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For something of a hobby of mine, I'm looking at different interplanetary trajectories for a Mars mission.

I've got a somewhat interesting case;

I only know basic calculus of a single variable (taken calculus 1), so I can't do the more in-depth multivariable and (I think) vector calculus required for true calculation of interplanetary trajectories, so for now, I'm sticking to algebraic equations which assume only two bodies and instantaneous Δv. (such as the vis-viva equation, and equations given on wiki for things like hohmann transfer and flight path angle)

So,

**here's the problem**;

I want to be able to calculate Mars transit time for non-hohmann transfer orbits. The method I'll use is to approximate the interplanetary flight path with a section of an ellipse, find the velocity and distance to get time for the flight.

The first step, is calculating the speed. That's rather simple, just an integral of the vis-viva equation with Δv/Δr, divided by the Δr to get average velocity.

The second step, finding the distance, is where I need some help.

The problem, from what I've seen, is finding the arc length of an ellipse from one point to another.

Most of the answers I've seen from looking around on the web are a bit above me, though, lol. But it looks like it can be done with just single variable calculus, so I'll give it a shot.