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How much stronger is the gravitational pull of the Sun on Earth, at 1 AU, than it would be if Earth were at 10AU, in the orbit of Saturn? How much stronger is the gravitational pull of the Sun on Earth, at 1 AU, than it would be if Earth were at 10AU, in the orbit of Saturn? 250X 25X 10X 100X 5X

User Copyflake
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1 Answer

6 votes

Answer:

100X

Step-by-step explanation:

r = Distance between the Sun and Earth

M = Mass of the Sun = 1.989 × 10³⁰ kg

m = Mass of the Earth = 5.972 × 10²⁴ kg

G = Gravitational constant = 6.67 × 10⁻¹¹ m³/kgs²

When r = 1 Au = 1.496×10¹¹ m


F_1=G(Mm)/(r^2)\\\Rightarrow F=G(Mm)/((1.496* 10^(11))^2)

When r = 10 Au = 1.496×10¹² m


F_2=G(Mm)/(r^2)\\\Rightarrow F=G(Mm)/((1.496* 10^(12))^2)

Dividing the forces we get


(F_1)/(F_2)=(G(Mm)/((1.496* 10^(11))^2))/(G(Mm)/((1.496* 10^(12))^2))\\\Rightarrow (F_1)/(F_2)=((1)/(10^(22)))/((1)/(10^(24)))\\\Rightarrow (F_1)/(F_2)=100\\\Rightarrow F_1=100F_2

Hence, the force when the Earth is 1 Au from the sun is 100 times greater than if the Earth was 10 Au from the Sun.

User Allan Scofield
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