[Spice_discussion] question concerning apparent velocities & light-time

Nat Bachman nathaniel.bachman at jpl.nasa.gov
Wed Jan 12 15:21:46 PST 2011

Hi Ian,

The light time calculation in SPICE is (currently)

The term in question is a result of the chain rule: the
derivative with respect to ET of Position(ET-LT) is

    d(Position(t)) |
    -------------- |         * d(ET-LT)/d(ET)
         dt        |

In the term

    +/- dLT/dET

the sign is determined by the radiation direction: negative
for the reception case and positive for the transmission case.

One can compare the velocity to that obtained by discrete
differentiation of position with respect to time and verify
that the agreement is much better than it would be without
the additional factor.

This is just calculus; there's no reference.

Best regards,

   -Nat Bachman

Nathaniel.Bachman at jpl.nasa.gov

Ian Avruch wrote:
> Hi,
> According to the documentation, for example module SPKEZR, since recently
> the light-time-corrected, apparent velocity includes a factor
> (1 - d(LT)/d(t_eph)).
> Can anyone provide a reference for this derivation?
> It doesn't match what I get starting from relativistic addition of 
> velocities,
> although I'm sure there needs to be a dilation term like that.
> Sorry if this dredges up old discussions; I wasn't able to them if so.
> Thanks much,
> -Ian

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