- #1

Feynstein100

- 162

- 16

**time-dilato-pause**.

The idea behind it is quite simple: for any satellite orbiting a massive object, there are two time dilations at work: one from SR because of how fast it's moving in its orbit (speed dilation - SD) and one from GR because of its position inside a gravitational well (gravity dilation - GD). The time dilations are measured relative to the surface of the massive object.

SD and GD are in opposition to each other because SD tries to slow time down whereas GD tries to speed time up (again, relative to the surface). So the thinking goes that at some distance from the surface, SD and GD cancel each other out and the satellite experiences time at the same rate as the surface. This distance is termed the time-dilato-pause and someone calculated that it lies at a distance of 1.5R from the surface of the object, with R being the radius of said object. Actually, the original calculation was for the earth but I'm sure it can be generalized to any massive object.

Anyway, it ocurred to me that this was significant because it would allow the satellite to experience the same time dilation as on the surface of a massive body (relative to a farway stationary observer) without actually being on the surface. So naturally, my first thought was black holes. If there is indeed a time-dilato-pause at a distance of 1.5R from the event horizon, would a satellite orbiting at that distance experience the same time dilation as the event horizon, i.e. infinite time dilation relative to a faraway stationary observer?

The orbit would be well inside the innermost stable circular orbit (ISCO). However, provided we give it energy from the outside continuously, the satellite would be able to maintain the orbit and escape, basically experiencing what crossing the event horizon would be like without actually crossing it.

So is this actually possible or is there something that I haven't accounted for?