Accuracy of orbital period measurement
Let’s say you have measured the at times and , separated by N orbital cycles. Then the orbital period, , becomes:
From error propagation theory we know that if:
in which we are ignoring the partial derivative of with respect to because we consider to be zero. The equation becomes:
Then using (1) in (2):
In real life and are typically reported with uncertainties of the order d. Therefore, for a system with period h and , separated by one year we expect an uncertainty of d for the orbital period.
Roche lobe plots
For all the following I’m using gnuplot.
f(x,y)=2/(((x**2+y**2)**2)*(1+q)) +2*q/((((x-a)**2+y**2)**2)*(1+q)) +(x – q/(1+q))**2 +y**2
set view 0,0,1.3
set xlabel “x”
set ylabel “y”
set isosamples 100,100
set size ratio -1
set cntrparam levels disc -2.2,-2.5,-3.55,-29.7,-100,-1000
splot [x=-6:6] [y=-6:6] -f(x,y)