SAMPLE LESSONS > A LEVEL GRAVITATIONAL FIELD

GEOSTATIONARY ORBITS

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WORKED EXAMPLES

EASY 1

Taking the Earth to be a perfect sphere of uniform density rotating about its polar axis, which of the following statements concerning the observed acceleration due to free fall, ɑ, at the surface of the Earth is true?
A

The value of ɑ at the equator is larger than that at the poles.
B

If the rate of rotation of the Earth slows down, ɑ at the equator increases.
C

If the radius of the Earth increases with its density remaining unchanged, ɑ at the poles decreases.
D

If the radius of the Earth increases with its density remaining unchanged, ɑ at the equator decreases.
Answer

EASY 2

Which statement about geostationary orbits is false?
A

All satellites in geostationary orbits need not have the same mass.
B

They have the same angular velocity as the Earth’s rotation on its axis.
C

All satellites in geostationary orbits need not have the same orbital radius.
D

They cause a satellite to remain vertically above any chosen fixed point on the equator so an antenna can point in a fixed direction and maintain a communication link with the satellite.
Answer

EASY 3

Which quantity is not necessarily the same for satellites that are in geostationary orbits around the Earth?
A

Angular velocity.
B

Centripetal acceleration.
C

Orbital period.
D

Kinetic energy.
Answer

MEDIUM 1

Answer

MEDIUM 2

Taking RE = 6.4 x 106 m and ME = 6.0 x 1024 kg, determine the height of a geostationary orbiting satellite above the Earth’s surface and its orbiting speed.
For geostationary orbit, T = 24 hrs = 24 x 60 x 60 = 8.64 x 104 s
Answer

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