A "geostationary" orbit is one which has the same angular velocity as the rotation of the planet on its axis.

**Question 1**

Considering the orbit of the earth to be a circle of radius 1·5×10^{8 }km and time period 365·25 days, | |

a) | calculate the angular velocity of the earth |

b) | calculate the mass of the sun. |

**Question 2**

A planet has a radius R = 5000km. A satellite is in orbit 10000km above the surface of the planet. The time period of the satellite's motion is 12·39 hours. Calculate the average density of the planet. |

**Question 3**

A satellite has a mass m = 300kg and is in a geostationary orbit around a planet of mass M = 8×10^{24 }kg. One "day" on this planet is 30 of your earthly hours (I speak as an inhabitant of the planet, which is called Yob and is many light years from here; but that is another story…) | |

a) | calculate the radius of the orbit |

b) | calculate the total energy possessed by the satellite |

c) | calculate the kinetic energy possessed by the satellite |

d) | calculate the speed of the satellite, in kmh^{-1}. |

**Question 4**

The satellite in the previous question now falls to an orbit of radius 10^{7}m. | |

a) | Calculate the total energy possessed by the satellite in its new orbit, and |

b) | the amount of work done on the satellite to cause it to fall to the new orbit. |

**Question 5**

a) | State Kepler’s laws of planetary motion. |

b) | At aphelion, the distance of the earth from the sun is 1·51×10^{8}km. At perihelion, it is 1·46×10^{8}km. For a short time near perihelion (e.g. a day) let the kinetic energy of the earth be K_{p} and for the same time near aphelion let it be K_{a}.Calculate the ratio K _{p}/K_{a}. |

**Question 6**

A star has two planets in orbit around it. Planet 1 has a time period of two (Earth) years and the average radius of its orbit is 2×10^{8 }km. Planet 2 is in an orbit of average radius 6×10^{8 }km. | |

a) | Calculate the time period of planet 2. |

b) | Calculate the mass of the star. |

**Question 7**

a)
| The distance from the centre of the earth to the centre of the moon is approximately 3·84×10^{8}m. The time period of the moon’s orbital motion is 27·3days. Calculate the magnitude of the centripetal acceleration of the moon as it moves round the earth. |

b) | If the radius of the earth is R then the distance from the centre of the earth to the centre of the moon is about 60R (see diagram below). |

Using this information, show that your answer to part a) can be used as evidence for Newton’s inverse square law of gravitation. |