What two facts did Newton need to be able to calculate the acceleration of the Moon?

1) the distance to the Moon and the diameter of the Moon.

2)the time it takes the Moon to make one revolution and the distance from the Earth to the sun.

3)the diameter of the Moon and the diameter of Earth.

4)the diameter of the Moon and the speed of the Moon's rotation.

5)the distance to the Moon and the time it takes the Moon to make one revolution.

Well, aren't we over the moon with all these options? Let's break it down, shall we? Newton needed two key facts to calculate the acceleration of the Moon: the distance to the Moon and the time it takes the Moon to make one revolution. So, option 5 is the one that's out of this world!

To calculate the acceleration of the Moon, Newton needed two specific facts. Let's analyze each answer choice to determine which facts are relevant.

1) the distance to the Moon and the diameter of the Moon.
- The distance to the Moon is relevant because it affects the gravitational force between the Moon and the Earth. However, the diameter of the Moon is not necessary to calculate the acceleration.

2) the time it takes the Moon to make one revolution and the distance from the Earth to the sun.
- While the distance from the Earth to the sun (Earth's semi-major axis) affects the gravitational force between the Earth and the sun, it is not directly related to calculating the acceleration of the Moon. The time it takes the Moon to make one revolution (the Moon's period) is also not necessary.

3) the diameter of the Moon and the diameter of Earth.
- Both the diameter of the Moon and the diameter of the Earth are not directly related to calculating the acceleration of the Moon.

4) the diameter of the Moon and the speed of the Moon's rotation.
- The diameter of the Moon is not necessary, but the speed of the Moon's rotation is not relevant to calculating the acceleration.

5) the distance to the Moon and the time it takes the Moon to make one revolution.
- The correct answer is the distance to the Moon and the time it takes the Moon to make one revolution. These two facts allow Newton to determine the orbital velocity of the Moon. By knowing the distance and the time, he was able to calculate the acceleration using his second law of motion (F=ma) along with the gravitational force equation (F=(GmM)/r^2), where G is the gravitational constant, m is the mass of the Moon, M is the mass of the Earth, and r is the distance between the Moon and the Earth.

1) the distance to the Moon and the diameter of the Moon.