Using orbit math to intersect orbits - Please help!

[ROldford]

I've been doing research trying to figure out how to use orbit math to help me intersect my craft's orbit with another orbit (i.e. ISS or Mir). I'm having trouble finding equations that can help me. Here's what I know I need to do:

1. Determine the true (or mean) anomaly of ISS at my periapsis

For this I need to figure out a conversion formula, but I have no idea what to use. I have a feeling that I might be able to use the longitude of periapsis or the longitude of the ascending node for both orbits and compare them, but I'm not sure.
I also figured out that since mean anomaly varies linearly over time, I could use the period to determine a mean anomaly rate (=T*360degrees), then use the time passed since periapsis or apoapsis to determine the mean anomaly at a certain time, but I think that might be a dead end.

2. Determine the radius distance of the ISS when it is at a certain true anomaly

So far, I've found a formula that relates radius and true anomaly, but it includes the semiparameter, which I can't easily calculate using the numbers in Orbit MFD. (That formula is r = p/(1 + e cos theta) where r = radius, p = semiparameter, e = eccentricity and theta = true anomaly. According to Orbiter Wiki: Front Cover Equations, that's the polar form equation.)

Ultimately, I'd like to have a set of equations that could be solved using only the numbers that appear in Orbit MFD. I believe those equations are stored in Equation MFD, so at that point, I'd be able to accurately calculate the intersection point between the ISS orbit and my orbit without having to read it directly off Orbit MFD by waiting for the ISS to pass over my periapsis. (That doesn't sound like a very NASA thing to do. )

If anyone can help me, I'd be very grateful. Thanks!

 

[tfr001]

This is maybe the best source of orbital equations I've found online, although it's in PDF format. You might have to do some work figuring out what all of their symbols stand for and how they relate to your particular problem. The part you want starts at page 125.
http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19630011221_1963011221.pdf
The NASA technical report server is a great public-domain source of lots of this kind of stuff.

 

[tblaxland]

1. Determine the true (or mean) anomaly of ISS at my periapsis

For this I need to figure out a conversion formula, but I have no idea what to use. I have a feeling that I might be able to use the longitude of periapsis or the longitude of the ascending node for both orbits and compare them, but I'm not sure.

You are in the same orbital plane? If yes, your ascending nodes should be the same and you can use the longitude of periapsis and true anomaly to compare angular position:

Your_LAN = ISS_LAN
Your_inc = ISS_inc
Your_true_anomaly = 0
Your_argument_of_periapsis = Your_LPe - LAN
ISS_argument_of_periapsis = ISS_LPe - LAN
Argument_of_ISS_position = ISS_true_anomaly + ISS_argument_of_periapsis - Your_argument_of_periapsis

This last line gives you the angle of how far ahead in the orbital plane the ISS is at that time. If you don't want to wait until you get to your periapsis to determine the ISS true anomaly at that moment, we then move to the second part of your question:

I also figured out that since mean anomaly varies linearly over time, I could use the period to determine a mean anomaly rate (=T*360degrees), then use the time passed since periapsis or apoapsis to determine the mean anomaly at a certain time, but I think that might be a dead end.

You can certainly do that. Once you have found the mean anomaly at whatever time, you then need to solve Kepler's equation numerically (there are no closed form solutions) so you can find the true anomaly at that time. See here for more info:
http://en.wikipedia.org/wiki/Keplers_laws#Summary

Are you a programmer? You might be interested in the Kepler Orbital Simulation Toolkit from cjp & I, that does these things for you:
[ame="http://www.orbithangar.com/searchid.php?ID=3825"]KOST 0.5[/ame]

2. Determine the radius distance of the ISS when it is at a certain true anomaly

So far, I've found a formula that relates radius and true anomaly, but it includes the semiparameter, which I can't easily calculate using the numbers in Orbit MFD. (That formula is r = p/(1 + e cos theta) where r = radius, p = semiparameter, e = eccentricity and theta = true anomaly. According to Orbiter Wiki: Front Cover Equations, that's the polar form equation.)

That same page contains a formula for calculating the semi-parameter (also known as the semi latus rectum): p = a(1-e^2); not too hard is it?