# Time Travel

A nit: if “strength of gravity” means the value of g, then it’s incorrect. The amount of dilation is due to the depth in your gravitational well (the gravitational potential), which is important if you compare two planets with each other. Since the force varies as 1/r^2 and the potential as 1/r, it’s possible to contrive a planet whose mass and size are such that gravity (g) is weaker, but you are “deeper in the well” and your clock runs slower (or the opposite). If you are talking about a single planet then the distinction doesn’t matter, but the details do. You don’t want to misapply the model because of a vague description such as this.

At the end he tells us that 24k miles will slow you be about 5 nanoseconds, but you may already have known that.

## 2 thoughts on “Time Travel”

1. Another nit: The shape of maximum surface gravitation for a homogeneous isotropic mass distribution (radius=R, spherical coordinates [r, theta, phi]) is not a sphere with radius R:

r(theta) = 2Rcos(theta) for a sphere
r(theta) = 5^(1/3)Rsqrt[cos(theta)] for a schmoo
2.6% better for the best point

For a sphere with radius “R” and volume “V,”
r(theta) = 2R[cos(theta)] = 2(3V/4pi)^(1/3)[cos(theta)]
r(theta) = (24V/4pi)^(1/3)[cos(theta)]

For the schmoo,
r(theta) = (15V/4pi)^(1/3)sqrt[cos(theta)]

F(schmoo)/F(sphere) = (6/5)[(5/8)^(1/3)] = 1.0259855680060…

2. So the main focus here distance compared to gravity? This proves that time travel is possible, but only to this extent so far, right?