What two facts did Newton need to be able to calculate the acceleration of the Moon?
A) the distance to the Moon and the diameter of the Moon
B) the time it takes the Moon to make one revolution and the distance from the Earth to the sun
C) the diameter of the Moon and the diameter of Earth
D) the diameter of the Moon and the speed of the Moon's rotation
E) the distance to the Moon and the time it takes the Moon to make one revolution
To calculate the acceleration of the Moon, Newton needed two specific facts. Let's analyze each option to find the correct answer:
A) the distance to the Moon and the diameter of the Moon: While having the distance to the Moon is relevant, the diameter of the Moon is not necessary to calculate its acceleration. Therefore, A) is not the correct answer.
B) the time it takes the Moon to make one revolution and the distance from the Earth to the Sun: This option provides two unrelated pieces of information, neither of which is directly relevant to calculating the Moon's acceleration. Therefore, B) is not the correct answer.
C) the diameter of the Moon and the diameter of Earth: Similar to option A, while having the diameter of the Moon is valuable, the diameter of Earth is not required to calculate the Moon's acceleration. Thus, C) is not the correct answer.
D) the diameter of the Moon and the speed of the Moon's rotation: The diameter of the Moon alone does not provide sufficient information to calculate acceleration. Additionally, the speed of the Moon's rotation is not directly related to its acceleration. Therefore, D) is not the correct answer.
E) the distance to the Moon and the time it takes the Moon to make one revolution: The correct answer is E. These two pieces of information, the distance to the Moon and the time it takes for the Moon to complete one revolution, are necessary to calculate the Moon's acceleration using Newton's Laws of Motion. By knowing the distance and the time taken, the change in velocity can be determined, which allows for the calculation of acceleration using the formula a = Δv / Δt.
So, the correct answer is E) the distance to the Moon and the time it takes the Moon to make one revolution.