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7.1.4 Orbits of moons, planets, comets and satellites

What keeps a body in orbit

Definition

Orbit

An orbit is the repeating path one body follows around another under the gravitational attraction between them.

  1. Every orbit is held together by gravitational attraction between the orbiting body and the much more massive body it travels around.
  2. The force always points from the orbiting body towards the centre of the body it circles, so a planet is pulled towards the Sun and a moon is pulled towards its planet.
  3. Orbit shapes lie between two extremes, a circle with the central body exactly in the middle, and a long thin ellipse with the central body well off to one end.
  4. The distance from the central body stays fixed in a circular orbit, so the orbital speed also stays fixed.
  5. The distance changes throughout an elliptical orbit, and the body moves fastest where it is closest to the central body and slowest where it is furthest away.
  6. The reason is that the gravitational field is strongest close in, so the pull that speeds the body up on the way in is far larger than the pull it feels at the far end of the orbit.

Orbits of planets and moons

Definition

Natural satellite

A natural satellite is a naturally formed body, such as a moon, that orbits a planet.

  1. The eight planets travel around the Sun on slightly elliptical paths that are so close to circles that they are usually drawn as circles.
  2. All of the planets orbit in the same direction and lie in almost the same flat plane, so the Solar System is shaped like a disc rather than a ball.
  3. The time for one complete orbit is the orbital period, and it grows rapidly with distance from the Sun, from about 888888 days for Mercury to about 165165165 years for Neptune.
  4. A natural satellite orbits its planet rather than the Sun, and these orbits are also close to circular.
  5. Our Moon takes about 272727 days to complete one orbit of the Earth at a mean distance of about 384 000 km384\,000\ \text{km}384000 km.
  6. A moon is carried around the Sun as well, because it stays with the planet that holds it while that planet completes its own orbit.

Orbits of comets

Definition

Comet

A comet is a small body of ice, dust and rock that orbits the Sun along a highly elliptical path.

  1. A comet follows a highly elliptical orbit around the Sun, so its path is a long stretched oval rather than a near circle.
  2. The Sun is not in the middle of that oval but close to one end, so the distance between the comet and the Sun changes enormously during a single orbit.
  3. The comet accelerates as it falls in towards the Sun, reaches its greatest speed at the closest point, then slows steadily as it climbs back out.
  4. It spends only a short part of each orbit near the Sun and most of it moving slowly through the outer Solar System, which is why comets are visible so rarely.
  5. Comet orbits are also tilted out of the plane of the planets, and some run round the Sun in the opposite direction to the planets.
  6. Halley's comet is the familiar example, returning to the inner Solar System roughly every 767676 years.

Orbits of artificial satellites

Definition

Artificial satellite

An artificial satellite is a human-made object placed in orbit around the Earth or another body in space.

Definition

Geostationary orbit

A geostationary orbit is a circular orbit above the equator in which a satellite takes exactly one day to travel once around the Earth, so it stays above the same point on the surface.

  1. An artificial satellite is put into a chosen orbit by a rocket, and the orbit is chosen to suit the job the satellite has to do.
  2. A low polar orbit passes over both poles at a height of a few hundred kilometres and takes about 909090 minutes for one circuit.
  3. The Earth turns underneath a polar satellite, so it passes over a fresh strip of ground on every orbit and can eventually photograph the whole surface, which suits weather monitoring, mapping and spying.
  4. A geostationary orbit lies directly above the equator at a height of about 36 000 km36\,000\ \text{km}36000 km and takes exactly one day for one circuit.
  5. Because the satellite and the ground turn together, the satellite stays above the same point on the equator and appears fixed in the sky.
  6. That is what a satellite television dish needs, since the dish can be bolted in one position and never has to track a moving target.
  7. Geostationary orbits therefore carry communication and broadcasting satellites, while polar orbits carry observation satellites.
Example

Speed of a geostationary satellite

  • A satellite orbits at a radius of 4.2×107 m4.2 \times 10^{7}\ \text{m}4.2×107 m measured from the centre of the Earth and takes one day for a complete circuit.
  • One day in seconds is 24×60×60=86 400 s24 \times 60 \times 60 = 86\,400\ \text{s}24×60×60=86400 s.
  • The distance travelled in one orbit is the circumference, 2πr=2π×4.2×107=2.64×108 m2\pi r = 2\pi \times 4.2 \times 10^{7} = 2.64 \times 10^{8}\ \text{m}2πr=2π×4.2×107=2.64×108 m.
  • Using v=xtv = \dfrac{x}{t}v=tx​ gives v=2.64×10886 400v = \dfrac{2.64 \times 10^{8}}{86\,400}v=864002.64×108​.
  • The orbital speed is about 3.1×103 m/s3.1 \times 10^{3}\ \text{m/s}3.1×103 m/s.
Example

Choosing an orbit for a task

  • A satellite is needed to send live pictures to fixed dishes on homes across the United Kingdom.
  • A fixed dish cannot follow a moving satellite, so the satellite must appear to stay still in the sky.
  • Only an orbit with a period of one day above the equator keeps pace with the turning Earth.
  • A geostationary orbit is therefore the correct choice, and a low polar orbit would put the satellite out of view within minutes.
Exam technique

Describing an orbit accurately

  • Name the shape and the central body together, for example a highly elliptical orbit around the Sun, because half an answer scores half the marks.
  • Quote a period when one is available, since 272727 days for the Moon or one day for a geostationary satellite is far stronger than saying the orbit is quick or slow.
  • Link the orbit to its use whenever a question mentions a satellite, because the mark is for the match between the orbit and the job.
  • Convert hours to seconds and kilometres to metres before substituting into any speed calculation.
  • Measure an orbital radius from the centre of the Earth, not from the ground, so add the radius of the Earth to any height given above the surface.
Common Mistake
  • Do not describe a comet orbit as circular, because the stretched ellipse is the whole point of the description.
  • Do not place the Sun at the centre of a comet orbit, since it lies close to one end of the ellipse.
  • Do not say a geostationary satellite is stationary, because it is moving at about 3 km/s3\ \text{km/s}3 km/s and only appears fixed from the turning ground.
  • Do not put a communications satellite in a polar orbit or an imaging satellite in a geostationary orbit, because each orbit suits only one of those jobs.
Self review
  • Name the force that keeps a planet in orbit around the Sun and state its direction.
  • Describe the shape of a comet orbit and say where the Sun sits within it.
  • Explain where a comet travels fastest and why.
  • State the period and position of a geostationary orbit.
  • Give one use of a low polar orbit and explain why that orbit suits it.
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7.1.4 Orbits of moons, planets, comets and satellites Revision Guide

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Revision notes for Edexcel GCSE Physics 7.1.4 Orbits of moons, planets, comets and satellites: explanations and worked examples.

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