5 ms·

> Once in orbit, I start accelerating until my clock ticked faster Note that this is wrong: you don't have to accelerate to make your clock tick faster. You ju

by pdonis 2y ago

> Once in orbit, I start accelerating until my clock ticked faster Note that this is wrong: you don't have to accelerate to make your clock tick faster. You just have to be in orbit at a high enough altitude for the speedup due to altitude to outweigh the slowdown due to your free-fall orbital speed.

alganet 2y ago
I was under the impression that the speed in orbit matters, therefore accelerating matters. From the paper: > Φ0 is the effective gravitational potential in the rotating frame, which is the sum of the static gravitational potential of the Earth, and a centripetal contribution This is just so I can catch up with a specific desired dilation relative to earth. I don't want to make my orbit higher, on the contrary, the less distance the better so communication is faster.
- pdonis 2y ago
  > I was under the impression that the speed in orbit matters It does. > therefore accelerating matters. No, it doesn't. In a free-fall orbit, proper acceleration is zero; you are weightless. "Accelerate" would mean firing your rockets to change your orbit. You don't want or need to do that. It is true that there is a coordinate acceleration for a body in a circular orbit, in coordinates centered on the Earth, but coordinate acceleration is irrelevant to what we are discussing. > This is just so I can catch up with a specific desired dilation relative to earth. As I said, you do that by staying in an appropriate free-fall orbit for a long enough time. You don't need or want to fire your rockets. > I don't want to make my orbit higher, on the contrary, the less distance the better so communication is faster. But the lower your orbit, the less your clock speeds up relative to Earth clocks. And if your orbit is low enough, your clock will actually run slow compared to Earth clocks (because the altitude effect no longer outweighs the effect of your orbital speed). For example, clocks on the ISS run slow compared to Earth clocks.
  - alganet 2y ago
    > "Accelerate" would mean firing your rockets to change your orbit That's almost what I meant! Spacecraft, acceleration to pick up speed (not to go higher), stock-exchange cheaters. I don't get the "don't need" or "don't want". It is part of my scenario. I also don't want a twin falling into a black hole, but it is a thought experiment that helps put things in perspective, specially for layman like me. I always heard of the scenario of the twin at the speed of light that remains younger. I am introducing an element of communication (originally, clocks with laser beams then stock exchange rates) into that scenario and trying to understand what the offsets mean. This is all above my paygrade, I know, so don't worry! I know I'm far from getting it and I don't want to bother :)
    - pdonis 2y ago
      > Spacecraft, acceleration to pick up speed (not to go higher) That would mean you would no longer be in a free-fall orbit, you would be moving faster than free-fall orbit speed, and your clock would run slower. Depending on how much you sped up, you might even end up having your clock run slower than Earth clocks. > stock-exchange cheaters Nothing you can possibly do with your rocket will enable you to cheat on the stock exchange. No matter what you do, you can't have your buddy's light signals contain information from his future. > I don't get the "don't need" or "don't want". You don't need or want to fire rockets to speed up if your objective is to have your clock run as fast as possible relative to Earth's at a given altitude. Indeed, if you really want your clock to run as fast as possible relative to Earth's clock at a given altitude, you should use your rocket to "hover" motionless (meaning zero speed relative to Earth's center of mass) at that altitude, not to speed up relative to free-fall orbital speed.
      - alganet 2y ago
        > Nothing you can possibly do with your rocket will enable you to cheat on the stock exchange. I'm not trying to come up with an experiment that enables stock-exchange cheating. I'm trying to come up with a thought experiment that highlights the effect of speed on time dilation, with the purpose of understanding what the accumulation of "microseconds per day" means, and in the spirit of the paper posted I want to put an element of information/communication there (clocks with laser beams, stock exchange, doesn't matter what it is, for this purpose they're equivalent). > Depending on how much you sped up, you might even end up having your clock run slower than Earth clocks. So there is at least a component of the "microseconds per day" offset formula that contributes to a slowing down compared to what is being orbited, is that correct? If I got this right, speed matters but it is negligible compared to other factors for objects like the moon or a human made satellite. That's OK. Like I said, I don't want to actually cheat in the stock exchange, I want to understand that effect.

by pdonis 2y ago

alganet 2y ago

I was under the impression that the speed in orbit matters, therefore accelerating matters. From the paper: > Φ0 is the effective gravitational potential in the rotating frame, which is the sum of the static gravitational potential of the Earth, and a centripetal contribution This is just so I can catch up with a specific desired dilation relative to earth. I don't want to make my orbit higher, on the contrary, the less distance the better so communication is faster.

pdonis 2y ago
> I was under the impression that the speed in orbit matters It does. > therefore accelerating matters. No, it doesn't. In a free-fall orbit, proper acceleration is zero; you are weightless. "Accelerate" would mean firing your rockets to change your orbit. You don't want or need to do that. It is true that there is a coordinate acceleration for a body in a circular orbit, in coordinates centered on the Earth, but coordinate acceleration is irrelevant to what we are discussing. > This is just so I can catch up with a specific desired dilation relative to earth. As I said, you do that by staying in an appropriate free-fall orbit for a long enough time. You don't need or want to fire your rockets. > I don't want to make my orbit higher, on the contrary, the less distance the better so communication is faster. But the lower your orbit, the less your clock speeds up relative to Earth clocks. And if your orbit is low enough, your clock will actually run slow compared to Earth clocks (because the altitude effect no longer outweighs the effect of your orbital speed). For example, clocks on the ISS run slow compared to Earth clocks.
- alganet 2y ago
  > "Accelerate" would mean firing your rockets to change your orbit That's almost what I meant! Spacecraft, acceleration to pick up speed (not to go higher), stock-exchange cheaters. I don't get the "don't need" or "don't want". It is part of my scenario. I also don't want a twin falling into a black hole, but it is a thought experiment that helps put things in perspective, specially for layman like me. I always heard of the scenario of the twin at the speed of light that remains younger. I am introducing an element of communication (originally, clocks with laser beams then stock exchange rates) into that scenario and trying to understand what the offsets mean. This is all above my paygrade, I know, so don't worry! I know I'm far from getting it and I don't want to bother :)
  - pdonis 2y ago
    > Spacecraft, acceleration to pick up speed (not to go higher) That would mean you would no longer be in a free-fall orbit, you would be moving faster than free-fall orbit speed, and your clock would run slower. Depending on how much you sped up, you might even end up having your clock run slower than Earth clocks. > stock-exchange cheaters Nothing you can possibly do with your rocket will enable you to cheat on the stock exchange. No matter what you do, you can't have your buddy's light signals contain information from his future. > I don't get the "don't need" or "don't want". You don't need or want to fire rockets to speed up if your objective is to have your clock run as fast as possible relative to Earth's at a given altitude. Indeed, if you really want your clock to run as fast as possible relative to Earth's clock at a given altitude, you should use your rocket to "hover" motionless (meaning zero speed relative to Earth's center of mass) at that altitude, not to speed up relative to free-fall orbital speed.
    - alganet 2y ago
      > Nothing you can possibly do with your rocket will enable you to cheat on the stock exchange. I'm not trying to come up with an experiment that enables stock-exchange cheating. I'm trying to come up with a thought experiment that highlights the effect of speed on time dilation, with the purpose of understanding what the accumulation of "microseconds per day" means, and in the spirit of the paper posted I want to put an element of information/communication there (clocks with laser beams, stock exchange, doesn't matter what it is, for this purpose they're equivalent). > Depending on how much you sped up, you might even end up having your clock run slower than Earth clocks. So there is at least a component of the "microseconds per day" offset formula that contributes to a slowing down compared to what is being orbited, is that correct? If I got this right, speed matters but it is negligible compared to other factors for objects like the moon or a human made satellite. That's OK. Like I said, I don't want to actually cheat in the stock exchange, I want to understand that effect.