Answer:
2/9 times as strong.
Explanation:
From the question given above, the following assumptions were made:
Initial mass of 1st planet (M₁ ) = M
Initial mass of 2nd planet (m₁ ) = m
Initial distance apart (r₁) = r
Initial Force of attraction (F₁) = F
Final mass of 1st planet (M₂) = 2M
Final mass of 1st planet (m₂) = constant = m
Final distance apart (r₂) = 3r
Final force of attraction (F₂) =?
Next, we shall obtain an expression to determine the new force. This can be obtained as follow:
F = GMm / r²
Cross multiply
Fr² = GMm
Divide both side by Mn
G = Fr² / Mm
Since G is constant, then we have
F₁r₁² / M₁m₁ = F₂r₂² / M₂m₂
Finally, we shall determine the new force as follow:
Initial mass of 1st planet (M₁ ) = M
Initial mass of 2nd planet (m₁ ) = m
Initial distance apart (r₁) = r
Initial Force of attraction (F₁) = F
Final mass of 1st planet (M₂) = 2M
Final mass of 1st planet (m₂) = constant = m
Final distance apart (r₂) = 3r
Final force of attraction (F₂) =?
F₁r₁² / M₁m₁ = F₂r₂² / M₂m₂
Fr² / Mm = F₂ × (3r)² / 2M × m
Fr² / Mm = F₂ × 9r² / 2Mm
Cross multiply
Fr² × 2Mm = F₂ × 9r² × Mm
Divide both side by 9r² × Mm
F₂ = Fr² × 2Mm / 9r² × Mm
F₂ = F × 2 / 9
F₂ = 2/9 F
Thus, the new force is 2/9 times the original force i.e 2/9 times as strong.
