# How far does the center of mass lie from the center of the earth?

• rmarkatos
In summary, to find the center of mass between the Earth and moon, we can use the equation Xcm=m1x1+m2x2/m1+m2, where x1 and x2 are the displacements of the masses from an arbitrary point on the line connecting them. For convenience, we can choose x = 0 to be the center of the Earth. The center of mass will then lie at a distance from the center of the Earth, which can be calculated using the equation.
rmarkatos
The Earth and moon are separated by a center-to-center distance of 3.85x10^8m. The mass of the Earth is 5.98x10^24kg and that of the moon is 7.35x10^22kg. How far does the center of mass lie from the center of the earth?

I know you have to use the equation
Xcm=m1x1+m2x2/m1+m2

I don't know what x1 or x2 and i am not exactly sure what you measure x1 and x2 from and that is probably why i can't figure out how to use the equation.

rmarkatos said:
The Earth and moon are separated by a center-to-center distance of 3.85x10^8m. The mass of the Earth is 5.98x10^24kg and that of the moon is 7.35x10^22kg. How far does the center of mass lie from the center of the earth?

I know you have to use the equation
Xcm=m1x1+m2x2/m1+m2

I don't know what x1 or x2 and i am not exactly sure what you measure x1 and x2 from and that is probably why i can't figure out how to use the equation.
Draw a line through the Earth and the moon. Pick any point you want on that line to call x = 0. Then do your calculation. When you find the CM, find the distance from there to the center of the earth. Some choices for x = 0 are more convenient than others, but you are free to make any choice you want.

the line you drawn is in between the Earth and moon? and you pick a point that is on line in between the moon and earth?

I really do not understand what you mean by that, my textbook does not do a good job of explaining it

rmarkatos said:
the line you drawn is in between the Earth and moon? and you pick a point that is on line in between the moon and earth?
The point you pick on the line is completely arbitrary. In this problem you are asked to find how far the center of mass is from the center of the earth, so a convenient choice would be the make x = 0 the center of the earth. That choice also makes the calculation a bit simpler than it would be for most other choices. x1 and x2 are the displacements (distance and + or - direction) of m1 and m2 from the point you choose to call x = 0.

## 1. What is the center of mass and how is it related to the center of the earth?

The center of mass is the point at which the mass of an object is evenly distributed. In the case of the earth, the center of mass is the point at which the mass of the entire planet is evenly distributed. This point is often referred to as the center of gravity, and it is directly below the center of the earth.

## 2. How is the distance of the center of mass from the center of the earth calculated?

The distance of the center of mass from the center of the earth is calculated using the formula for the center of mass of a sphere. This formula takes into account the mass and radius of the earth, as well as the distribution of mass within the planet. It is a complex equation that requires advanced mathematical calculations.

## 3. Does the center of mass of the earth change over time?

Yes, the center of mass of the earth can change over time due to various factors such as the movement of tectonic plates, changes in the distribution of water and ice, and gravitational interactions with other celestial bodies. However, these changes are relatively small and do not significantly affect the overall position of the center of mass.

## 4. How does the location of the center of mass affect the earth's rotation and orbit?

The location of the center of mass has a direct impact on the earth's rotation and orbit. The earth's rotation is constantly influenced by the pull of gravity towards the center of mass, which helps to maintain its stability and axial tilt. The center of mass also plays a crucial role in the earth's orbit around the sun, as it determines the strength and direction of the gravitational force between the two bodies.

## 5. Is the center of mass always located at the exact center of the earth?

No, the center of mass is not always located at the exact center of the earth. As mentioned before, it is influenced by various factors and can shift slightly over time. Additionally, the earth is not a perfect sphere, so the center of mass may be slightly offset from the center due to variations in density and composition within the planet.

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