Mars Explorer

I was watching with delight the pictures from the Mars Explorer and my brother-in-law phoned asking questions ...

>Which you couldn't answer, right?
Well ... uh, yes. I mean no. In particular, why launch the Explorer at a particular time, how long would it take, what initial velocity ...?

>Yeah, so?
So I thought it'd be neat to play a Mars Explorer game ... on an Excel spreadsheet, like so:

1. Pick some initial position for Mars.
2. Pick some initial velocity for the Explorer.
3. Click a button and watch as the Explorer is launched (from Earth) and its trajectory displayed.
4. See how close you came to Mars.
5. Repeat 1, 2 and 3 to improve your "closest approach" to Mars.

>Watch? Watch what?
A picture of the trajectory, like this, which shows the Earth and Mars revolving about the Sun ... and the Explorer trajectory.

>What's that green line?
The direction of the initial velocity that you specified.

>I assume there's a spreadsheet, eh?
Well, it isn't finished because I need to correct the units and some parameters: I had to look up the masses and rotational periods for Earth and Mars and I need to ...

>I know the rotational period for Earth!
Yeah, so do I. Anyway, it's fun to play with, though it crashes from time to time. Maybe somebuddy smarter than I can fix the spreadsheet.

>That's just about everybuddy and ...
Listen!
As it is now, it's assumed that Earth and Mars travel in a common plane at constant angular speed (in a perfect circle about the Sun) and the Explorer experiences only gravitational attraction due to the Sun, Earth and Mars (ignoring, say, Venus) and the spreadsheet solves (using Runge-Kutta integration) a couple of second-order differential equations and ...

>Runge-who?
Don't worry about it. Just play.

>So how do I get the spreadsheet?
Just RIGHT-click here and Save Target to download a ZIPd spreadsheet.