At some point during their orbit, the location of the Earth Moon relative to the

Question

At some point during their orbit, the location of the Earth Moon relative to the Sun will be as shown in the figure below. What are the magnitude and direction of the force by the Moon due to the Sun and the Earth? (The mass of the Moon is 7.35 times 10^22 kg. The Earth has a mass 5.97 times 10^24 kg. and the Sun has a mass 2.00 times 10^30 kg. in the figure, the distance from the Moon to the Earth is 3.94 times 10^8 m and the distance from the moon to the Sun is 1.50 times 10^11 m.) What are the magnitude and direction of the forces exerted by the Sun and the Earth on the Moon? At what angle does the net force act? below the Sun-Moon Line Determine the orbital speed of a satellite that circles the Earth with a period of 1.70 times 10^4 s. The mass of the Earth is 5.97 times 10^24 kg. A satellite is launched to orbit the Earth at an altitude of 1.05 times 10^7 m for use in the Global Positioning system (GPS). Take the mass of the Earth to be 5.97 times 10^24 kg and its radius 6.38 times 10^6 m. What is the orbit period of this GPS satellite? With what speed, does it orbit the Earth?

Explanation / Answer

Force between sun and moon FSM = GMSMM /r2 = 6.67*10-11(2*1030*7.35*1022) / (1.5*1011)2
   = 4.358*1020 N
Force between earth and moon = GMEMM /r2 = 6.67*10-11(5.97*1024*7.35*1022) / (3.84*108)2
   = 1.984*1020 N
Both the forces are perpendicular therefore by pythagoras theorem
   = (4.3582+ 1.9842)1/2 *1020 = 4.79*1020 N
Direction = tan-1(1.984 /4.358) = 24.478 degree

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