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# How Did Early Players Find Out Kerbin's Radius/Mass?

## Question

In these newer versions, the information panel in the map view gives players access to many variables such as the GM of the planet, it's radius, atmosphere height and many other things. However, in the early days of KSP (like when it was free), players used actual mathematics to figure out Kerbin's mass. My question is how did they figure out the mass of Kerbin (probably using V^2 = GM(2/alt - 1/sma)) without knowing the radius of the planet?

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Radius can be derived given orbital velocity, period, and altitude. You use period and velocity to derive orbit circumference and radius, then subtract altitude.

Mean density can be derived from orbital period, semi-major axis, and gravitational constant via Kepler's Third Law. Once you have mean density and radius, you can derive mass.

Not sure how you experimentally determine gravitational constant, may be assumed to be equivalent to real value. Or it may be something you can derive from the local gravitational field and orbit.

Or you could peek at configuration files.

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I wound up writing up a procedure for determining the mass and radius of unknown bodies using two elliptical orbits around said bodies a couple years ago. It requires tywo, because you've got two unknowns (mass and radius), therefore you need two equations, and doesn't rely on the orbits being absolutely circular.

You'll need to know the altitudes of apoapses, altitudes of periapses, and the periods of both orbits, all of which can be obtained from the map screen (or at least, could be obtained once the map screen showed up, and began giving apoapse and periapse times. That was...0.11, if I recall correctly?)

At any rate, the procedure can be found here: http://forum.kerbalspaceprogram.com/threads/16177-Analytically-Solving-for-Gravitational-Parameter-and-Body-Diameter?p=229143&viewfull=1#post229143

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We always knew Kerbin's surface gravity and radius because the devs talked about them. Similarly, discussions about the Mun meant that we had a good idea of that before 0.12 came out. I used a method much like ajburges's to find the mass of Minmus in 0.15 and when it changed in 0.17, and much like maltesh's to get initial planet masses in 0.17. (It's much easier with circular orbits, though). That said, getting planet masses out of the API is much more accurate.

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