Orbital Mechanics software or refresher tutorial

[SpaceBadger]

Looking for understandable online tutorials or better yet software to do the calculations for me.

My last physics, trig, math analysis, and calculus classes were in high shool, 32+ years ago. I got A grades and did well enough on CLEP tests not to retake these subjects in college. I enjoyed all of those subjects at the time, especially the ability to do space-related mathematical thought experiments, but subsequent grad school and career have involved almost zero math, and unused skills grow extremely rusty.

I can still figure easy stuff like Hohmann transfers and basic elliptical orbits, and I think I have the concepts for changing orbits by maneuvers, but the math part is eluding me.

Among other things, I want to be able to at least:

1) Calculate non-optimal interplanetary travel using extra fuel - faster than Hohman transfer, but not the simple straight-line accelerate halfway then flip and decelerate. I can visualize this as using a higher delta-V burn to get into an ellipse that will intercept faster than the Hohmann transfer, then doing another burn at the end to circularize and match orbits w destination, but the actual math has me boggled.

2) Figure the delta-V changes to go to higher/lower orbits and dock with something there. Again, I think I have the concepts but not the math.

I realize that we can skip over a lot of this w CT reactionless thrusters and continuous acceleration flipover courses, but I'd like to run a campaign without those.

I don't know whether it is age or current medications or too much alcohol in college or what, but I definitely have a harder time learning new material than I did 30+ years ago. I checked a wiki page on orbital mechanics and maneuvering and it was mostly Greek to me.

Again, either a pointer to some simple refresher course, or better yet some software that would let me plug in numbers and get answers, would be greatly appreciated.

 

[SpaceBadger]

I am pretty sure these formulae will require calculus (changing gravitational attraction as you move towards or away from primary body, even changing rates of change perhaps...) but I have forgotten how to do it.

 

[Timerover51]

Based on Maxwell Hunter's book, Thrust into Space, once you get up to velocities around 500,000 feet per second, you can pretty much ignore the effects of planetary gravitational fields, and plot direct courses. Now that does not assume accelerate half way and then decelerate the other half, as at one G acceleration, you would get up to 500.000 feet per second in about 4 hours.

 

[SpaceBadger]

Based on Maxwell Hunter's book, Thrust into Space, once you get up to velocities around 500,000 feet per second, you can pretty much ignore the effects of planetary gravitational fields, and plot direct courses. Now that does not assume accelerate half way and then decelerate the other half, as at one G acceleration, you would get up to 500.000 feet per second in about 4 hours.

Well, yes, at 500,000 feet/sec (152.4 km/sec) I agree you wouldn't worry much about planetary orbital velocities, just aim and go. If you have reactionless thrusters, then yes, of course that would be the way to do it, very simple. The thing is, I said I intended to use this for calculating courses without using reactionless thrusters. That's the whole point of the exercise.

What sort of M-drive did you have in mind that would let you accelerate at 1 G for 4 hours, and then presumably do the same to decelerate again at the end of your trip? Even giving you the benefit of starting and ending in orbit, and rounding off figures and ignoring matching orbital velocities, you are still talking about a total change in velocity (delta-V) of over 300 km/sec!

 

[Timerover51]

Well, yes, at 500,000 feet/sec (152.4 km/sec) I agree you wouldn't worry much about planetary orbital velocities, just aim and go. If you have reactionless thrusters, then yes, of course that would be the way to do it, very simple. The thing is, I said I intended to use this for calculating courses without using reactionless thrusters. That's the whole point of the exercise.

What sort of M-drive did you have in mind that would let you accelerate at 1 G for 4 hours, and then presumably do the same to decelerate again at the end of your trip? Even giving you the benefit of starting and ending in orbit, and rounding off figures and ignoring matching orbital velocities, you are still talking about a total change in velocity (delta-V) of over 300 km/sec!

I would be assuming the use of high-efficiency fusion reaction engines with a specific impulse around 4 million seconds, which is given in the Thrust Into Space book. A quick and dirty calculation shows that with that exhaust velocity, a delta vee change of around 1 Million feet per second can be achieved with a reaction mass equal to 25% of the initial mass of the ship. So, for a ship massing 400 tons, it would take 100 tons of Liquid Hydrogen fuel burned with very high efficiency.

 

[warwizard]

Fusion rocket: 2.8% of ship's volume in fuel used to do the 8 hrs of burn, assumming ship's mass averages 1 mt per m3. (T4 FF&S PP 105 Table 167)

 

[Timerover51]

Fusion rocket: 2.8% of ship's volume in fuel used to do the 8 hrs of burn, assumming ship's mass averages 1 mt per m3. (T4 FF&S PP 105 Table 167)

I guess that is the difference between Real World data, and Traveller handwavium. Against that, the Thrust Into Space book was released in 1965, so the data was out there already.

 

[SpaceBadger]

Thanks for the followups, timerover and warwizard. I am going to have to take a hard look at those numbers, because the best most optimistic estimates I've seen for fusion rockets or fusion or antimatter pulse systems is from 30,000 to 36,000 seconds Isp, which is still about a factor of 100 less than timerover's numbers, and I don't think I even want to try to ballpark the Isp on that fusion rocket from FF&S. (By comparison, something already pretty powerful like NERVA has estimated Isp of 800 to 1200 seconds, and chemical rockets way down in the 200 to 500 seconds range.)

 

[Timerover51]

Thanks for the followups, timerover and warwizard. I am going to have to take a hard look at those numbers, because the best most optimistic estimates I've seen for fusion rockets or fusion or antimatter pulse systems is from 30,000 to 36,000 seconds Isp, which is still about a factor of 100 less than timerover's numbers, and I don't think I even want to try to ballpark the Isp on that fusion rocket from FF&S. (By comparison, something already pretty powerful like NERVA has estimated Isp of 800 to 1200 seconds, and chemical rockets way down in the 200 to 500 seconds range.)

If you want and I have the time, I could transcribe the Thrust Into Space data for you. I would make sure that it is properly cited down to page number, and give all credit to Maxwell Hunter, the author. I believe that this would come under the "fair use for research" provisions of current copyright law.

 

[SpaceBadger]

BTW, after posting here (and posting similar questions on other game forums over the years) it finally occurred to me that my best friend from high school is an actual certified Rocket Scientist (well, aerospace engineer, close enough) so I emailed him about it. He is not practicing in that field any more, but had a class in orbital mechanics in college that he enjoyed very much and kept the textbook, so has promised to dig that up and see if he can send me some rough estimation procedures within my calculus-impaired math comprehension. If I get anything useful, I'll share it here.

 

[SpaceBadger]

OK, thanks, timerover, I would like to see that if you find the time for it!

 

[Timerover51]

OK, thanks, timerover, I would like to see that if you find the time for it!

I will try to get it done this week and post it here. I will see how much fission data that I can include too.

 

[whartung]

1) Calculate non-optimal interplanetary travel using extra fuel - faster than Hohman transfer, but not the simple straight-line accelerate halfway then flip and decelerate. I can visualize this as using a higher delta-V burn to get into an ellipse that will intercept faster than the Hohmann transfer, then doing another burn at the end to circularize and match orbits w destination, but the actual math has me boggled.

The term you're looking for here is Hyperbolic Orbits. The mechanics of the orbit I believe are less complicated than the actual timing of the maneuver (notably, launch itself).

I realize that we can skip over a lot of this w CT reactionless thrusters and continuous acceleration flipover courses, but I'd like to run a campaign without those.

Well the nut is not the duration of the acceleration, it's the magnitudes. A 1G drive is really, really powerful. It's what makes space travel practical at all, frankly, everything else simply takes too long. A 10G (1G for 10 hours, 5G for 2, etc.) burn will get you to Jupiter in a month (with an appropriate decel as well, but you need to compensate for gravity). In TNE, 10G burn is 20 G-Turns, since they use 1/2 hour turns, and the measure fuel by G-Turns.

So, unless you have severely limited fuel, even a 1G drive is going to be a "turn and burn" solution. Put Jupiter in the cross hairs and hold down the Turbo button, then coast for a bit and correct.

I've been dabbling with dynamic "turn and burn" plots, in that I constantly aim and correct, I'm not calculating a whole lot. Kind of amusing, at the moment, I can get the ship from Earth to Jupiter, but when it gets there, the ship gets confused and starts accelerating away -- hard! So, still working out the heuristics to get the ship in to a parking orbit. But I'm at least getting close.

 

[aramis]

10 G-Hours =360000m/s = 3.6e5m/s
semi-major axis, Jupiter 778.57x10^9 m = 7.7857e11
semi-major axis, earth 149.60x10^9 m = 1.496e11
Closest approach 6.2897e11

1.747e6 sec. = 485h = 20 days

10 G-hours is 20 days CLOSEST approach to jupiter. And requires another nearly-10 G-hours to enter orbit.

(at furthest, it's about 2.578e6 sec. or about 30 days)

Double those if you have to use your 10G-Hours of fuel for both ends.... which, you do. It's about 1.5 months at closest, and 2 months at furthest.

 

[SpaceBadger]

I've been dabbling with dynamic "turn and burn" plots, in that I constantly aim and correct, I'm not calculating a whole lot. Kind of amusing, at the moment, I can get the ship from Earth to Jupiter, but when it gets there, the ship gets confused and starts accelerating away -- hard! So, still working out the heuristics to get the ship in to a parking orbit. But I'm at least getting close.

Sounds like fun. What software are you using for that?

 

[Travellerspud]

you might check this out

http://orbit.medphys.ucl.ac.uk/

 

[whartung]

Sounds like fun. What software are you using for that?

Oh, just something I'm writing in Java. Real basic physical simulation and then adding logic to control the actual ship. Has the Sun, Earth, and Jupiter in it, all 3 bodies affect the ship, though I only have the Sun affect the Earth and Jupiter for their orbits.

Right now it works "OK", in that the ship will go from A to B, I can have it either burn the entire way, or I can set a max speed for it to stop accelerating. When it gets to the target, it's then actively orbits it (active as in it's thrusting all the time, it's not a true orbit).

It's funny to watch it decelerate. Without the max speed option, it never coasts, so it flickers between accelerating and decelerating, like a bad driver.

It's clearly too ham fisted to converge on the target the way it's supposed to, so I need to work on that. But it's cool to watch it orbit.

It was blasting away from the target early on because I had it triggering "decelerate" (which simply inverts the projected vector). However since it was past the target, it would fly away from it. Now I have a little better logic for deceleration.

With a 1G motor, and 10Ghr max speed, it never decelerates. It accelerated to cruise speed, and then it finds that it's passing the target and goes in to orbit. With out a max speed, it will decelerate.

Kind of magic to see it all sorta work.

 

[Timerover51]

OK, thanks, timerover, I would like to see that if you find the time for it!

Looks like you are planning on using "whartung" material. I will put the fusion data on the back burner then.

 

[SpaceBadger]

Looks like you are planning on using "whartung" material.

Huh?

I will put the fusion data on the back burner then.

Whenever it is convenient for you, then.

 

[whartung]

I stumbled on this, I don't know if this is what you're looking for or not.

But it's mostly in english, though I think it was set by the folks that typeset T4s FF&S.

http://www.projectrho.com/rocket/supplement/orbitalmech.html

DU is, basically, au (astronomical unit). TU is a "time unit". It's explained in this paragraph:

The gravitational parameter mu is equal to GM, where G is Newton's gravitational constant and M is the mass of the central body. For the Sun, mu = 1.32715 x 10^11 km^3/s^2, but we can make our lives a lot simpler by choosing units such that this constant works out to be 1. It turns out that if we use astronomical units (AU) for our distance unit and 5.0227 x 10^6 sec for our time unit, the gravitational parameter is 1 DU^3/TU^2. The time unit was chosen so that the velocity of the Earth in its orbit is 1 DU/TU. You can convert back to standard units at any time by multiplying times by 5.0227 x 10^6 sec (which is 58.13 days), or by multiplying velocities by 29.79 km/s (the orbital velocity of the Earth). It may seem a bit odd, but it is actually much easier to work in these units.

But it does talk about higher power orbit transfers, and it's step by step.

I don't think it takes in to account things like the gravity effect of other bodies (notably Jupiter -- it's a big hole in our sky). But it might be a start closer to what you were looking for vs my "turn and burn" Flash Gordon technique.