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> 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 accelera

by 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.
    - pdonis 2y ago
      > 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 I'm not sure what you mean by "compared to what is being orbited". We are comparing a clock in a free-fall orbit to a clock on Earth. > speed matters but it is negligible compared to other factors for objects like the moon or a human made satellite For the Moon, yes, the speed effect is small compared to the altitude effect. For human made satellites, it isn't. For example, as I have already said, clocks on the ISS run slow compared to Earth clocks--because in low Earth orbit, the slowdown due to speed is greater than the speedup due to altitude.
      - alganet 2y ago
        If the moon orbited earth a little bit faster, would the number of microseconds per day accumulated change (even if ever so slightly)? In other words, is the speed a determining factor in the offset? Your answer seems to indicate that yes. So, in principle, I should be able to come up with a thought experiment that highlights what that speed means. Would this hypothetical faster moon, billions of years orbiting earth at a different speed, look geologically younger than our regular speed moon? (genuine don't know, but that's the kind of coloquial illustrative example I'm looking for).
- pdonis 2y ago
  > a twin falling into a black hole > the twin at the speed of light that remains younger Neither of these are actual scenarios in relativity. I'm not sure where you are getting them from but your information appears to be garbled. There is a so-called "twin paradox" in relativity (not actually a paradox so the name is a misnomer), where two twins who take different trips (in the original scenario, one stays at home and one travels out to a distant star and back again at high speed) can end up with one younger than the other when they meet up again. But neither twin can travel at the speed of light; that's impossible for an ordinary object like a person. And neither twin can fall into a black hole, because if they did they could never come back out to meet up with the other twin.
  - alganet 2y ago
    Nice, I'm glad you got the reference despite my lack of proper terminology. It's a thought experiment, no one actually wants a twin paradox, but it is worth thinking about it. I'm sure you get my point.

by pdonis 2y ago

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.
  - pdonis 2y ago
    > 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 I'm not sure what you mean by "compared to what is being orbited". We are comparing a clock in a free-fall orbit to a clock on Earth. > speed matters but it is negligible compared to other factors for objects like the moon or a human made satellite For the Moon, yes, the speed effect is small compared to the altitude effect. For human made satellites, it isn't. For example, as I have already said, clocks on the ISS run slow compared to Earth clocks--because in low Earth orbit, the slowdown due to speed is greater than the speedup due to altitude.
    - alganet 2y ago
      If the moon orbited earth a little bit faster, would the number of microseconds per day accumulated change (even if ever so slightly)? In other words, is the speed a determining factor in the offset? Your answer seems to indicate that yes. So, in principle, I should be able to come up with a thought experiment that highlights what that speed means. Would this hypothetical faster moon, billions of years orbiting earth at a different speed, look geologically younger than our regular speed moon? (genuine don't know, but that's the kind of coloquial illustrative example I'm looking for).
pdonis 2y ago
> a twin falling into a black hole > the twin at the speed of light that remains younger Neither of these are actual scenarios in relativity. I'm not sure where you are getting them from but your information appears to be garbled. There is a so-called "twin paradox" in relativity (not actually a paradox so the name is a misnomer), where two twins who take different trips (in the original scenario, one stays at home and one travels out to a distant star and back again at high speed) can end up with one younger than the other when they meet up again. But neither twin can travel at the speed of light; that's impossible for an ordinary object like a person. And neither twin can fall into a black hole, because if they did they could never come back out to meet up with the other twin.
- alganet 2y ago
  Nice, I'm glad you got the reference despite my lack of proper terminology. It's a thought experiment, no one actually wants a twin paradox, but it is worth thinking about it. I'm sure you get my point.