How far is the center of mass of the Earth-Moon system from the center of the Earth? The Earth's mass is 5.97e24 Kg, the Moon's mass is 7.4e22 Kg, and the distance between their centers is 3.8e8m.
draw a line between earth's center E and moon's center M. Let the system center of mass be at C. If EC=x,
5.97*10^24*x = 7.4*10^22*(3.8*10^8-x)
x = 4.65*10^6
Note that C is very close to E. In fact, it is only
Mm/(Me+Mm) = 1.24% of the way to the moon.
if C is too close to earth,steve ans is wrong then.it should be a relatively small value compared to 4.65×10^6
its quite simple .understand as in the concept of moments.f1d1=f2d2...... centre of mass is like c.o.g of a system
but the guy is correct anyway.
To find the distance of the center of mass of the Earth-Moon system from the center of the Earth, we need to use the principle of center of mass. The center of mass is the weighted average position of the masses in a system.
To calculate the center of mass, we need to consider the masses of both the Earth and the Moon and their respective distances from the reference point (in this case, the center of the Earth).
Let's denote:
- Mass of the Earth: M1 = 5.97e24 Kg
- Mass of the Moon: M2 = 7.4e22 Kg
- Distance between the Earth and the Moon: R = 3.8e8 m
The formula to calculate the center of mass is:
R_cm = (M1 * R1 + M2 * R2) / (M1 + M2)
Where:
- R_cm is the distance of the center of mass from the reference point
- M1 and M2 are the respective masses
- R1 and R2 are the respective distances from the reference point (in this case, the center of the Earth)
In this case, since we want to find the distance of the center of mass from the center of the Earth, R1 would be 0 (as it is the reference point). Thus, the formula simplifies to:
R_cm = (M2 * R) / (M1 + M2)
Now, let's substitute the given values into the formula:
R_cm = (7.4e22 Kg * 3.8e8 m) / (5.97e24 Kg + 7.4e22 Kg)
Calculating the expression on the right side of the equation will give us the distance of the center of mass from the center of the Earth.
Alternatively, we can use a calculator or a programming language with floating-point capabilities to input the expression directly and get the result:
R_cm ≈ 4.67e6 m
Therefore, the center of mass of the Earth-Moon system is approximately 4.67 million meters (4.67e6 m) away from the center of the Earth.