What is the centroid of the earth-moon system and how is it calculated?

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Discussion Overview

The discussion centers on the calculation of the centroid (or center of mass) of the Earth-Moon system, exploring how this point is determined and its implications for the orbits of the Earth and Moon. The scope includes theoretical calculations and conceptual understanding of orbital mechanics.

Discussion Character

  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant inquires about the method for calculating the centroid of the Earth-Moon system and whether it is the point around which both bodies orbit.
  • Another participant explains the calculation process for the center of mass, suggesting the Earth as a reference point and detailing the steps involved, including mass and distance considerations.
  • A participant reports a calculated distance of 4768 km, indicating that the Earth revolves around a point below its surface.
  • Further, the same participant questions whether this positioning could be problematic, comparing it to a scenario with an artificial satellite like the International Space Station, where the center of mass would be very close to the Earth's center.
  • Another participant adds that while the centroid is a point at a given instant, the motion over time results in an oscillating elliptical spiral due to the Earth's rotation and the Moon's elliptical orbit.

Areas of Agreement / Disagreement

Participants express varying interpretations of the centroid's implications and calculations, with no consensus reached on the nature of the orbit or the significance of the calculated distance.

Contextual Notes

The discussion includes assumptions about the reference point for calculations and the nature of orbits, which may not be fully resolved. The relationship between the Earth and Moon's movements and their center of mass is also noted as complex.

Ry122
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How do you calculate the centroid of the earth-moon system?
Is it this exact point that the moon-earth system orbits? Is it an elliptical or circular orbit?
 
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Center of mass:
Pick a reference point (the center of the Earth is a good reference point, since that's the origin for you geocentric equatorial coordinate system). You measure all distances from your reference point.

Multiply the distance of object 1 (Earth?) by its mass.

Multiply the distance of object 2 (Moon?) by its mass.

Add the results together.

Divide the total mass (sum of the Earth's mass and Moon's mass).

That gives you the center of mass relative to your reference point.

If you're using the center of Earth as your reference, then its distance is zero, making your calculation even easier. It's just the Moon's distance times its mass divided by the total mass of the Earth and Moon.

And this is the exact point that both the Earth and Moon orbit around. The orbit could be either circular or elliptical as long as the total energy for both orbits stays constant (with the total energy being the sum of kinetic energy and potential energy). The angular momentum of the two body system also has to stay constant, so the orbit of one will affect the orbit of the other.
 
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thanks. I got 4768km so I take it the Earth revolves around a point below its surface.
 
Ry122 said:
thanks. I got 4768km so I take it the Earth revolves around a point below its surface.

Would you consider that to be a problem? Consider a system in which we had no moon but just one artificial satellite, say the International Space Station. The space station and the Earth would mutually rotate around a point somewhere pretty much exactly at the center of the Earth (off by a very small amount).
 
Ry122 said:
thanks. I got 4768km so I take it the Earth revolves around a point below its surface.

At a instant in time it is a "point" but over the lunar month it is an oscillating elliptical spiral because of the Earth's rotation and the moon's elliptical orbit
 
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