04-06-2017, 11:59 PM
There is a formula that converts eccentric anomaly to true anomaly and vice versa:
\[\tan(\nu/2)=\sqrt{\frac{1+e}{1-e}}\tan(E/2)\]
I just noticed that \[\sqrt{\frac{1+e}{1-e}}=\exp(\tanh^{-1}(e))\] which could save some keystrokes (or precious program steps) on a calculator which has atanh function.
Also this is a rare opportunity to use that built in function that almost nobody ever uses.
\[\tan(\nu/2)=\sqrt{\frac{1+e}{1-e}}\tan(E/2)\]
I just noticed that \[\sqrt{\frac{1+e}{1-e}}=\exp(\tanh^{-1}(e))\] which could save some keystrokes (or precious program steps) on a calculator which has atanh function.
Also this is a rare opportunity to use that built in function that almost nobody ever uses.