Answer:
the center of mass is Rcm = 0.725 R Earth
Explanation:
The concept of center of mass is of great importance in all physics, since on this all external forces of the system can be considered applied, in the collision analysis it gives an ideal reference system for resolution
The equation for the center of mass is
Rcm = ∑ mi ri / Mt
With Rcm and ri being vector quantities, "m" is body mass and MT total mass
If we write this equation for our system we have
Rcm = (M1 r1 + M2 r2) / (M1 + M2)
M1 and M2 are the mass of the Earth and the Moon respectively, r1 and r2 are the distances measured from our reference system. As they indicate that we place the most massive reference system we place it on planet Earth. The data taken a textbook.
M1 = 5.98 10²⁴ Kg
M2 = 7.36 10²² Kg
Distance from Earth to the moon on average 3.84 10⁸ m
How the coordinate system is placed on Earth
r1 = 0
r2 = 3.84 10 8 m
Rcm = 0 + 7.36 10²² 3.84 10⁸ / (5.98 10²⁴ + 7.36 10²²)
R cm = 2.826 10³¹ / (598 10²² + 7.36 10²²)
Rcm = 2.826 10³¹ / 611.34 10²²
R cm = 4.62 10⁶ m
we are asked to give this distance as a fraction of the radius of the Earth, we divide the two quantities
R earth = 6.37 10⁶ m
Fraction = R cm / R Earth
Fraction = 4.62 10⁶ / 6.37 10⁶
Fraction = 0.725
In summary the center of mass is
Rcm = 0.725 R Earth
