Orbits. Newton suggested that an object could be put into orbit if it were launched from a high hill at a high speed

Size: px

Start display at page:

Download "Orbits. Newton suggested that an object could be put into orbit if it were launched from a high hill at a high speed"

Donald Paul
5 years ago
Views:

1 Satellites & Obits

2 Obits Newton suggested that an object could be put into obit if it wee launched fom a high hill at a high speed If the launch speed was high enough, the object would fall aound Eath (fee fall)

3 If the launch speed was high enough, the object would fall aound Eath (fee fall) This speed is sometimes called the escape speed (speed needed to escape the gavitational foce at the suface) This occus when the centipetal foce at the suface of planet = gavitational foce (assume cicula obits)

4 mv v F c = F g g mg OR mv mv Gm 1 m Gm m 1 v Gm 1

5 Example Detemine the escape speed fo Eath. mv mg v = 7.91 x 10 3 m/s v g

7 Example A satellite is in obit aound an asteoid. The satellite is.60 x 10 5 m fom the cente of the asteoid and has an obital peiod of 6.08 x 10 3 s. Detemine the mass of the asteoid.

8 Solution 4 m 1 T If m and m 4 Gm 1 T F c = F g Gm m mass of satellite

9 s kg N m m m GT 4 1 m T 1 Gm 4 1 Gm T 4 T m =.81 x 10 0 kg

12 Obital Speeds F c = F g mv Gm 1 m and if m m mass of satellite v v Gm 1 Gm 1 m 1 = mass of object at focus (planet)

13 Obiting All objects at the same adius of obit move at the same speed This is why things appea weightless in obit, eveything is moving at the same speed

16 Matian Moon Phobos fom Mas Expess Phobos obits so close to Mas that fom some places it would appea to ise and set twice a day

17 Intenational Space Station (ISS) and the Shuttle Atlantis on mission STS- 13. obiting about 350 km above the Eath's suface

18 Example Calculate the speed and obital peiod of the space shuttle when it is 80 km above the suface of Eath.

19 Solution F c = F g mv Gm m 1 Gm v 1 v Gm 1

20 v T π T π v

21 Example Geosynchonous satellites have a peiod equal to the otation of Eath (4 hous) so they appea to be stationay in the sky. Calculate the altitude (height above Eath s suface) of geosynchonous satellites. F c = F g

22 We know T = 4 hous, m Eath and need Divide by mass of satellite Multiply by and T Divide by m 4 m m Gm m T 1 T 4 Gm 1 4T 1 T 4 T Gm 1 T 4 4 Gm T 3 4 Gm 3 T Gm Gm T T 3 1 m Gm T 1 3 Gm1T 3 Gm Gm T Gm mgm m 4 1 Gm T 1

23 3 GmT 4 N m Watch the units! kg 86400s 3 kg = 4.69 x 107 m fom cente of planet 4 Altitude (height above suface) = 3.59 x 10 7 m

24 Gavity Assist

25 Lunation

26 aound 70 BCE Geek astonome Aistachus used geomety to accuately calculate the Moon's distance, in tems of the adius of Eath, fom the eclipse duation

27 Sta Keple is slightly smalle and coole than the Sun and is 600 LY away. The planet, Keple b, is > X the adius of Eath and obits slightly close in, but lies in the habitable zone whee liquid wate could exist on the suface.

28 Equinox Eath s obit is tilted with espect to its obit aound the sun This is the cause of the seasons At an equinox, the Eath's teminato, the dividing line between day and night, becomes vetical

29 As Eath evolves aound the Sun, the teminato tilts so that nothen hemisphee gets less daily sunlight causing winte in the noth.

30 Exoplanets How do you detect a planet tillions of km away? Look at the light!

32 Light fom sta dims when the planet comes between the sta and the telescope Tansit of exoplanet CoRoT-Exo-1b Copyight: CoRoT exo-team

33 The speed of an planet (satellite, etc.) is given by v = Gm m = mass at the cente of the system (sun, etc.) Assumes most of the mass is at cente

34 Speed of Stas speed v = Gm most of the mass at the cente of galaxy Distance fom galactic cente

35 The equation v = Gm pedicts that the stas nea the cente should otate faste than the stas at the edge

37 The obseved speeds mean most of the galaxy mass is not at the cente, but spead though out the galaxy The mass doesn t emit light so can t be seen

38 Dak Matte Most galaxies show the same speeddistance elationship that doesn t match the pedictions

39 Black Holes

40 Global Positioning System Each GPS satellite tansmits an accuate time signal The eceive calculates the distance fom the satellite

41 Global Positioning System Each signal places the eceive on a cicle Whee the cicles intesect is the location of the eceive

42 #8, 11, 1, 13 P 86

Chapter 5: Uniform Circular Motion

Chapter 5: Uniform Circular Motion Chapte 5: Unifom Cicula Motion Motion at constant speed in a cicle Centipetal acceleation Banked cuves Obital motion Weightlessness, atificial gavity Vetical cicula motion Centipetal Foce Acceleation towad