Question #248193

(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

1
Expert's answer
2021-10-10T15:55:26-0400

(a)gravitational force

Fg=Gmpmmr2=6.67×1011×8.25×1024×2.30×1022(2.30×108)2=23.925×1019  NF_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)moon's acceleration (in m/s ) toward the planet

am=Fmm=Gmpr2=6.67×1011×(8.25×1024)(2.30×108)2=10.40×103  m/s2a_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)planet's acceleration (in m/s ) toward the moon

ap=Fmp=Gmmr2=6.67×1011×2.30×1022(2.30×108)2=2.9×105  m/s2a_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

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