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Orbits and satellites questions
An orbit is gravity supplying the centripetal force, and everything else follows from that one substitution. Out of it come Kepler's third law, the kinetic, potential and total energy of a satellite, escape velocity, and the geostationary orbit that stays above one point on the equator.
19 original questions · 53 marks · the orbits and satellites notes · Gravitational fields
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A satellite moves in a circular orbit around a planet. State what provides the centripetal force on the satellite and give its direction.
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The gravitational attraction of the planet on the satellite (1); directed towards the centre of the planet (the centre of the orbit) (1).State the relationship between the orbital period T and the orbital radius r for satellites orbiting the same planet.
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T2 ∝ r3: the square of the orbital period is proportional to the cube of the orbital radius (1).State two features of a geostationary orbit.
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Any two of the following, one mark each (2): period of 24 hours, equal to the Earth's rotation period; orbit is circular and lies in the equatorial plane; satellite moves west to east, in the same sense as the Earth's rotation, so it stays above a fixed point on the equator.A satellite is moved from a low circular orbit to a higher circular orbit around the same planet. State what happens to its orbital speed and to its orbital period.
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The orbital speed decreases, since v = √(GM/r) (1); the orbital period increases (1).Explain why the orbital speed of a satellite in a circular orbit does not depend on the satellite's mass.
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In GMm/r2 = mv2/r the satellite's mass m cancels, leaving v = √(GM/r) (1).Satellite B orbits a planet at four times the orbital radius of satellite A. Determine the ratio of B's orbital period to A's.
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T2 ∝ r3, so TB/TA = 43/2 (1)
TB/TA = 8 (1)A satellite orbits a planet of mass 6.0 × 1024 kg in a circular orbit of radius 7.0 × 106 m. Calculate the orbital speed of the satellite.
G = 6.67 × 10−11 N m2 kg−2Mark scheme
GMm/r2 = mv2/r, so v = √(GM/r) (1)
v = √(6.67 × 10−11 × 6.0 × 1024/(7.0 × 106)) (1)
v = 7561 m s−1 (1)A satellite travels at 7561 m s−1 in a circular orbit of radius 7.0 × 106 m. Calculate its orbital period.
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T = 2πr/v = (2π × 7.0 × 106)/7561 (1)
T = 5817 s (about 97 minutes) (1)Calculate the radius of a geostationary orbit around a planet of mass 6.0 × 1024 kg that rotates with a period of 24 hours (86 400 s).
Compare a low Earth orbit with a geostationary orbit. Refer to altitude, period and one typical use of each.
By treating the gravitational force as the centripetal force, derive the relationship T2 = 4π2r3/GM for a satellite in a circular orbit of radius r about a planet of mass M.
A moon of a distant planet orbits at a radius of 4.0 × 108 m with a period of 27 days. A second moon of the same planet orbits at a radius of 1.0 × 108 m. Determine the orbital period of the second moon, in days.
Show that the escape velocity from a point at distance r from a planet's centre is √2 times the speed of a satellite in a circular orbit of radius r.
A satellite of mass 500 kg orbits a planet of mass 6.0 × 1024 kg in a circular orbit of radius 8.0 × 106 m. Calculate the kinetic energy, the gravitational potential energy and the total energy of the satellite.
A moon orbits a planet of mass 6.0 × 1024 kg with an orbital period of 1.0 × 105 s. Determine the radius of its orbit.
Explain why a geostationary satellite must orbit directly above the equator.
An astronomer measures the orbits of four moons of a newly discovered planet:
moon W: r = 1.0 × 108 m, T = 2.0 days
moon X: r = 2.0 × 108 m, T = 5.7 days
moon Y: r = 4.0 × 108 m, T = 16.0 days
moon Z: r = 3.0 × 108 m, T = 9.0 days
The astronomer suspects that one measurement is wrong. Deduce which moon's data are inconsistent with the others.A satellite in a low orbit experiences a small drag force from the outer atmosphere. Explain why the satellite's speed increases as a result of the drag, even though its total energy decreases.
A satellite of mass 600 kg is to be moved from a circular orbit of radius 9.0 × 106 m to a circular orbit of radius 1.8 × 107 m around a planet of mass 6.0 × 1024 kg. Calculate the minimum energy that must be supplied.
G = 6.67 × 10−11 N m2 kg−2
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