The center of a moon of mass m is a distance D from the center of a planet of mass M. At some distance x from the center of the planet, along a line connecting the centers of planet and moon, the net force on an object will be zero.

Question Continuation

Derive an expression for x in terms of m, M, and D. b) If the net force is zero a distance ⅔D from the planet, what is the ratio R of the mass of the planet to the mass of the moon, M/m?

a. x = (D√M/m)/(√M/m + 1)

b. The ratio R of the mass of the planet to the mass of the moon=4:1

Explanation:

Given

m = Mass of moon

M = Mass of the planet

D = Distance between the centre of the planet and the moon

Net force = 0

Let Y be a point at distance x from the planet

Let mo = mass at point Y

a.

Derive an expression for x in terms of m, M and D.

Formula for Gravitational Force is

F = Gm1m2/r²

Y = D - x

Force on rest mass due to mass M (FM) =Force applied on rest mass due to m (Fm)

FM = G * mo * M/x²

Fm = G * mo * m/Y²

Fm = G * mo * m/(D - x)²

FM = Fm = 0 from the question

So,

G * mo * M/x² = G * mo * m/(D - x)² divide both sides by G * mo

M/x² = m/(D - x)² --- Cross Multiply

M * (D - x)² = m * x²

M/m = x²/(D - x)² ---_ Find square roots of both sides

√(M/m) = x/(D - x) Multiply both sides by (D - x)

(D - x)√(M/m) = x

D√(M/m) - x√(M/m) = x

D√(M/m) = x√(M/m) + x

D√(M/m) = x(√(M/m) + 1) Divide both sides by √M/m + 1

x = (D√M/m)/(√M/m + 1)

b. Here x = ⅔D

FM = G * mo * M/x²

Fm = G * mo * m/(D - x)²

FM = Fm

G * mo * M/x² = G * mo * m/(D - x)² divide both sides by G * mo

M/x² = m/(D - x)² --- (Substitute ⅔D for x)

M/(⅔D)² = m/(D - ⅔D)²

M/(4D/9) = m/(⅓D)²

9M/4D = m/(D/9)

9M/4D = 9m/D Divide both side by 9/D

M/4 = m

M = 4m

M/m = 4

M:m = 4:1

So, the ratio R of the mass of the planet to the mass of the moon=4:1

report!

explanation:

physics means: "the branch of science concerned with the nature and properties of matter and energy. the subject matter of physics, distinguished from that of chemistry and biology, includes mechanics, heat, light and other radiation, sound, electricity, magnetism, and the structure of atoms."

it was given as a lesson and guide for prayer.