Question

1/12 Determine the angle o at which a particle in Jupiter's circular orbit experiences equal attractions from the sun and from Jupiter. Use Table D/2 of Appendix D as needed. Sun m i Ꮎ + Jupiter Not to scale Problem 1/12 1/13 Consider a woman standing on the earth with the sun directly overhead. Determine the ratio Res of the force which the earth exerts on the woman to the force which the sun exerts on her. Neglect the effects of the rotation and oblateness of the earth.

Answer 1

m sun of Jupiter Not to scale * 1/12 Sol:- MJ. From the table of "Solar system constants. mass of Jupiter mass of sun Now, substitute Mg=317-8 and Ms = 333000 [as per the Table D/2] in the above Equation. MS SO, MJ = 317.8 MS 333000 - 9.5435 x104 where, the distance between sun and Jupiter which is same as distance between sun and Particle dsy and distance between Jupiter and particle dJM Now, from the length of arc formula, dJM = 6 xds] 0 we can find the angle co).

G NOW, According to Newton's law of gravitation, the force of attraction on particle'm'due to sun is given by, Msom Fs ds where, G' > Universal gravitational constant. m's mass of the particle: similarly, force of attraction on particle'm' due to Jupiter is given by, Fs = G Mjom dTM * Now Equate forces due to sun and Jupiter given by eq (2) and Eq (3) & Ms.M G. My ng dis dom Ms ds] MJ dJM Ms. MJ &3x0² [from Eq (1)] dys MI Ms o² = 9.5438104 O = 0.0309

Now convert the angle of radians into degrees O = 0.0309 x 180° o=1.77° .: The angle required to experience same force on particle by sun and Jupiter is 1.77°

* 1/13 sol: The gravitational force experienced by the sun on the woman is given by Fsw- -> Eq(1) Gms mw Vsw Here, Esw - Gravitational force experienced by the sun on the woman. G - Universal gravitational constant. ms= Mass of sun. mw= mass of woman. Ysws Distance between sun and woman and which will be equal to the distance between sun and earth. Similarly, the gravitational force experienced by the earth on the waran is given by, GMemw FEW = Eq (2) fr

Let 'Res is the ratio of gravitational force experienced by the earth on the woman to gravitational force experienced by the sun on the woman. Res = FEW Eq(3) Fow * Now substitute values of Fow and few Values in Eq(3), we get (si me mu Res Gms mw rsu er me mu .X 82 osw omshow Res e ME X osw ms Eq (4) Now substitute the values as per Diy table ME= 5.972 X 10 kg ms= 1.9891 x 180kg. Vsw= 1.5x10" mi 8= 6.3781 x 100m

By substituting all the above values in Eq(4), we get (1-5 x 10') 5 Res= x 24 972X10 16:3781x106)? 30 1-9891X10 Res= 1660 :: the ratio of gravitational force experienced by the earth on the woman to gravitational force experienced by the sun on the woman is 1660.
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