Question

Consider two celestial objects with masses m1 and m2 with a separation distance between their centers r. If the first mass m1 were to double and the second mass m2 were to triple, what would happen to the magnitude of the force of attraction

Answer 1

The new magnitude of the force of attraction will be 6 times the original force of attraction

How to determine the initial force

• Mass 1 = m₁
• Mass 2 = m₂
• Gravitational constant = G
• Distance apart = r
• Initial force (F₁) = ?

F = Gm₁m₂ / r²

F₁ = Gm₁m₂ / r²

How to determine the new force

• Mass 1 = 2m₁
• Mass 2 = 3m₂
• Gravitational constant = G
• Distance apart (r) = r
• New force (F₂) =?

F = Gm₁m₂ / r²

F₂ = G × 2m₁ × 3m₂ / r²

F₂ = 6Gm₁m₂ / r²

But

F₁ = Gm₁m₂ / r²

Therefore

F₂ = 6Gm₁m₂ / r²

F₂ = 6F₁

Thus, the new magnitude of the force of attraction will be 6 times the original force of attraction

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