Question

Anna Litical analyzes the force between a planet and its moon, varying the mass of

the moon and the distance between the moon and the planet. Her data is shown
below. Which force ranking is consistant with Anna's data?
Trial Mmoon (kg)
1
6 x 1022
2
6 x 1022
3
3 x 1022
d (km)
3500
7000
7000
Trial 3 is the largest, trial 1 is the smallest
Trial 3 is the largest, trial 2 is the smallest
O Trial 1 is the largest, trial 3 is the smallest
Trial 1 is the largest, trial 2 is the smallest

Answer 1

Trial 1 is the largest, trial 3 is the smallest

Step-by-step explanation:

Given:

Trial 1

M₁ = 6·10²² kg

d₁ = 3 500 km = 3.5·10⁶ м

Trial 2

M₂ = 6·10²² kg

d₂ = 7 000 km = 7·10⁶ м

Trial 3

M₃ = 3·10²² kg

d₃ = 7 000 km = 7·10⁶ м

___________

F - ?

Gravitational force:

F₁ = G·m·M₁ / d₁² = m·6.67·10⁻¹¹·6·10²² / (3.5·10⁶)² = 0.37·m (N)

F₂ = G·m·M₂ / d₂² = m·6.67·10⁻¹¹·6·10²² / (7·10⁶)² = 0.08·m (N)

F₃ = G·m·M₃ / d₃² = m·6.67·10⁻¹¹·3·10²² / (7·10⁶)² = 0.04·m (N)

Trial 1 is the largest, trial 3 is the smallest