Jump to content

Recommended Posts

A while ago I had a question that went a little like this:

"Planet Kerbin has a radius of from its center and gravity of G. Two identical rockets launch from the equator at opposite sides, and start accelerating along the rotation of the planet with the velocity of V. At what time after they finished acceleration did they reach maximum distance from each other, and what was the distance?"

It also said in its prefix that "people attempting this question might want to find out a little about Kepler's laws."

I think I got the answer, but I am not sure if it is right, as I didn't know any good method of doing such a calculation. Could you please help me by telling me how do you find out these variables algebraicly?

I also found the only picture that I had of this question, and here is a graph that went with it

sCUwyMB.jpg

Edited by Rover 6428
Link to post
Share on other sites

If the two rockets was launched for opposite sides of the planets and having an equal trajectory they will be most distanced then they reach the new Ap assuming the circulation burn V*T is high enough to raise Ap above the initial Ap.
We need to know the orbital speed they had at initial Ap then they was suborbital too. 
If V*T+ initial speed is lower then needed to raise Ap, initial Ap is the time they are most separated. 

In short you are traveling at V*T+ initial speed at Pe, use this to calculate Ap, twice that is the maximum distance, then calculate then you get there 

Link to post
Share on other sites
3 hours ago, magnemoe said:

In short you are traveling at V*T+ initial speed at Pe, use this to calculate Ap, twice that is the maximum distance, then calculate then you get there 

okay, so algebraecally, how would i find the Ap if I know gravity and the final velocity at Pe? Or how do you calculate an orbital period of such an eliptical orbit?

Link to post
Share on other sites
1 minute ago, Rover 6428 said:

okay, so algebraecally, how would i find the Ap if I know gravity and the final velocity at Pe? Or how do you calculate an orbital period of such an eliptical orbit?

I don't know the formulas i just pointed out the logic. 

Link to post
Share on other sites
13 hours ago, magnemoe said:

If the two rockets was launched for opposite sides of the planets and having an equal trajectory they will be most distanced then they reach the new Ap assuming the circulation burn V*T is high enough to raise Ap above the initial Ap.
We need to know the orbital speed they had at initial Ap then they was suborbital too. 
If V*T+ initial speed is lower then needed to raise Ap, initial Ap is the time they are most separated. 

In short you are traveling at V*T+ initial speed at Pe, use this to calculate Ap, twice that is the maximum distance, then calculate then you get there 

Pretty much. We need to step through the launch burns (since they are not instantaneous) to get the final orbits. And depending on what the final orbits are, an algebraic solution may not exist.

On 1/9/2020 at 3:21 PM, Rover 6428 said:

 

sCUwyMB.jpg

 

Okay, this helps enormously because of the assumptions that they have the same semi-major axis, orbit orientations such that they are most distant from each-other at apoapsis, both are at periapsis at burnout, and both are at periapsis at the same time. This will require some explanation.

Most fractions of an orbit are a huge hassle to calculate. Full ones are easy, and it takes exactly half an orbit to get between periapsis and apoapsis. But beyond that, you get into the messy realm of converting between mean anomaly (time, sort of), eccentric anomaly, and true anomaly (actual position along an orbit). If the initial orbits are sufficiently different, the maximum distance on the first orbit will have one (or neither!) ships at apoapsis, so will require calculating intermediate distances.

For orbits exactly opposite of each-other with different apoapses/periods, you could still get times given the known start positions (something like 1.5 orbits for one and 2.5 for the other. Exact values depend on the orbits)

The only easy(ish) part is finding some orbital parameters after burnout (given the above assumptions):

Ap + Pe == 2a

Ap = (1+e)*a

Pe = (1-e)*a

Energy = v^2/2 - GM/r = -GM/(2a)

T^2 = (4π^2/GM)*a^3

Where r is current distance, v is current velocity, e is eccentricity, a is semi-major axis, GM is the planet's mass*gravitational_constant, and T is time.

Link to post
Share on other sites

Energy conservation ought to give you the AP (just like it lets you back out bullet velocity from the height reached by a ballistic pendulum).

The kinetic energy the ships have after their boost gets converted back into potential energy.

It'll be a system of equations, though, because you also need to know what the velocity will be at AP to know how much KE stays in that form.  KEP + PEP =  KEA + PEA.  Remember to calculate your PE from the center of Kerbin (gravitational zero point) rather than from ground level, though, or your height will be off by the PE of Kerbin's radius.  And of course, you have to calculate PE with an inverse square law applied to the value for g.

Might be better to just launch a craft (via hyperdit?), let KSP tell you its Ap height, double that, and subtract Kerbin's diameter.

Link to post
Share on other sites
This thread is quite old. Please consider starting a new thread rather than reviving this one.

Join the conversation

You can post now and register later. If you have an account, sign in now to post with your account.
Note: Your post will require moderator approval before it will be visible.

Guest
Reply to this topic...

×   Pasted as rich text.   Paste as plain text instead

  Only 75 emoji are allowed.

×   Your link has been automatically embedded.   Display as a link instead

×   Your previous content has been restored.   Clear editor

×   You cannot paste images directly. Upload or insert images from URL.

×
×
  • Create New...