A question of mathematics

[James.Denholm]

I need some help. Specifically, I need some formulas for an up-coming pdf (which is to be my first contributation to
Orbiter). If you know your maths, read on.

First of all:

Formulas relating to the Energy Project, which is a launch vehicle by Kulch.
I know that these would be better placed at the main Orbiter forums, but M6 doesn't have a good track record, if you
know what I mean. NOTE: If you know of a better launch vehicle, please tell me.

1: Is their a formula to figure out the Minimum Point-of-Release Distance (in degrees) in relation to the orbit altitude
(set in the launch dialog)? (See Fig1, Min PoRD = Minimum Point-of-release Distance)

2: Is there a formula to work out the time from launch to release? Or is it the same for all launches?

Fig1:


Secondly:

General Formulas

1: Is there a way of working out if a radius from a certain point (Point 1 in Fig2) crosses an orbit (Target Orbit in Fig2)?

2: Is there a way of working out the altitudes and co-ordinates of those 2 (or more) points (X Point 1 & 2 in Fig2)?

3: Is there a way of working out how many degrees it is from a certain point (X Point 1 or 2 in Fig2) to a major part of
the orbit (say, the apoasis or pheparsis (sorry, can't spell))?

4: Is there then a way of working out how far back (in degrees) a craft would be, x seconds before reaching a certain
point (X Point 1 or 2 in Fig2)? In other words, how would I figure out the average speed (degrees per second) of a
craft over a section of it's orbit, from, say, Point X - 90 degrees to Point X?

5: How do I figure out Relative Velocity?

Fig2:


For those confused, don't worry.

For those who answer, thanks.

[James.Denholm]

sorry to bump, but I kinda need help here.

[BrianJ]

Hi James,
regarding questions1 & 2 (Energy spacecraft), I'd imagine that the time-to-release will depend on various factors such
as payload mass and the desired final orbit parameters (inclination, altitude, etc.)

General Formulas questions:
1 & 2: I have a hunch it'll be easier to figure this out if you work in Polar Coordinates - try googling for something
like "cartesian to polar coordinates"

3 & 4: this page may be of help
http://www.braeunig.us/space/orbmech.htm

5.  velocity of A relative to B = (velocity A) - (velocity B)

James.Denholm a écrit:
When I take over the world, the currency of choice will be choclate-chip cookies.

That puts a new spin on the phrase "Put your money where your mouth is"

Good luck.

[James.Denholm]

lol, thanks Brian.