Question

(a) Find the magnitude of the gravitational force (in N) between a planet with mass 8.25 ✕ 10²⁴ kg and its moon, with mass 2.30 ✕ 10²² kg, if the average distance between their centers is 2.30 ✕ 10⁸ m.

 __N

(b) What is the moon's acceleration (in m/s²) toward the planet? (Enter the magnitude.)

 __m/s²

(c) What is the planet's acceleration (in m/s²) toward the moon? (Enter the magnitude.)

__ m/s²

Answer 1

(a)

$F_g = G \frac{m_pm_m}{r^2} = \frac{6.67 \times 10^{-11} \times 8.25 \times 10^{24} \times 2.30 \times 10^{22}}{(2.30 \times10^8)^2} \\ = 23.925 \times 10^{19} \;N$

(b)

$a_m = \frac{F}{m_m} = G \frac{m_p}{r^2} \\ = \frac{6.67 \times 10^{-11} \times (8.25 \times 10^{24})}{(2.30 \times 10^8)^2} \\ = 10.40 \times 10^{-3} \;m/s^2$

(с)

$a_p = \frac{F}{m_p} = G\frac{m_m}{r^2} \\ = \frac{6.67 \times 10^{-11} \times 2.30 \times 10^{22}}{(2.30 \times 10^8)^2} \\ = 2.9 \times 10^{-5} \;m/s^2$