Orbital motion, natural and artificial satellites

State — 2 marks

A communications satellite is placed in a geostationary orbit above the Earth's equator. This type of satellite remains fixed above the same point on Earth's surface and is used for broadcasting television signals and weather monitoring.

(a) State what is meant by a geostationary orbit. [1 mark]
(b) State the orbital period of a geostationary satellite. [1 mark]

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(a) An orbit where the satellite remains/stays above the same point on Earth's surface (accept: fixed position relative to Earth or does not move relative to the Earth's surface)
(b) 24 hours (accept: 24 h or one day or 86400 s)

Calculate — 5 marks

The International Space Station (ISS) orbits Earth at an altitude of approximately 400 km above the surface. It completes one full orbit every 90 minutes. Scientists need to understand the orbital characteristics of the ISS to plan satellite operations and ensure safe navigation in space.

(a) The ISS orbits Earth once every 90 minutes. Calculate the orbital period of the ISS in seconds. [1 mark]
(b) The radius of Earth is 6,371 km. The ISS orbits at an altitude of 400 km above Earth's surface. Calculate the orbital radius of the ISS (distance from Earth's centre to the ISS) in metres. [2 marks]
(c) Using your answer from part (b), calculate the orbital speed of the ISS in m/s. (Use the equation: v = 2πr/T, where r is the orbital radius and T is the orbital period from part (a)) [2 marks]

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(a) 90 minutes × 60 = 5,400 seconds (1 mark)
(b) Orbital radius = Earth's radius + altitude (1 mark)
(b) 6,371 km + 400 km = 6,771 km = 6,771,000 m or 6.771 × 10⁶ m (1 mark)
(c) Correct substitution into v = 2πr/T with r = 6,771,000 m and T = 5,400 s (1 mark)
(c) v = (2 × π × 6,771,000) / 5,400 = 7,900 m/s or 7.9 × 10³ m/s or 7.9 km/s (1 mark)

Define — 4 marks

The International Space Station (ISS) orbits Earth at an altitude of approximately 400 km. It completes one orbit every 90 minutes and remains in a stable circular orbit without the need for continuous thrust. The station's orbit is maintained by the gravitational force between Earth and the ISS.

(a) Define orbital velocity. [1 mark]
(b) Define gravitational field strength and explain why it varies with distance from Earth's centre. [2 marks]
(c) The ISS experiences gravitational force from Earth. Explain why this force does not cause the ISS to fall towards Earth's surface, despite the continuous gravitational attraction. [1 mark]

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(a) The velocity required for an object to maintain a stable circular orbit around a celestial body / the velocity at which gravitational force provides exactly the centripetal force needed for circular motion
(b) Gravitational field strength is the gravitational force per unit mass / measured in N/kg or m/s²
(b) It varies inversely with the square of distance from Earth's centre / follows an inverse square law / decreases as distance increases because the gravitational force is distributed over a larger area (sphere) at greater distances
(c) The gravitational force acts as the centripetal force, providing the acceleration needed to keep the ISS moving in a circular path / the ISS is in continuous free fall but its horizontal velocity means it continuously 'misses' Earth as it falls

Evaluate — 3 marks

A communications satellite orbits Earth at a fixed position above the equator, always remaining above the same location on the ground. This type of satellite is called a geostationary satellite and is used for broadcasting television signals and weather monitoring.

(a) State what provides the centripetal force that keeps a geostationary satellite in orbit around Earth. [1 mark]
(b) A geostationary satellite must have an orbital period of exactly 24 hours. Explain why this requirement is important for its function as a communications satellite. [1 mark]
(c) Evaluate whether a geostationary satellite could be placed in orbit at the same height above the North Pole as it is above the equator and still function as described. [1 mark]

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(a) Gravitational force (from Earth) / gravity provides the centripetal force
(b) The 24-hour orbit matches Earth's rotation, so the satellite remains stationary relative to a fixed point on Earth's surface / the same location on the ground, allowing continuous signal transmission to/from that location
(c) No, it could not function / would not remain above a fixed location because at the poles, a satellite in a circular orbit would move relative to the rotating Earth / the orbital plane would not rotate with Earth / it would pass over different locations on Earth's surface as it orbits

Orbital motion, natural and artificial satellites

State — 2 marks

Calculate — 5 marks

Define — 4 marks

Evaluate — 3 marks

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