1. 1.3 GRAVITATION AND SATELLITES

2. There is a mutual force of attraction between any two objects that is directly proportional to each of the masses, 5 kg 13 kg 5 kg 1 kg Newton’s Universal Law of Gravitation

3. is inversely proportional to the square of the distance between their centres, Newton’s Universal Law of Gravitation

4. and acts along the line joining their centres. Newton’s Universal Law of Gravitation

6. Calculate the gravitational force on a 450 kg satellite orbiting a planet of mass 7.4 x 10 24 kg if the orbit radius is 6.5 x 10 6 m. Example 1

7. Why does the Earth orbit the Sun and not the other way around? Orbiting Planets

8. PROPORTIONALITIES

9. Consider the satellite orbiting the planet from the previous example. What would happen to the magnitude of the force in the previous example if: (a)the satellite’s mass was changed to 225 kg? (b)the orbital radius tripled? (c)the mass of the satellite was halved and its orbital radius was reduced to 2/3 of its original size? Example 2

10. What would happen to the force on the satellite if: (a)The mass of the planet was trebled. (b)The distance between the satellite and the planet was doubled. (c)The distance between the satellite and the planet was halved. (d)The mass of the planet was doubled and the mass of the satellite was quadrupled. (e)The mass of the satellite was halved and its distance from the planet was reduced to ¾ of the original distance. Practice Questions

11. The weight of an object equals the gravitational force between it and the planet. Derivation: Acceleration due to Gravity

12. Find the acceleration due to gravity of Mars given that the mass of Mars is 6.4 x 10 23 kg and its radius is 3.4 x 10 6 m. Example 3

13. Application: Satellites

15. Derivation: Speed of a Satellite

16. Note: The speed only depends on the mass of the central planet and the orbital radius. For a fixed radius, there is only one possible speed.

17. Derivation: Period of a Satellite

18. Note: The period only depends on the mass of the central planet and the orbital radius.

19. Possible Orbits

20. For a satellite to stay in a circular orbit: There must be a centripetal acceleration towards the centre of the orbit. The gravitational force (which is directed towards the centre of the Earth), supplies this acceleration. Hence, the centre of the Earth must coincide with the centre of the satellite’s orbit. Possible Orbits

21. Launching Low Altitude Satellites The speed of the launch site adds to the final speed of the satellite. Thus, less fuel is needed.

22. Geostationary Satellites These satellites stay over the same point on the Earth’s surface. https://www.youtube.com/watch?v=FsfcIEmR_b0

23. Geostationary Satellites In order to remain above the same point, there are certain orbital requirements: Rotation West to East The satellite must orbit in the same direction that the Earth rotates to stay above the same point. Equatorial Orbit The satellite must orbit in a plane perpendicular to the Earth’s rotational axis and the centre of orbit must coincide with the centre of the Earth.

24. Polar orbit satellite video rotational axis Geostationary Satellites

26. Polar orbit satellite video Geostationary Satellites

27. https://www.youtube.com/watch?v=FsfcIEmR_b0 Polar Orbits These satellites orbit over the poles.

28. polar orbits geostationary orbit Comparing Orbits

29. Satellite Uses Geostationary Mainly used for communications as reception points on the Earth’s surface can remain fixed since the satellite’s relative position does not change. Sometimes used for weather monitoring.

30. Satellite Uses Polar Mainly used for surveillance and meteorology because: Low altitude provides a closer view of the Earth, providing photos with a higher resolution.

31. They travel around the Earth many times a day (e.g. 12). Since the Earth rotates perpendicular to the satellite’s orbit, patchwork photos can be constructed.