# Naked Science Forum

## Non Life Sciences => Physics, Astronomy & Cosmology => Topic started by: hamdani yusuf on 03/04/2017 10:46:22

Title: Which clock is faster: clock in ISS or clock in geostationary satellite?
Post by: hamdani yusuf on 03/04/2017 10:46:22
Both clocks experience microgravity, in a state of freefall. But they move at different speed relative to the earth. They are also at different gravity potential.

Which clock ticks faster?
Title: Re: Which clock is faster: clock in ISS or clock in geostationary satellite?
Post by: chris on 03/04/2017 10:50:56
Ticks faster relative to what?
Title: Re: Which clock is faster: clock in ISS or clock in geostationary satellite?
Post by: evan_au on 03/04/2017 11:16:52
The effects of velocity (special relativity, red curve) and gravitational potential (general relativity, green curve) and total (blue curve) are illustrated here:
https://en.wikipedia.org/wiki/File:Orbit_times.svg

The ISS is in Low Earth Orbit (LEO), and orbits at similar altitude to those reachable by the (now defunct) space shuttle. At these altitudes, the gravitational effects are similar to those on Earth's surface. However, the velocity is far higher than Earth's surface (measured relative to an inertial frame of reference based on the center of the Earth), so time on the ISS goes more slowly than time on Earth's surface.

At geostationary altitude, the rotational velocity is much slower than the ISS, and farther out of the Earth's gravitational well than the ISS. So time at geostationary altitude runs faster than time on the Earth's surface (or LEO).

If you want to do the maths for yourself, see:
https://en.wikipedia.org/wiki/Error_analysis_for_the_Global_Positioning_System#Calculation_of_time_dilation
Title: Re: Which clock is faster: clock in ISS or clock in geostationary satellite?
Post by: hamdani yusuf on 25/12/2020 08:57:21
The effects of velocity (special relativity, red curve) and gravitational potential (general relativity, green curve) and total (blue curve) are illustrated here:
https://en.wikipedia.org/wiki/File:Orbit_times.svg

The ISS is in Low Earth Orbit (LEO), and orbits at similar altitude to those reachable by the (now defunct) space shuttle. At these altitudes, the gravitational effects are similar to those on Earth's surface. However, the velocity is far higher than Earth's surface (measured relative to an inertial frame of reference based on the center of the Earth), so time on the ISS goes more slowly than time on Earth's surface.

At geostationary altitude, the rotational velocity is much slower than the ISS, and farther out of the Earth's gravitational well than the ISS. So time at geostationary altitude runs faster than time on the Earth's surface (or LEO).

If you want to do the maths for yourself, see:
https://en.wikipedia.org/wiki/Error_analysis_for_the_Global_Positioning_System#Calculation_of_time_dilation
I asked SpaceX in their Twitter account about the amount of time correction they put into the clocks in their satellites, but I get no reply so far.
Title: Re: Which clock is faster: clock in ISS or clock in geostationary satellite?
Post by: evan_au on 25/12/2020 20:52:05
Quote from: hamdani Yusef
I asked SpaceX in their Twitter account about the amount of time correction they put into the clocks in their satellites, but I get no reply so far.
Only atomic clocks are accurate enough to detect these time deviations.
- And a constant time offset is only applicable to a satellite in a circular orbit, with a fixed altitude and speed.
- SpaceX capsules are intended to operate at different speeds, from "stationary" on Earth's surface, to LEO orbital speed
- SpaceX capsules are intended to operate at different altitudes, from Earth's surface to LEO (but maybe the Moon or Mars, one day)
- The GPS atomic clocks are designed to operate in weightlessness. SpaceX capsules are subjected to violent vibration during launch, orbital maneuvers and re-entry, and atomic clocks are not expected to operate accurately under these conditions.
- So inserting a fixed time offset would not be very useful

In Low-Earth Orbit, it is much easier to get regular time updates from the GPS satellites, which broadcast accurate (pre-adjusted) time down to the surface of the Earth
- Or to use the US TDRS satellites which support communication to LEO
https://en.wikipedia.org/wiki/Tracking_and_Data_Relay_Satellite_System

It is more challenging to keep time in deep space (GPS satellites have their antennas facing towards Earth, rather than away).
- At present, timing is provided by the Deep Space Network, which accurately tracks radial distance and speed.
- Scientists are considering using distant pulsars to provide an accurate timer reference (if you discount the occasional starquake)
- I suspect that astronauts in deep space would choose to keep time sync with Earth's surface
- The only exception would be if they were doing high-accuracy experiments in their lab, in which case they could use an atomic clock calibrated on Earth's surface (not offset), as that will be absolutely accurate when the spaceship is in a different frame of reference.
- The only time you need to take into account time offsets is if you are communicating with people in a different frame of reference (which is what GPS satellites do).
See: https://en.wikipedia.org/wiki/Pulsar_timing_array
Title: Re: Which clock is faster: clock in ISS or clock in geostationary satellite?
Post by: hamdani yusuf on 25/12/2020 21:12:57
Title: Re: Which clock is faster: clock in ISS or clock in geostationary satellite?
Post by: evan_au on 26/12/2020 10:34:09
Quote from: hamdani yusef
The goal of Starlink is to provide broadband communications, not distribute time with atomic-clock accuracy.

As the Starlink satellite appears over the horizon, passes somewhere overhead, and disappears towards the far horizon, the frequency suffers significant Doppler shift. The data signal similarly changes rate as the satellite moves towards you and away from you. Simultaneously, it will be moving towards or away from the Earth station serving your district.

These Doppler shifts have a far greater impact than the relativistic time dilation. But the Doppler shifts are handled by electronics that tracks the transmit frequency of the satellite.
Title: Re: Which clock is faster: clock in ISS or clock in geostationary satellite?
Post by: hamdani yusuf on 28/12/2020 00:10:43
Quote from: hamdani yusef
The goal of Starlink is to provide broadband communications, not distribute time with atomic-clock accuracy.

As the Starlink satellite appears over the horizon, passes somewhere overhead, and disappears towards the far horizon, the frequency suffers significant Doppler shift. The data signal similarly changes rate as the satellite moves towards you and away from you. Simultaneously, it will be moving towards or away from the Earth station serving your district.

These Doppler shifts have a far greater impact than the relativistic time dilation. But the Doppler shifts are handled by electronics that tracks the transmit frequency of the satellite.
I think it's necessary  for those satellites to have accurate internal clocks to help locating their trajectories to prevent collisions. At least it would be useful for crosschecking other methods.
Title: Re: Which clock is faster: clock in ISS or clock in geostationary satellite?
Post by: Petrochemicals on 28/12/2020 02:39:54
]
I think it's necessary  for those satellites to have accurate internal clocks to help locating their trajectories to prevent collisions. At least it would be useful for crosschecking other methods.
The clocks reset fron the ground every orbit. Once in orbit Every satellite has the same distance to earth and the same gravitation level. Simples.
Title: Re: Which clock is faster: clock in ISS or clock in geostationary satellite?
Post by: hamdani yusuf on 28/12/2020 05:23:32
]
I think it's necessary  for those satellites to have accurate internal clocks to help locating their trajectories to prevent collisions. At least it would be useful for crosschecking other methods.
The clocks reset fron the ground every orbit. Once in orbit Every satellite has the same distance to earth and the same gravitation level. Simples.
By taking data of the clock values right before they are reset, they should be able to infer how much time dilation is experienced by those satellites.
Title: Re: Which clock is faster: clock in ISS or clock in geostationary satellite?
Post by: evan_au on 28/12/2020 06:02:54
Quote from: hamdani yusuf
I think it's necessary  for those satellites to have accurate internal clocks to help locating their trajectories to prevent collisions. At least it would be useful for crosschecking other methods.
What do you mean by "accurate"?
- It's quite cheap these days to have a clock accurate to milliseconds per day.
- But to detect relativistic effects, you need clocks accurate to microseconds per day, which basically leaves you with atomic clocks.

A satellite in LEO has to withstand extremes of heat and cold, as it orbits in and out of Earth's shadow. That makes accuracy more challenging.

A way of accurately measuring time (ie distance, needed for orbit determination) is to have a responder on the satellite.
- Every time the satellite passes over a ground station, the ground station sends out a series of pings, to which the satellite replies.
- Each reply includes an accurate measure of the processing time for the answer (by accurate, a clock accurate to milliseconds per day can measure 1ms processing time accurate to nanoseconds).
- By plotting the delays (ie distance) as the satellite approaches and recedes from the ground station, a very accurate measure of the orbit can be determined.
- And with LEO constellations, satellites are always passing over ground stations.

This technique puts a large and expensive atomic clock on the ground, where it can be easily maintained; and puts a small and cheap responder in every satellite.

One day, small, cheap, accurate and robust optical clocks will become available, and then they will be installed on virtually every satellite. This will allow every satellite to measure relativistic effects.
- But there have already been enough experiments proving Relativity to extraordinary precision, so I don't know why anyone would bother.
See: https://en.wikipedia.org/wiki/Atomic_clock#Optical_clocks
Title: Re: Which clock is faster: clock in ISS or clock in geostationary satellite?
Post by: hamdani yusuf on 28/12/2020 09:53:42
One day, small, cheap, accurate and robust optical clocks will become available, and then they will be installed on virtually every satellite. This will allow every satellite to measure relativistic effects.
- But there have already been enough experiments proving Relativity to extraordinary precision, so I don't know why anyone would bother.
If it's really cheap, why wouldn't they? Curiosity is a strong motivation.
Title: Re: Which clock is faster: clock in ISS or clock in geostationary satellite?
Post by: evan_au on 28/12/2020 11:13:15
Quote from: hamdani yusuf
If it's really cheap, why wouldn't they?
Because today, optical clocks are large, complex, fragile and temperamental. Operational lifetimes are measured in hours, not years.

Optical Clock experiments over the past decade look very promising, but they are not yet considered a reliable or reproducible replacement for ground-based atomic clocks, let alone satellite-based clocks.