Answer :
Answer: mass of moon = 7.350 * 10²² Kg
Mass of earth = 5.98 * 10²⁴Kg
Explanation:
acceleration due to gravity = (gravitational constant * mass of the body) / (distance from the centre of mass)²
g = Gm/r²
G = 6.673 * 10^-11
g(moon) = 1.62 m/s²
r (moon) = 1.74 *10⁶
g = GM/r²
M = gr² / G
M = 1.62 * (1.74 * 10⁶)² / 6.673 * 10^-11
M = 7.350 * 10²² Kg
Mass of moon = 7.350 * 10²² Kg
Mass of earth =?
g = GM / r²
M = gr² / G
g = 9.8 m/s²
G = 6.673 * 10 ^-11
r = 3.84 * 10⁸m
M = 9.8 * (3.84 * 10⁸)² / 6.673 * 10^-11
M = 5.98 * 10²⁴ Kg
Mass of the earth = 5.98 * 10²⁴kg
The answer to the given questions would be as follows:
Mass of the moon = [tex]7.350[/tex] × [tex]10^{22} Kg[/tex]
Mass of the Earth = [tex]5.98[/tex] × [tex]10^{24} Kg[/tex]
Find the gravity
As we know,
The acceleration caused through gravity:-
= [tex](gravitational constant[/tex] × [tex]mass of the body)/(distance from the center of[/tex] [tex]mass)^2[/tex]
Given that,
The radius of the moon(r) [tex]= 1.74[/tex] × [tex]10^6[/tex]
Distance [tex]= 3.84[/tex] × [tex]10^8[/tex]m
Time for a revolution [tex]= 27.3[/tex]
Acceleration on Moon(g) [tex]= 1.62 m/s^2[/tex]
Since Mass [tex]= gr^2 / G[/tex]
[tex]= 1.62[/tex] ×[tex](1.74[/tex] × [tex]10^6)^2 / 6.673[/tex] × [tex]10^{-11}[/tex]
∵ Moon's mass [tex]=[/tex] [tex]7.350[/tex] × [tex]10^{22} Kg[/tex]
Since,
g(gravity [tex]= 9.8 m/s^2[/tex]
G(Gravitational constant) [tex]= 6.673[/tex] × [tex]10^{-11}[/tex]
r(Radius) [tex]= 3.84[/tex] × [tex]10^8[/tex]m
Using the formula,
[tex]= 9.8[/tex] × [tex](3.84[/tex] × [tex]10^8)^2 / 6.673[/tex] × [tex]10^{-11}[/tex]
∵ Earth's mass [tex]=[/tex] [tex]5.98[/tex] × [tex]10^{24} Kg[/tex]
Learn more about "Radius" here:
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