1.To do some sums! 2.To define what a satellite is 3.To describe two popular types of orbit for man-made satellites 4.To connect Satellite motion with.

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Presentation transcript:

1.To do some sums! 2.To define what a satellite is 3.To describe two popular types of orbit for man-made satellites 4.To connect Satellite motion with circular motion 5.To look at Kepler’s third law Book Reference : Pages 66-67

MercuryVenusEarthMarsJupiterSaturn Radius/ m Orbit Period/ 10 7 s r 3 / T 2 ?????? Please calculate the missing figures

Definition : an object with a small mass in orbit around an object with a large mass The objects can be either natural satellites... i.e. Moons & planets or man-made satellites, space craft and space stations.

a.The path of a celestial body or an artificial satellite as it revolves around another body. b.One complete revolution of such a body.

Discuss and make a list of some of the common uses for man-made satellites

Communication TV & Radio Telephone (Relay of calls & “Sat phones”) WeatherSpy Sat Nav Scientific monitoring (remote sensing) Astronomy Now classify each as to whether in terms of orbit it needs to “stay put” or whether it needs to “move”

When we need a Satellite to “stay still” in a relative position we use a geostationary orbit TV Some Comms

When we need a Satellite to “move” and provide coverage for a large proportion of the Earth’s surface we use a polar orbit Weather, spy, remote sensing etc

Some applications such as “Satnav” (GPS) require a constellation of many satellites. A SatNav will receive from several satellites at the same time

The force of gravitational attraction for a satellite can be equated to a centripetal force acting upon the satellite Planet of Mass m Velocity v Force F Sun mass M Radius r Planetary Motion

The Gravitational force can be given by F = G mM/r 2 The centripetal force on the planet of mass m can be given by F = mv 2 /r Hence we can equate the two and simplify GM/r = v 2 This gives us the speed of the satellite in orbit

GM/r = v 2 Moreover since Speed = circumference of orbit / Period of orbit Speed = 2  r / T  GM/r = 4  2 r 2 / T 2 Which can be rearranged thus GM/4  2 = r 3 / T 2

For a given set of planets e.g. Our solar system where M is the mass of the sun, The left hand side will be a constant GM/4  2 = But if the LHS is a constant, then the RHS must also be a constant = r 3 / T 2 Kepler’s third law!

Newton’s law of gravitation was developed as a direct result of Kepler’s work

Calculate GM/4  2 where M is the mass of the Sun. (2.0 x10 30 kg) Where have we seen this figure today? Show that the height of a geostationary satellite is 35600km (note you are on the right lines if you get 42000km) Mass of Earth = 6.0x10 24 kg Radius of Earth = 6400km