# Find mean anomaly knowing true anomaly? [closed]

I know how to find the true anomaly by knowing the eccentric anomaly and finding eccentric anomaly by knowing the mean anomaly. M >> E >> True anomaly ... ok.

But how to find anomaly eccentric and mean anomaly , only knowing true anomaly? True anomaly >> E >> M ? (inverse)

Anomaly of planetary orbits and Kepler's formulas

## closed as unclear what you're asking by Ryan Unger, peterh, sammy gerbil, Yashas, Michael SeifertMar 1 '17 at 14:13

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I think this is quite straightforward. If you have the true anomaly $\nu$, then the eccentric anomaly $E$ is found from $$\tan \frac{E(t)}{2} = \left(\frac{1+e}{1-e}\right)^{-1/2} \tan \frac{\nu(t)}{2},$$ where $e$ is the eccentricity.

Then you use Kepler's equation to find the mean anomaly $M$ $$M(t) = E(t) - e \sin E(t).$$

• (t) the time since passing through the perielium I do not have. – Sidney Scholze Feb 28 '17 at 22:04
• @SidneyScholze $\nu(t)$ means $\nu$ as a function of time. Time can be measured from any zero point. – Rob Jeffries Feb 28 '17 at 23:11