Answer:
100X
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
[tex]F_1=G\frac{Mm}{r^2}\\\Rightarrow F=G\frac{Mm}{(1.496\times 10^{11})^2}[/tex]
When r = 10 Au = 1.496×10¹² m
[tex]F_2=G\frac{Mm}{r^2}\\\Rightarrow F=G\frac{Mm}{(1.496\times 10^{12})^2}[/tex]
Dividing the forces we get
[tex]\frac{F_1}{F_2}=\frac{G\frac{Mm}{(1.496\times 10^{11})^2}}{G\frac{Mm}{(1.496\times 10^{12})^2}}\\\Rightarrow \frac{F_1}{F_2}=\frac{\frac{1}{10^{22}}}{\frac{1}{10^{24}}}\\\Rightarrow \frac{F_1}{F_2}=100\\\Rightarrow F_1=100F_2[/tex]
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.
