30 Jun
2011
30 Jun
'11
12:10 a.m.
Earth's velocity in orbit ~ 30 km/sec ~ 10^-4 c
http://en.wikipedia.org/wiki/Earth%27s_orbit
If we increase the speed, the orbit becomes eccentric (e>0):
v/vcircular = sqrt(1+e)
But if the eccentricity e equals or exceeds 1, then the Earth escapes from orbit.
Corresponding to a parabola and hyperbola, respectively. I wonder what happens if we have a solar system in the real projective plane, where all conics are indistinguishable? Then there is no definition of 'escaping from orbit'. Designing a set of physical laws invariant under projective transform would be difficult, though. Sincerely, Adam P. Goucher