Finding Center of Mass Between Earth and Satellite

[Kaxa2000]

The center of mass between two equally sized planets would be right in the center. When you find the center of mass between the Earth and a satellite how would I find the distance offset from the hypothetical midpoint of the earth? The Earth contributes more to the center of mass when paired with the satellite.

 

[tiny-tim]

Hi Kaxa2000!

Use moments … where is the point for which MD = md?

 

[Kaxa2000]

The midpoint would be directly in the center hypothetically. The new midpoint when you pair it to the satellite is what I'm supposed to find but I'm not sure how?

 

[chenying]

The midpoint would be directly in the center hypothetically. The new midpoint when you pair it to the satellite is what I'm supposed to find but I'm not sure how?

Assuming that the planet and the satelite are aligned on the x-axis on a straight line, the center of mass of the system would simply be:

center of mass = (M(of earth)*x1 + m(of satelite)*x2)/(M+m)

x1 and x2 represent where the each object is on the x-axis.

So, let's say that x1(position of the earth) is at the origin of the x-axis and that the satellite is at some value of x2.

Plugging your numbers in, the answer would simply be:

(m(of satelite)*x2)/(M+m)

 

[Kaxa2000]

How would you solve for x2? Don't you have 2 unknowns ...the center of mass and x2?

 

[chenying]

How would you solve for x2? Don't you have 2 unknowns ...the center of mass and x2?

What variables were given to you? If you know the distance of the satellite from the earth, it is the variable x2.

 

[RoyalCat]

What variables were given to you? If you know the distance of the satellite from the earth, it is the variable x2.

Ignore what I wrote earlier, I misread completely.