Determining mass using orbital elements

Izack

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Be forwarned: I have no higher experience than high-school mathematics and physics (although they were the best math and physics high school had to offer ;))

I was wondering if there were a way to calculate the mass of an object given only its velocity relative to its primary and the radius of its orbit, assuming an eccentricity of 0. (Or given its mean orbital radius, where e < 1.)

This would be useful as a quicker way of discovering the mass of a cluster of docked vessels in Orbiter, so long as I needed an accuracy no better than 4 significant digits.
 

Linguofreak

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Be forwarned: I have no higher experience than high-school mathematics and physics (although they were the best math and physics high school had to offer ;))

I was wondering if there were a way to calculate the mass of an object given only its velocity relative to its primary and the radius of its orbit, assuming an eccentricity of 0. (Or given its mean orbital radius, where e < 1.)

This would be useful as a quicker way of discovering the mass of a cluster of docked vessels in Orbiter, so long as I needed an accuracy no better than 4 significant digits.

No. You can figure out the mass of the primary from orbital elements, but not of the secondary. (This isn't quite true IRL when you get to secondaries whose masses are significant fractions of the mass of the primary (you can determine the combined mass of primary and secondary from orbital elements, so if you know the mass of the primary, you also know the mass of the secondary), but because of simplifications in orbiter, the mass of a vessel has absolutely *no* effect on its orbital parameters. (And for any vehicle of reasonable mass (ie, less than that of a mid-sized moon), it wouldn't have any measurable effect even IRL).
 

Izack

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(Late reply)
I should have seen that coming. Thanks for the pointer, Linguofreak.

So, just for fun, could the Moon's mass be estimated given an average altitude of ~384 400km and a mean orbital velocity of 1.03km/s?
 

Izack

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If I also knew the force of gravity between the two, Newton's law of universal gravitation would work. Otherwise, I still don't see how. :shrug:
 

jedidia

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If I also knew the force of gravity between the two, Newton's law of universal gravitation would work.

ah, sorry. I assumed this was known.
 

Eagle

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If you know your orbital period (do you have a watch and can see stars?) and your semi-major axis (do you have some idea of the body's radius and your altitude? A ground radar and ability to measure angles make this easy) and your mass <<< what you're orbiting then you can make a good first order estimate.

Your Equation is: (hotlinked from Wikipedia)
9b100ec42941dd658a75575c8fc888d1.png

T-Orbital Period
M-Major body mass
m-Minor body mass(assumed negligible)
a-Length of semi-major axis
G-Gravitational Constant

Oh and you'll also be able to calculate your eccentricity while you're measuring the semi-major axis.

Not to mention you can use a star's spectral type to get an idea of its mass and measure the movement of its planets over a period of 24 hours and get some very rough (1-2 significant figures) orbital parameters on them.
 
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Izack

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As I'm pondering these equations, I'm starting to mull over the idea of making a planetary analysis kit for Orbiter (Mass, density, etc). It would be a good opportunity to dive into both astrophysics and addon development for Orbiter (two things I plan on doing someday anyway.)
Who knows, it could be a hit with the Orbiter Galaxy in the works.
 
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