In this problem, you will calculate the location of the center of mass for the Earth-Moon system. The mass of the Moon is 7.35x10^22 kg, the mass of the Earth is 6.00x10^24 kg, and the mass of the sun is 2.00x10^30 kg. The distance between the Moon and the Earth is 3.80x10^5 km. The distance between the Earth and the Sun is 1.50x10^8 km.
Calculate the location xcm of the center of mass of the Earth-Moon system. Use a coordinate system in which the center of the Earth is at x=0 and the Moon is located in the positive x-direction. Express your answer in kilometers to three significant figures.

The centre of mass of the Earth-moon system is 4600 km from the centre of the Earth.

Centre of mass is at x = +4600 km

Explanation:

Given,

Mass of the moon = (7.35×10²²) kg

Mass of the Earth = (6.00×10²⁴) kg

Mass of the Sun = (2.00×10³⁰) kg

Distance between the Earth and the moon = (3.80×10⁵) km

Distance between the Earth and the Sun = (1.50×10⁸) km

With the right assumption that the Earth and the moon are on the same straight line on the x-axis,

Centre of mass is given as

C.M = (Σmx)/(Σm)

For the Earth-moon system, let the centre of the earth be at x=0, then the moon is at x = (3.80×10⁵) km away on the positive x-axis.

C.M = (Σmx)/(Σm)

Σmx = (6.00×10²⁴) × (0) + (7.35×10²²) × (3.80×10⁵) = (2.793 × 10²⁸) kg.km

Σm = (6.00×10²⁴) + (7.35×10²²) = (6.0735 × 10²⁴) kg

CM = (2.793 × 10²⁸) ÷ (6.0735 × 10²⁴)

CM = (4.599 × 10³) km = 4599 km = 4600 km to 3 s.f

The centre of mass of the Earth-moon system is 4600 km from the centre of the Earth.

Hope this Helps!!!

molecules are free to separate from each other and will take on the shape of the container. molecules move completely at random and high speeds. they vibrate in a fixed position and do not move around much. molecules expand to the edge of their container.