Question

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.

Answer 1

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

Step-by-step 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!!!