Trying to teach myself orbital mechanics: Question about True Anomaly.

[TrabantDeLuxe]

Hi,

So, I've decided to finally teach myself Orbital Mechanics. I'm not mathematically challenged, however I just need some clarification. So, the big question:

What is the domain of True Anomaly? Could someone explain a bit about this?

Okay, so I get the following: At periapsis, we have theta = 0. At apoapsis, we have theta = pi. But when we from apoapsis towards periapsis (the 'inbound' leg), does theta assume negative values or is it customary to assume positive values? In the first case the domain of theta would be -pi < theta < pi, in the second 0 < theta < 2*pi. For elliptical orbits, the choice of convention does not seem to matter, but for hyperbolic orbits it seems that it does matter since all of a sudden hyperbolic cosines and sines come in to play.

I'm sorry if this question is a bit fuzzy - I'm still learning!

Cheers,

deLuxe.

[Bill Phil]

I'm pretty sure it just increases in multiples of Pi. Starting at periapse theta is 0, but it's also 2Pi.

Basically, radians.

[MinimumSky5]

Radians measure how far along a circle or ellipse something is, so both 2pi and 0pi are correct (just as 1pi and 3pi are correct at the apoapsis). 0pi implies that it has just started moving or you have just started measuring, and 2pi implies that a full orbit has taken place. Radians are cumulative, like distance, there is no limit, like temperature.

[K^2]

Hyperbolic trig functions have the same period as regular ones. So it doesn't matter. True anomaly θ can have a domain of the form a < θ < a + 2À for any a. But some choices might be more convenient than others. I'd probably go with ±Ã€ for hyperbolic orbits just because it makes book-keeping easier.

[TrabantDeLuxe]

Thanks guys!