The quest for proper time

[Gondos]

Hi,
I'm trying to integrate proper time on vessels in Orbiter but I'm not sure about the time scales involved.
The goal is to have the computed proper time on a vessel landed on Earth elapse at a similar rate as Terrestrial Time.
Here is what I tried :
- integrate τ from a weak-field approximation:
dτ/dt = sqrt(1-v²/c²+2U/c²)
with
U=-Σi(GMi/ri) over all planets/moons + the sun
- dt is SimDT and v and ri are velocities and positions in the "global frame" of Orbiter.

If we plot the resulting τ-simt for a DG landed at Cape Canaveral over several years it gives this:

The slope is about 0.49s per year, suspiciously close to the scaling factor between TCB and TDB.
Now it's not clear to me what exactly is the ephemeris time used in Orbiter's VSOP, but I think it's ET=TDB. I'm not sure how it should affect the formula.
I guess the formula computes dτ/dTCB instead of dτ/dTDB.
Anyway, let's see what happens if we scale our equation, given the definition of TDB : TDB = TCB − LB×(JDTCB − T0)×86400 + TDB0
dτ/dt = sqrt(1-v²/c²+2U/c²) / (1-LB)

Now this looks close to the TT-TDB formula (-0.001658 * sin(g) - 0.000014 * sin(2.0*g) shown in red)

Over a longer time span (244 years here), we can notice a drift of 9.20μs/year (enjoy the pretty aliasing^^) :


It looks like τ-simt ≈ TT-TDB + drift error, and if simt = TDB then τ = TT + drift error

So the questions are :

• what's actually computed by the first equation?
• is applying the scale factor a valid way of realizing TT?
• what could account for the 9.20μs/year drift?

Integration is done with fixed timesteps of 5000s starting at MJD 51547.01.
Thanks

 

[Thunder Chicken]

So the questions are :

• what's actually computed by the first equation?
• is applying the scale factor a valid way of realizing TT?
• what could account for the 9.20μs/year drift?

Integration is done with fixed timesteps of 5000s starting at MJD 51547.01.
Thanks

I'm not fully understanding what you are working on, but my experience with computational modeling and numerical simulation causes me to suggest that you change the size of the time steps and repeat the calculation and see if that has an impact on that drift and your other results. Numerical error due to approximating differential equations with algebraic series expressions is directly related to time step size and the method of integration.

Making the time step smaller should increase numerical accuracy, but if you simply want to see if that has an effect quickly, you could try just repeating the simulation with a larger time step. Halving or doubling the time step would be fine for this exercise.

 

[n72.75]

Orbiter uses TDB.

I think it would be very hard to say exactly where the error is coming from other than to really go through all possible error sources and quantify them. E.g. if the error in Earth velocity is x ppm, what effect does that have on your drift error etc.


Something easy to check might be the GM values for all the VSOP bodies. Changing simt step length and ephemeris calculation interval (more VSOP terms) might be interesting. You might find it makes it better/worse but it won't tell you exactly what the cause is.