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Geostationary Orbits (AQA A Level Physics): Revision Note

Exam code: 7408

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Katie M

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Synchronous Orbits

  • A synchronous orbit is:

An orbit in which the orbital period of the satellite is equal to the rotational period (or length of day) of the planet or body it is orbiting

  • The following characteristics are implied:

    • Equal Period

      • The time taken for the satellite to complete one full orbit is exactly the same as the time taken for the planet to rotate once on its axis

    • Same Angular Speed

      • The satellite has the same angular speed (or angular velocity) as the planet it is orbiting

  • Synchronous orbits usually refer to satellites (the orbiting body) around planets (the body being orbited)

  • A synchronous orbit can be in any plane and at any longitude

    • It does not have to be above the equator or above a fixed point on the surface

Geosynchronous Orbits

  • A geosynchronous orbit is an Earth-centred synchronous orbit

    • The orbital period is 24 hours (matching Earth's rotation)

    • They may have inclined orbits

    • They may have slightly elliptical orbits

    • The object in orbit does not stay above one fixed point on the Earth's surface

Geostationary Orbits

Geostationary Orbit

  • A geostationary orbit is a specific type of geosynchronous orbit around the Earth

  • A geostationary orbit must meet the following criteria:

    • The orbital period is 24 hours (matching Earth's rotation)

    • The orbit must be in the plane of the equator

    • The object in orbit does stay above one fixed point on the Earth's surface

  • Geostationary satellites are used for telecommunication transmissions (e.g. radio) and television broadcasts

  • A base station on Earth sends the TV signal up to the satellite, where it is amplified and broadcast back to the ground to the desired locations

  • The satellite receiver dishes on the surface must point towards the same point in the sky

    • Since the geostationary orbits of the satellites are fixed, the receiver dishes can be fixed too

Low Orbits

  • Some satellites are in low orbits, which means their altitude is closer to the Earth's surface

  • One example of this is a polar orbit, where the satellite orbits around the north and south poles of the Earth

  • Low orbits are useful for taking high-quality photographs of the Earth's surface. This could be used for:

    • Weather

    • Military applications

Geostationary orbit satellite, downloadable AS & A Level Physics revision notes

Geostationary satellite in orbit

Worked Example

The table gives data for two types of satellite, a low-Earth orbit (LEO) and a geostationary orbit

Orbit type

T / min

h / km

LEO

89

250

Geostationary

X

Y

For the geostationary orbit, calculate

(i) the orbital period X in minutes.

(ii) the height Y above the Earth's surface that a geostationary satellite will orbit in km.

Answer:

Part (i)

Step 1: Convert the time period from seconds to minutes

  • The period of a geostationary orbit is X = 24 hrs

    • The period of a geostationary orbit is X = 24 × 60 = 1440 minutes

Part (ii)

Step 1: List the known quantities

  • Period of the LEO, TL = 89 min

    • Period of a geostationary orbit, TG = 1440 min

    • Height above Earth of the LEO, hL = 250 km

    • Radius of the Earth, R = 6.37 × 106 m (from the data sheet)

Step 2: Recall the relationship between orbital period and radius

  • Orbital period T is related to the radius r of the orbit by T squared space proportional to space r cubed

Step 3: Convert the proportional relationship into an equation

fraction numerator T subscript G superscript 2 over denominator T subscript L superscript 2 end fraction space equals space fraction numerator r subscript G superscript 3 over denominator r subscript L superscript 3 end fraction

r subscript G superscript 3 space equals space r subscript L superscript 3 open parentheses T subscript G over T subscript L close parentheses squared

r subscript G space equals space cube root of r subscript L superscript 3 open parentheses T subscript G over T subscript L close parentheses squared end root space equals space r subscript L open parentheses T subscript G over T subscript L close parentheses to the power of bevelled 2 over 3 end exponent

Step 4: Evaluate a final value for Y

  • Orbital radius of LEO:   

r subscript L space equals space R space plus space h subscript L space equals space open parentheses 6.37 cross times 10 to the power of 6 close parentheses space plus space open parentheses 250 cross times 10 cubed close parentheses space equals space 6.62 cross times 10 to the power of 6 space straight m

  • Orbital radius of geostationary: 

r subscript G space equals space open parentheses 6.62 cross times 10 to the power of 6 close parentheses open parentheses 1440 over 89 close parentheses to the power of bevelled 2 over 3 end exponent space equals space 4.235 cross times 10 to the power of 7 space straight m

  • Height above the Earth's surface: 

Y = open parentheses 4.235 cross times 10 to the power of 7 close parentheses space minus space open parentheses 6.37 cross times 10 to the power of 6 close parentheses space equals space 3.6 cross times 10 to the power of 7 space straight m

  • Height above the Earth's surface:  Y = 36 000 km

Examiner Tips and Tricks

Make sure to memorise the key features of a geostationary orbit, since this is a common exam question. Remember:

  • Equatorial orbit

  • Moves west to east

  • Period of 24 hours

You will also be expected to remember that the time period of the orbit is 24 hours for calculations on a geostationary satellite.

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Katie M

Author: Katie M

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Katie has always been passionate about the sciences, and completed a degree in Astrophysics at Sheffield University. She decided that she wanted to inspire other young people, so moved to Bristol to complete a PGCE in Secondary Science. She particularly loves creating fun and absorbing materials to help students achieve their exam potential.