What if the earth suddenly stopped orbiting the sun? The gravitational pull would suddenly no longer have the earth's inertia to counteract it, and the earth would plummet into the sun. But how fast? How long would it take?
What if both bodies were point masses (i.e., had no volume), there was no other motion, and were no other bodies around? Now THAT, I can approximate. :)
These are the results of that model, evaluated each second, starting at t = 0:
Names: ------ t = time r = Earth-Sun separation (orbital radius) F = gravitational force a = acceleration due to gravity D = distance covered V = velocity (based on Δdistance) A = acceleration (based on Δvelocity)
Formulae: --------- F(M1, M2, r) = G * M1 * M2 / r2 a(M, r) = F(M, Mother, r) / M D(t) = D(t - 1) + V(t - 1) + A(t - 1) V(t) = D(t) - D(t - 1) A(t) = V(t) - V(t - 1)
Constants: ---------- Me = Massearth = 5.974 x 1024 kg Ms = Masssun = 1.989 x 1030 kg r(0) = Earth's mean orbital radius = 1.496 x 1011 m G = Gravitational constant = 6.673 x 10-11 m3 / (kg * s2)
t = 0 s (0 days) ---------------- D(t) = 0.000 x 100 m (0.000 x 100%) r(t) = 1.496 x 1011 m F(t) = 3.543 x 1022 kg * m / s2
ae(t) = 0.005931 m / s2 De(t) = 0.000 x 100 m Ve(t) = 0.000 x 100 m / s Ae(t) = 0.000 x 100 m / s2
as(t) = 1.781 x 10-8 m / s2 Ds(t) = 0.000 x 100 m Vs(t) = 0.000 x 100 m / s As(t) = 0.000 x 100 m / s2
t = 5,486,400 s (63.5 days) --------------------------- D(t) = 1.328 x 1011 m (88.78%) r(t) = 1.679 x 1010 m (< 1.6 days) F(t) = 2.814 x 1024 kg * m / s2
ae(t) = 0.4710 m / s2 De(t) = 1.328 x 1011 m Ve(t) = 1.185 x 105 m / s Ae(t) = 0.4640 m / s2
as(t) = 1.415 x 10-6 m / s2 Ds(t) = 3.989 x 105 m Vs(t) = 0.3559 m / s As(t) = 1.426 x 10-6 m / s2
t = 5,578,579 s (64.57 days) ---------------------------- D(t) = 1.496 x 1011 m (100.00%) r(t) = 5.839 x 106 m (< 1.07155947865 sec) F(t) = 2.326 x 1031 kg * m / s2
ae(t) = 3.893 x 106 m / s2 De(t) = 1.496 x 1011 m Ve(t) = 5.449 x 106 m / s Ae(t) = 1.042 x 106 m / s2
as(t) = 11.69 m / s2 Ds(t) = 4.493 x 105 m Vs(t) = 16.37 m / s As(t) = 3.129 m / s2
60 ms
Charts are plotted through 5,486,400 sec (63.5 days). Gravity goes insane after that. Be careful of y-axis units; they're inconsistent (for different scales), and some are unusual (e.g., gigameters).
405 msView the code (masochists only)