martes, 5 de junio de 2012

A conjecture

Probably it's not such a new idea but, anyway, I wonder what would happen if gravity weren't a real constant? Let's say, if it were a function of time. I'd propose to consider the following:

g(t) = g0 + g1 sinωt

Now, the observed gravity of Earth would be a mean value,


g = g0 + g1 /2πω (cos 2πω-cos 0) = g0

Since gravity of Earth depends on gravity constant (and vice versa), we can conclude that,


G(t) = G+ (GMT/ R2T) g1 sinωt

The simple equation mg=mdv/dt slightly changes to


m a = m dv/dt = mg + mg1 sinωt


so,


v (t) = g t + g1/ω [cos ωt-1]




Obviously, frequency "ω" should be enormous, and its clear that when it tends to infinite, the last term vanishes.
It does not seem very likely, because as a result of all that,


S (t) = 1/2 gt2 -g1/ω2 sin ωt - (g1/ω) t


which looks a little weird… Again, the most interesting thing is that if ω is big enough, the last two terms would be very little and when ω tends to infinite, they simply vanish (into thin air, as it were); and of course, the last term, "- (g1/ω t)", that is so intriguing.