How far is the center of mass of the Earth-Moon system from the center of the Earth? The Earth's mass is 5.97×1024 kg, the Moon's mass is 7.4×1022 kg, and the distance between their centers is 3.8×108 m.
M is the mass of the Earth, m is the mass of the Moon. r is =3.8•10^8 m
M•x =m• (r-x).
x =m•r/(M+m).
3.76 x 10^8
To find the distance from the center of mass of the Earth-Moon system to the center of the Earth, we can use the concept of center of mass.
The center of mass is the point where the system's mass is concentrated or balanced. In this case, we can assume that the Earth-Moon system can be treated as a two-body system, with the Earth and Moon as the two bodies.
The center of mass of a two-body system lies along the line connecting the two masses and divides this line according to their mass ratio. In other words, the distance of the center of mass from the center of the Earth is given by:
d = (m1 * r1) / (m1 + m2)
where d is the distance from the center of the Earth to the center of mass, m1 is the mass of the Earth, m2 is the mass of the Moon, and r1 is the distance between their centers.
Plugging in the given values:
m1 = 5.97×10^24 kg
m2 = 7.4×10^22 kg
r1 = 3.8×10^8 m
d = (5.97×10^24 kg * 3.8×10^8 m) / (5.97×10^24 kg + 7.4×10^22 kg)
Now, we can plug this into a calculator to get the precise value.