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The further a world is from its sun, the slower it needs to move
to stay in orbit. For a circular orbit, Velocityworld =
sqrt(masssun/distance). Kinetic energy =
0.5*massworld*velocity2.
Since velocity increases with 1/distance, the kinetic energy required
for a circular orbit goes to infinity as the distance goes to zero.
The period of a world in a circular orbit is 2*pi*radius/velocity, and velocity is proportional to sqrt(1/radius), so the period is proportional to 2*pi*radius3/2. That's Kepler's third law of orbits. For example (as in the inner and outer worlds in the example), a world at 4 times the distance should have an orbit 8 times as long. |
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