# Whats the time dependency of r and angle in Hohmann transfer?

Reading Bate Muller White and trying to find time dependency of angle and distance of Hohmann transfer orbit. Basically I'd like to plot how the vehicle flies from earth to mars and where it is in transfer during over time. I'd expect a function $$\nu(t) = ...$$ or something but mostly see only $$t-t_0 = ...$$ expressions, giving the time of flight from Earth to Mars (eq. 4.2.4).

Given the position (true anomaly) you can calculate time from perihelion as Bates shows. Unfortunately, the equation cannot be inverted. As a practical matter, choose several true anomalies from 0 to $$\pi$$ radians, calculate eccentric anomaly (formula 4.2-8) and then time since perihelion. Plot the true anomaly and time pairs, put a curve through them and pick off true anomaly at equal intervals.

The reference the OP used is first edition of Fundamentals of Astrodynamics. The equation is 4-4 in the second edition.

Be sure to use radians for E in the equation.

• – uhoh
Commented Jun 17 at 7:27
• This approach makes a lot of sense... for calculating the eccentric anomaly $cos E = \frac{e + cos \nu}{1 + e cos \nu}$, where do I get $e$ from for the Hohmann transfer Earth -> Mars? Commented Jun 21 at 20:29
• Using eq. 1.7.4 maybe $e = \frac{r_a - r_p}{r_a + r_p}$ Commented Jun 21 at 20:35