Peskie
New member
Greetings. This is my first time starting a new topic on this forum, I hope I put it in the right place. And I'll apologize up-front for the long post.
Recently I happened to cross paths with http://en.wikipedia.org/wiki/Rama_(spacecraft) and thought about adding a Rama vessel to Orbiter with a set of scenarios.
Rendezvous with Rama was always one of my favourite Sci-Fi books. Many years ago when first reading it I recall doing the calculations to check Clarke's description of the diameter, rotation, and centripetal acceleration and being pleasantly surprised that all the math worked out (i.e. Clarke had done the math when writing the book). So I figured I'd be able to use the books descriptions of Rama's orbit to create a matching orbit within Orbiter...
Has anyone else tried doing this? A forum and Google search turned up nothing.
I tried doing it and ran into difficulties. Basically the time from around Venus to the specified perihelion doesn't work for a hyperbolic orbit; the orbit would need to be elliptical for the time and distance specified (details below). Perhaps someone here can see if I've made a mistake in my procedure, assumptions, or understanding of the text.
Here are the relevant bits of information from the book that could be used to come up with an orbit:
So I tried to come up with some orbital elements using the scenario editor to adjust the orbit of a random vessel to see what it gave.
Now I just need an eccentricity that gives:
The problem is that to get #2 the eccentricity needs to be <1! According to the scenario editor, with an eccentricity of 1.0000001 (the closest value to 1 that it will let me enter) I get a PeT of only ~1.97e6 seconds (~22.8 days). (An eccentricity of 0.99 @ 0.816 AU still only gives a PeT of 2.14e6 seconds).
Is there *any* way to make a hyperbolic orbit that takes ~40d to go from ~0.72 AU to <0.134 AU from Sol? If I'm right and there isn't, does it seem reasonable to just go with an eccentricity of 1.05 so that in my scenario there would be only ~1.7e6 seconds=19.8 days from intercept to perihelion?
Given that this post has become quite long I'll leave the discussion on what to do with Endeavor's departure time and Rama's near Sol course correction to a future post.
Thanks!
Recently I happened to cross paths with http://en.wikipedia.org/wiki/Rama_(spacecraft) and thought about adding a Rama vessel to Orbiter with a set of scenarios.
Rendezvous with Rama was always one of my favourite Sci-Fi books. Many years ago when first reading it I recall doing the calculations to check Clarke's description of the diameter, rotation, and centripetal acceleration and being pleasantly surprised that all the math worked out (i.e. Clarke had done the math when writing the book). So I figured I'd be able to use the books descriptions of Rama's orbit to create a matching orbit within Orbiter...
Has anyone else tried doing this? A forum and Google search turned up nothing.
I tried doing it and ran into difficulties. Basically the time from around Venus to the specified perihelion doesn't work for a hyperbolic orbit; the orbit would need to be elliptical for the time and distance specified (details below). Perhaps someone here can see if I've made a mistake in my procedure, assumptions, or understanding of the text.
Here are the relevant bits of information from the book that could be used to come up with an orbit:
- 31/439 Rama "was detected while it was still outside the orbit of Jupiter" (Chapter 2). That would be at >~5.77 AU from Sol. This was sometime in 2031.
- It's on a hyperbolic orbit relative to Sol; eccentricity > 1
- "Perhaps during the next few years some spaceship on its ordinary business might be routed close enough to get good photographs." (Ch2) This should give an approximate upper limit on the velocity/eccentricity (too high and it wouldn't stay in the solar system for years).
- "An actual rendezvous was most unlikely; [...] cutting across the orbits of the planets at more than a hundred thousand kilometers an hour." (Ch2) That's 27.78 km/s but it's not clear if that's out by Jupiter or by the inner planets (the wikipedia page seems to assume that it's the speed at detection).
- Several months later Rama is observed by a lunar telescope to have a rotational period of ~4 minutes.
- At some unspecified time later there was a meeting and then "Three months later, the space-probe, rechristened Sita, was launched from Phobos, the inner moon of Mars. The flight time was seven weeks [...]". "The two bodies would pass each other at two hundred thousand kilometers an hour." (Ch3) Once I've got the basic orbit figured out I could use this information to rotate the orbit around Sol to line it up for the specified intercept (e.g. tweak the argument of periapsis and possibly the inclination and LAN).
- Around a month later Endeavour rendezvous with Rama. It's unclear where Endeavour starts from, only that "the ship had been on a routine mission, checking and emplacing asteroid warning beacons" (Ch4); and "it had been necessary to rob three other ships [...] even with all the extra propellant [...] Rama was already inside the orbit of Venus when Endeavour caught up with it. No other ship could have done so." That's within ~0.72 AU of Sol.
- "In forty days they would reach perihelion, and pass within twenty-million kilometers of the Sun." (Ch4) That gives PeR = ~20e9 m = 0.134 AU and at around 0.72 AU from Sol a PeT = ~40 days = 3.456e6 seconds.
So I tried to come up with some orbital elements using the scenario editor to adjust the orbit of a random vessel to see what it gave.
- for simplicity I initially started with:
- inclination of 0
- longitude of ascending node 0
- argument of perapsis of 0
these coould be adjusted later to have the path cross near enough to Mars for the specified intercepts.
- a perihelion of 20e9 m = 0.134 AU
Now I just need an eccentricity that gives:
- Vel ~27.78 km/s at ~5.77 AU from Sol (if I use the value as the detection velocity as the wikipedia page does)
- PeT ~3.456e6 seconds at ~0.72 AU from Sol
The problem is that to get #2 the eccentricity needs to be <1! According to the scenario editor, with an eccentricity of 1.0000001 (the closest value to 1 that it will let me enter) I get a PeT of only ~1.97e6 seconds (~22.8 days). (An eccentricity of 0.99 @ 0.816 AU still only gives a PeT of 2.14e6 seconds).
Is there *any* way to make a hyperbolic orbit that takes ~40d to go from ~0.72 AU to <0.134 AU from Sol? If I'm right and there isn't, does it seem reasonable to just go with an eccentricity of 1.05 so that in my scenario there would be only ~1.7e6 seconds=19.8 days from intercept to perihelion?
Given that this post has become quite long I'll leave the discussion on what to do with Endeavor's departure time and Rama's near Sol course correction to a future post.
Thanks!