Question

The gravitational force between the Sun (mass -1.99 1030 kg) and Mercury (mass 3.30 x 1023 kg) is 899 1021 N. How far is Mercury from the Sun?

Answer 1

The gravitational force between the two objects is given by:
$F=G \frac{m_1 m_2}{d^2}$
where
$G=8.99 \cdot 10^{-11} m^3 kg^{-1} s^{-2}$ is the gravitational constant
$m_1 = 1.99 \cdot 10^{30} kg$ is the Sun mass
$m_2 = 3.30 \cdot 10^{23} kg$ is the mass of Mercury
and d is the distance between Sun and Mercury. Since we know the force:
$F=8.99 \cdot 10^{21} N$
we can re-arrange the formula to find d:
$d= \sqrt{ G \frac{m_1 m_2}{F} }=6.98 \cdot 10^{10}m$

Answer 2

Answer:

B - 6.98 x 10^7 km

Explanation:

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