two_free_riders - TWO FREE RIDES PLUS SPEED AND SIZE OF...

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Unformatted text preview: TWO FREE RIDES PLUS SPEED AND SIZE OF MOON A The earth gives us two free rides (i) Due to rotation of Earth about its axis EQUATOR Time for Rotation = 24 hours Radius of Earth = 4000 miles = 6400 km Our Latitude = 45° ' Radius of 6R = RE sin 45 = RE cos 45 Speed Due to Rotation = 327%Rmph : 27: x 4000>< sm45 w 700mph . 24 , \ , E 1120 km/hour ‘ (ii) Due to revolution of Earth around the sun Radius of Earth’s Orbit = 93,000,000 miles Time for Revolution =1 year = (365.25 x 24) hours 27r><93><106 Speed due to Revolution = 235.25 x 24 m 67,000 mph 1w Speed and Size of Moon: To access speed of moon we need two observers to go out at midnight on a full moon night and observe a star such that the moon intercepts the light from the star. Star is very far so light from it is a parallel beam. Both observers on same latitude so both have same velocity V0 due to Earth’s rotation. The picture is Moon “ -\ VM (1 = distance between 01 and 02 o 6—— V0 .\ o 02 Ed :01 At time t1 moon intercepts light from star as seen by 01 Picture at 1‘, VM 0 <“ V0 0 02 d 0| %9 At time t2 moon intercepts light from star as seen by 02 t2 Picture VM 6! ea 0 O O O 02' 02 01' 01 02 ' 02 = 01'0] = distance travelled by observer due to motion of Earth Hence VM (t2 “t1):d+Vo(t2 ‘5) 0’ Speed of moon VM = (t2 ”t1) Once we know VM a single observer can “measure” diameter of moon. Again, concentrate on light from a star being intercepted by moon. VM at td light just disappears 6—— Vo 0 VM . . a at IA l1ght JUS’E appears 00': VOUA —rd) 0' 0 Distance mobbed by moon = dM + V0 (tA — td) Where dM = diameter of moon VM “A “Q” = dM +V0(tA ‘31:) dM =(VM —VO)(tA —td) Which will allow us to measure dM . ...
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