I have a series of observations, measurements made at various times $t$. I now need to determine the most likely value of $R$ (distance) using the model below. The guide says I should find the value of $R$ which minimises the values of $\Delta RA$ across all times, $t$.
The model is: $$ tan(\Delta RA)={ Xcos(Dec_0 + \mu t)sin(RA_0 + \nu t)-sin(wt) \over Xcos(Dec_0 + \mu t)cos(RA_0 + \nu t)-cos(wt) } $$
where; $$ X={R\over R_Ecos\lambda} $$
- $t$ is a variable of time
- $\Delta RA$ varies with time (i.e. there are different values for each row in the table)
- Every other variable, except for $R$, are already determined constants.
With the known values substituted, we have: $$ tan(\Delta RA)={ \left({R \over 2115}\right) cos(14.174550 - 0.003488 t) sin(0.814907 - 0.000468 t) - sin(15.04 t) \over \left({R \over 2115}\right) cos(14.174550 - 0.003488 t) cos(0.814907 - 0.000468 t) - cos(15.04 t) } $$
How would I even begin to work this out?