Moving aphelion

[rthorvald]

Is it possible to make the aphelion of an object move around the star at a given rate?

Let me explain:

I have two objects, both with the same Period, both in the same plane.
Object number one is in a circular orbit.
Object number two is in a very eccentric orbit.
Is it possible to set this up so that the aphelion of Object 2 always touches the actual body of object 1?

- rthorvald

[selden]

Celestia does not yet support precession of orbits, which is what you're describing. It only has precession of planetary axes. You'd have to use an xyz trajectory.

[rthorvald]

Celestia does not yet support precession of orbits, which is what you're describing. It only has precession of planetary axes. You'd have to use an xyz trajectory.

Aha, thank you. But an XYZ file is out of the question. I am trying to make an Aldrin orbital cycler (or whatever it is called), and an XYZ would only be practical for a very limited time.

Is there a (plain english) method for calculating the Period needed for an object travelling in one orbit to touch two objects travelling in two different other orbits on a regular basis?

- rthorvald

[selden]

Is there a (plain english) method for calculating the Period needed for an object travelling in one orbit to touch two objects travelling in two different other orbits on a regular basis?

Yes.

Oh, you want to know what it is?

The semimajor axis of an orbit which touches two other orbits is the one half of the sums of the semimajor axes of those two other orbits:

a = (a1+a2)/2

a = semimajor axis

In our solar system, the period of an orbit around the Sun, measured in Earth years, is the square root of the cube of that orbit's semimajor axis, measured in Astronomical Units, so

P = sqrt(((a1+a2)/2.0)**3)

or, equivalently,

P = ( (a1+a2)/2.0 )**1.5

Does this help?

p.s.
You neglected to ask "what's the eccentricity of this orbit?"

It's the the apocenter of the orbit minus the pericenter of the orbit, divided by the sum of the apocenter and pericenter. If the orbits of the two planets are circular, then the apocenter distance is the semimajor axis of the orbit of the outer planet, and the pericenter distance is the semimajor axis of the orbit of the inner planet.

e = (a2 - a1)/ (a2 + a1)

(If the orbits of the planets are elliptical, then the Hohmann orbit's parameters have to change with time. In other words, a cyclical orbit cannot be described accurately using Keplerian orbital parameters. Gravitational effects have to be used to make it work properly. Celestia can't model that.)

Here's a diagram of one such orbit.



And here's the SSC I used to generate it

Code: Select all

"planet one" "alphard" {

   Radius 20000
   Color [ 0 1 1]

   EllipticalOrbit {
      Period 1
      SemiMajorAxis 1
}}

"planet two" "alphard" {

   Radius 10000
   Color [ 1 0 0]

   EllipticalOrbit {
      Period        2.828427 # sma**1.5
      SemiMajorAxis 2
}}


"Hohmann orbit" "alphard" {

   Radius 1
   Color [ 1 1 0]

   EllipticalOrbit {
      Period        1.837117    # ((a1+a2)/2)**1.5
      SemiMajorAxis 1.5         # (a1+a2)/2.
      Eccentricity 0.3333333    # (a2-a1)/(a2+a1)
}}

.

[rthorvald]

(If the orbits of the planets are elliptical, then the Hohmann orbit's parameters have to change with time. In other words, a cyclical orbit cannot be described accurately using Keplerian orbital parameters. Gravitational effects have to be used to make it work properly. Celestia can't model that.)

Selden, thank you very much for your detailed reply and example: it certainly helped. Though your last remark (Above) tells me i can??t do this in Celestia, since the orbits of both planet A and B are slightly elliptical. (0.044 and 0.041, respectively). Nor can i change these values just to facilitate this.

I wonder if i can??t have the craft orbit a point between the two planets instead, and have that orbit touch the two planet orbits (BTW, while this is a workaround for Celestia, is something like this possible in reality?) It will make it possible to have the craft touch both planets once every full orbit - by letting the orbital center of the ship have the same period as planet A while the ship orbits with the period of planet B.

But then there will be a slight cyclic drift because of the differences in eccentricity. How can i find the eccentricity of this orbital center so that it matches either A or B? That way, the ships orbit will always touch at least one of them at the same point, while the cyclic variation only happens at the other end...

- rthorvald

[selden]

If you're willing to accept non-physical configurations, all sorts of things are possible

I'll have to think about it for a while.