Question

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

Answer 1

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.