Lagrange points

Thanks guys it was bothering me enought to me on a quest to find a formula and some usable data for placing them in game. I War is only concerned with the L<font size="1">1</font id="size1"> point.

My simple version was: r = 1/(x+1)

where x is the square root of the ratio of the two masses m<font size="1">2</font id="size1">/m<font size="1">1</font id="size1"> and r is the proportion of distance from m<font size="1">1</font id="size1"> to m<font size="1">2</font id="size1">

It turns out it is not at the point of gravitational equilibrium as I had thought. For the object to stay in the same place relative to each body it must also orbit the center of mass at the same rate as the smaller body. This requires some gravitational pull to provide centripetal force. And therefore will be nearer the larger body than my formula will place it.

Fortunately the periods of orbital rotation do not need to be known for the formula (I dont think planets orbit in I War).

It is explained here.
www.ottisoft.com/samplact/Lagrange%20point%20L1.htm

The formulae need masses for the planets to be useful.

Earthlike planets

density ~ 5000kg/m³
size 2,000,000 - 6,500,000 m

Moons
size upto 2,000,000 m

Gas giants
density ~ 1000Kg/m³
size 25,000,000 - 100,000,000 km

volume from the radius 4pi/3 * r³

Stars 0.1M - 10M

M = mass of the sun = 1.98892 × 10^30 kg

I cant see myself designing a system for I War but for those of you that do the L points can be placed authentically if you dont mind the maths.

Jumbo

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