1© Manhattan Press (H.K.) Ltd. 6.5 Satellite system of the earth Orbital motion of satellite Orbital motion of satellite Synchronous satellite and parking orbit Synchronous satellite and parking orbit Energy of satellite Energy of satellite Weightlessness Weightlessness

2 © Manhattan Press (H.K.) Ltd. Orbital motion of satellite 6.5 Satellite system of the earth (SB p. 227) Moon – only natural satellite of earth Artificial satellites – man put them around earth Go to More to Know 20 More to Know 20

3 © Manhattan Press (H.K.) Ltd. Orbital motion of satellite 6.5 Satellite system of the earth (SB p. 228) launching speed of satellite at its orbital height

4 © Manhattan Press (H.K.) Ltd. Orbital motion of satellite 6.5 Satellite system of the earth (SB p. 228) Paths of satellite: Go to More to Know 21 More to Know 21 Go to More to Know 22 More to Know 22 Go to Example 9 Example 9

5 © Manhattan Press (H.K.) Ltd. Synchronous satellite and parking orbit 6.5 Satellite system of the earth (SB p. 230) Synchronous satellites – move around earth at the same as the rotation of earth about its axis Go to More to Know 23 More to Know 23

6 © Manhattan Press (H.K.) Ltd. Synchronous satellite and parking orbit 6.5 Satellite system of the earth (SB p. 230) (a) period = 24 hours (appear stationary seen from earth), no relative displacement, called geostationary satellites (b) orbit around earth in same direction as rotation of earth (west to east) (c) plane containing orbits of synchronous satellites = plane containing the equator

7 © Manhattan Press (H.K.) Ltd. Synchronous satellite and parking orbit 6.5 Satellite system of the earth (SB p. 230) (c) its radius of orbit and height Go to More to Know 24 More to Know 24 Go to Example 10 Example 10

8 © Manhattan Press (H.K.) Ltd. Energy of satellite 6.5 Satellite system of the earth (SB p. 234)

9 © Manhattan Press (H.K.) Ltd. Energy of satellite 6.5 Satellite system of the earth (SB p. 234) Closer to earth’s surface, satellite loses energy (due to atmospheric friction) and moves to lower orbit  KE increases

10 © Manhattan Press (H.K.) Ltd. Energy of satellite 6.5 Satellite system of the earth (SB p. 235) Satellite moves in a spiral path towards earth Go to More to Know 25 More to Know 25 Go to Example 11 Example 11

© Manhattan Press (H.K.) Ltd. Weightlessness 6.5 Satellite system of the earth (SB p. 237) Weightlessness occurs when - we are in free-falling motion - in spacecraft moving in circular orbit around earth Go to More to Know 26 More to Know 26 Astronaut experiences no reaction, he feels weightless

12 © Manhattan Press (H.K.) Ltd. End

13 © Manhattan Press (H.K.) Ltd. Types of artificial satellites Communication satellites are always used for transmitting of television or telephone signals between two places. Weather satellites are used for transmitting the pictures of cloud pattern for weather forecasting. Return to Text 6.5 Satellite system of the earth (SB p. 227)

14 © Manhattan Press (H.K.) Ltd. Paths of satellite for different speed (v) 1. A part of ellipse for v v > 4. A parabola for v = 5. A hyperbola for v > where is the launching speed required for a circular orbit near the earth and is the escape speed of the earth. Return to Text 6.5 Satellite system of the earth (SB p. 228)

15 © Manhattan Press (H.K.) Ltd. Launching a satellite (a) Normally, we use a two-stage rocket to (i) raise a satellite to the desired height, and (ii) give the satellite the correct speed and direction by the launching rocket. (b) At lift off, the rocket with spacecraft on top is held down by clamps on the launching pad for a few seconds until the exhaust gases have built up an upward thrust which exceeds the rocket’s weight. The rocket rises vertically initially and after this is gradually tilted by the guidance system. The first- stage rocket lifts the spacecraft with the second- stage rocket to the desired height, then separates and falls back to the earth. 6.5 Satellite system of the earth (SB p. 229)

16 © Manhattan Press (H.K.) Ltd. Launching a satellite (cont’d) (c) The spacecraft with the second-stage rocket casts in free flight to its orbital height where it is momentarily moving horizontally. The second-stage rocket then fires and increases the speed to that required for a circular orbit at the height. Then the spacecraft is separated from the second-stage rocket with the launching speed required. 6.5 Satellite system of the earth (SB p. 229) Return to Text

17 © Manhattan Press (H.K.) Ltd. Q: Q:For a satellite which is close to the earth’s surface, its radius of orbit may be assumed to be equal to the earth’s radius = 6.38 × 10 6 m. Estimate (a) the speed, and (b) the period of the satellite. Solution 6.5 Satellite system of the earth (SB p. 229)

18 © Manhattan Press (H.K.) Ltd. Solution: Return to Text 6.5 Satellite system of the earth (SB p. 229)

19 © Manhattan Press (H.K.) Ltd. Synchronous satellite is also known as geostationary satellite or communication satellite. 6.5 Satellite system of the earth (SB p. 230) Return to Text

20 © Manhattan Press (H.K.) Ltd. Synchronous satellites Most of communication satellites are synchronous satellites. 6.5 Satellite system of the earth (SB p. 231) Return to Text

21 © Manhattan Press (H.K.) Ltd. Q: Q:Two widely-separated planetary systems, whose suns of masses S 1 and S 2, planet P 1 of mass M 1 and planet P 2 of mass M 2 are observed to have circular orbits of equal radii. What are the relationship between S 1 and S 2 if P 1 completes one orbit in half the time taken by P 2 ? Solution 6.5 Satellite system of the earth (SB p. 231)

22 © Manhattan Press (H.K.) Ltd. Solution: Return to Text 6.5 Satellite system of the earth (SB p. 231)

23 © Manhattan Press (H.K.) Ltd. Loss in total energy of satellite If the total energy of the satellite reduces, the radius of orbit (r) decreases. However, the kinetic energy of the satellite increases because the increase in the gravitational force by the earth (F = ) accelerates the satellite towards the earth. Hence, the satellite moves faster. 6.5 Satellite system of the earth (SB p. 235) Return to Text

24 © Manhattan Press (H.K.) Ltd. Q: Q: A body of mass m is released from rest at a height h above the earth’s surface of mass M E and radius R E. (a) (i) Derive an expression for the speed (v) with which the body will strike the earth’s surface in terms of h, M E, R E, and the gravitational constant (G). (ii) Hence, estimate the speed with which a meteorite will strike the earth’s surface. (b) (i) If h is small compared to R E, derive an expression for the gravitational potential energy (U) of the body when it is at a height (h) above the earth in terms of m, h, M E, R E, and G. (Neglecting terms in h/R E of powers greater than one) (ii) If the gravitational potential energy of the body is redefined as V = mg o h where g o is the acceleration due to gravity on the earth’s surface, express U in terms of V. [Mass of earth (M E ) = 5.98 × kg; radius of earth (R E ) = 6.38 × 10 6 m] Solution 6.5 Satellite system of the earth (SB p. 235)

25 © Manhattan Press (H.K.) Ltd. Solution: 6.5 Satellite system of the earth (SB p. 236)

26 © Manhattan Press (H.K.) Ltd. Solution (cont’d): Return to Text 6.5 Satellite system of the earth (SB p. 236)

27 © Manhattan Press (H.K.) Ltd. Feeling of weight in space The astronaut experiences reaction when the spacecraft is launching or moving from one orbit to another orbit. 6.5 Satellite system of the earth (SB p. 237) Return to Text