Question

Find the magnitude of the gravitational force (in N) between a planet with mass 6.25 ✕ 1024 kg and its moon, with mass 2.90 ✕ 1022 kg, if the average distance between their centers is 2.50 ✕ 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

here,

the mass of Planet , Mp = 6.25 * 10^24 kg

mass of Moon , Mm = 2.9 * 10^22 kg

average distance between their centers , r = 2.5 * 10^8 m

a)

the magnitude of gravitational force , F = G * Mp * Mm /r^2

F = 6.67 * 10^-11 * 6.25 * 10^24 * 2.9 * 10^22 /(2.5 * 10^8)^2 N

F = 1.93 * 10^20 N

b)

the moon's acceleration (in m/s2) toward the planet , a1 = F /Mm

a1 = 1.93 * 10^20 /(2.9 * 10^22) m/s^2

a1 = 6.67 * 10^-3 m/s^2

c)

the Planet's acceleration (in m/s2) toward the planet , a2 = F /Mp

a2 = 1.93 * 10^20 /(6.25 * 10^24) m/s^2

a2 = 3.09 * 10^-5 m/s^2