 The wrong direction
A satellite moves in a circular equatorial orbit with the same period as the Earth’s rotation, but westwards. Could a fixed dish on the ground stay pointed at it?
Show answer
No. It goes round in the opposite direction to the ground, so its longitude changes relative to the ground. It returns to a given longitude twice per Earth rotation, but it is overhead only for an observer on the Equator. A fixed dish would lose it.
The radius of a geostationary orbit
For a circular orbit, T² = 4π²r³/GM. Fixing the period fixes the radius:
So every geostationary satellite is the same distance from the Earth’s centre, whatever its mass. They can only be spaced out at different longitudes round this one circle.
Worked example 3
The height of a geostationary satellite
Problem
The Earth has mass 5.97 × 10²⁴ kg and radius 6.37 × 10⁶ m, and it rotates once in 8.62 × 10⁴ s. Find the radius of a geostationary orbit, the satellite’s height above the surface and its orbital speed.
Show full solution
Orbital radius
Method
Substitute into r = (GMT²/4π²)^(1/3).Reason
The period must equal the Earth’s rotation period.Working
Answer
r = ((6.67 × 10⁻¹¹ × 5.97 × 10²⁴ × (8.62 × 10⁴)²)/4π²)^(1/3) = 4.22 × 10⁷ m
Height
Method
Subtract the Earth’s radius.Reason
r is measured from the centre.Working
Answer
h = 4.22 × 10⁷-6.37 × 10⁶ = 3.58 × 10⁷ m, about 36 000 km
Speed
Working
Answer
v = (2π r)/T = (2π × 4.22 × 10⁷)/(8.62 × 10⁴) = 3.07 × 10³ m s⁻¹
Quick check
The orbital radius is about 6.6 Earth radii, so the field strength there is only about 1/44 of its surface value.
Check your understanding 3 A heavier satellite
An engineer suggests putting a heavier geostationary satellite in a lower orbit. Explain why this cannot work.
Show answer
The satellite’s mass cancels in GMm/r² = mrω², so the radius depends only on the Earth’s mass and the period. A lower orbit has a shorter period, so the satellite would move across the sky.
Uses of geostationary satellites
Communications. A dish on the ground can point in a fixed direction without tracking the satellite. The satellite relays television and telephone signals between places that can both see it.
Weather monitoring. The satellite looks down on the same large region all the time, so repeated images show how clouds and storms develop.
A geostationary satellite cannot see everything. The Earth blocks its view of the far side, and from the Equator it sees the polar regions only at a very low angle, or not at all. Several satellites are needed to cover all longitudes, and none of them gives a good view of the poles.
Check your understanding 4 Imaging the poles
A company proposes eight geostationary satellites evenly spaced around the Earth. It claims that covering all longitudes will let it take clear overhead images of both poles. Explain the flaw, and suggest an orbital plane that would let a satellite pass directly over both poles.
Show answer
All eight satellites would still be above the Equator. Changing longitude gives different views around the Earth, but does not put any satellite above a pole; the poles remain hidden or viewed at a very low angle. A polar orbital plane would allow direct passes over both poles, although that satellite would move across the sky rather than remain geostationary.
Common mistakes
- Saying a geostationary satellite is not moving. It moves in a circle; it only stays still relative to the ground.
- Giving only one condition, such as the 24-hour period. All four are needed.
- Thinking a satellite’s height depends on its mass. Every geostationary orbit has the same radius.
- Forgetting to subtract the Earth’s radius to find the height above the surface.
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Syllabus and review details
- GCE A-Level H1 Physics 2027 · 2027
8867 Content Overview, PDF pages 8–9; Subject Content, PDF pages 10–18
Last reviewed: