What is the value of Mu needed for orbit calculations in the Earth-moon system?

In summary, the person is asking about using a routine that uses Mu (GM) for calculations and is wondering which value of Mu to use for the orbit of the moon around the earth. Another person suggests using MKS units and including other force terms for more accurate calculations. They also mention that for low Earth orbits, the new Mu would be the gravitational constant multiplied by the mass of Earth. Additionally, the person mentions the Gaussian constant for sun-relative orbits as a useful number for comparing other planets' orbits to Earth's.
  • #1
kepler
29
0
Hi again,

I was able to solve the previous problems I had, with some study over the net and some books.
Now I have a different problem: I have a routine that uses Mu (GM) for calculations; for the planets, Mu = GaussK * GaussK * ( 1 + mass ), where GaussK is the Gaussian constant (0.01720209895) and mass is the mass of the planet divided by the mass of the sun ( for earth, mass = 1/328900.56, for example ).
Now, I want to use the same routine, but for the orbit of the moon around the earth. Wich value of Mu must I use to maintain the proportion and the functionality of the routine?

Please someone answer as soon as possible.

Kepler
 
Last edited:
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  • #2
kepler said:
Hi again,

I was able to solve the previous problems I had, with some study over the net and some books.
Now I have a different problem: I have a routine that uses Mu (GM) for calculations; for the planets, Mu = GaussK * GaussK * ( 1 + mass ), where GaussK is the Gaussian constant (0.01720209895) and mass is the mass of the planet divided by the mass of the sun ( for earth, mass = 1/328900.56, for example ).
Now, I want to use the same routine, but for the orbit of the moon around the earth. Wich value of Mu must I use to maintain the proportion and the functionality of the routine?

Please someone answer as soon as possible.

Kepler
I don't do canonical units for anything except sun-relative orbits. For orbit simulations and transfer calculations in the Earth-moon system, I'd stay with MKS units. In fact, there's so much perturbing going on throughout most of this volume that I'd probably use rotating coordinates and include the centrifugal, coriolis and torquey force terms, as well as a time-dependent force vector for the solar perturbation. The rotating system would have a varying angular speed, in order to keep the Earth and moon on the X axis, hence the need for the torquey force term.

But if you confine yourself to low Earth orbits, your new Mu would be the gravitational constant (G) multiplied by the mass of Earth. As for your new GaussK, remember that the Gaussian constant for sun-relative orbits is equal to 2 pi / 365.256898326. It's a handy number for getting other planets' orbits scaled in comparison to Earth's orbit.

Jerry Abbott
 
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1. What is Mu (GM) and how is it used in calculations?

Mu (GM) is a mathematical constant that represents the product of the gravitational constant G and the mass of a celestial body M. It is commonly used in calculations involving orbital mechanics, such as determining the orbital period or velocity of a satellite around a planet.

2. How is Mu (GM) related to Kepler's Third Law?

Kepler's Third Law states that the square of the orbital period of a planet is directly proportional to the cube of its average distance from the sun. Mu (GM) is used in this law to represent the mass of the central body, allowing for the calculation of the orbital period of a planet.

3. Can Mu (GM) be used for any celestial body?

Yes, Mu (GM) can be used for any celestial body with a known mass and gravitational constant. It is commonly used for objects in our solar system, but can also be applied to other celestial bodies such as stars or galaxies.

4. How do you calculate Mu (GM) for a given celestial body?

Mu (GM) can be calculated by multiplying the gravitational constant G (6.67430 × 10^-11 m^3/kg/s^2) by the mass of the celestial body M in kilograms. This will give the value of Mu (GM) in units of m^3/s^2.

5. What units is Mu (GM) typically expressed in?

Mu (GM) is typically expressed in units of m^3/s^2, however it can also be expressed in other units such as km^3/s^2 or mi^3/s^2 depending on the context and preferences of the user.

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