Use the data of this table to find the point between Jupiter and the Sun at whic

Question

Use the data of this table to find the point between Jupiter and the Sun at which an object can be placed so that the net gravitational force exerted by Jupiter and Sun on this object is zero.

Body Mass (kg) Radius (m) Period (s) from Still (m)
Mecury 3.18 X 1023 2.43 X 106 7.60 X 106 5.79 X 1010 2.97
Venus 4.88 X 1024 6.06 X 106 1.94 X 107 1.08 X 1011 2.99
Earth 5.98 X 1024 6.38 X 106 3.156 X 107 1.496 X 1011 2.97
Mars 6.42 X 1023 3.37 X 106 5.94 X 107 2.28 X 1011 2.98
Jupiter 1.90 X 1027 6.99 X 107 3.74 X 108 7.78 X 1011 2.97
Saturn 5.68 X 1026 5.85 X 107 9.35 X 108 1.43 X 1012 2.99
Uranus 8.68 X 1025 2.33 X 107 2.64 X 109 2.87 X 1012 2.95
Neptune 1.03 X 1026 2.21 X 107 5.22 X 109 4.50 X 1012 2.99
Pluto 1.27 X 1023 1.14 X 106 7.82 X 109 5.91 X 1012 2.96
Moon 7.36 X 1022 1.74 X 106 - - -
Sun 1.991 X 1030 6.96 X 108 - - -

Explanation / Answer

gravitational force between the object of mass m and jupiter = gravitational force between the object of mass m and Sun

G*Mj*m/x^2 = G*Ms*m/(6.99*10^7 - x)^2

Mj = 1.9*10^27 Kg

Ms = 1.991*10^30 Kg

1.9*10^27/x^2 = (1.991*10^30)/(6.99*10^7 - x)^2

(6.99*10^7 - x)^2 / x^2 = (1.991*10^30)/ (1.9*10^27) = 1047.9

(6.99*10^7/x ) - 1 = sqrt(1047.9) = 32.37

6.99*10^7/x = 1+32.37 = 33.37

x = (6.99*10^7)/33.37 = 2.09*10^6 m From the Jupiter

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