Help with totalling AU between worlds

[zero]

I am at the moment going through plotting a game set in our solar system that uses Reaction Drives to travel between each planet.

I want to get travel distances accurate between each world, and whilst I know the AU each planet is from the sun and how to total the closest and furthest distances in AU from that, I am stuck when the planets are between those two areas.

I basically need some teaching in how the distances in orrery programs like Solar System Live, a webpage I visit, can be used to total AU for journeys between planets that do not involve the Earth, such as for example, a journey from Jupiter to Neptune or Mars to Uranus etc, on a given date.

Whilst I could handwave and use the minimum distance or maximum thanks to plot, I don't want to, as I'm going hard scifi and want to use actual dates and know exactly how many AU would lie between two planets for a trip, so I don't have to rely on blasting off from Earth or using it as a destination every single trip.

Any help put in layman's terms to help a guy learn this stuff would be greatly appreciated,

Thanks in advance!

 

[far-trader]

Would a simple trig equation work? Using the sun as one point of the triangle, knowing the angle at that point (choosing where in the sky the two planets are to each other) and the length of the two legs (the distance from the sun to each of the two planets), solve for the third leg (your trip distance)?

a² = b² + c² - 2bc cos A (I think)

 

[rust]

Well, this is rocket science. :shock:

A table of ephemerides, not difficult to find on the Internet, can give
you the rather precise positions of the planets for any date, and it is
also not difficult to calculate the straight line distances between pla-
nets with these data.
However, these straight line distances are somewhat meaningless, be-
cause the spaceship would have to move on a curved transfer orbit to
travel between planets, and this orbit depends on the amount and du-
ration of the spaceship's acceleration, the orbital speed of the planets,
their gravitational influences, and so on.

I am not convinced that the added degree of realism for a roleplaying
game would be worth the effort to delve into higher mathematics, so
in my view a compromise as it is used for example in the GURPS Spa-
ceships PDF would be good enough.

 

[far-trader]

...However, these straight line distances are somewhat meaningless, be-
cause the spaceship would have to move on a curved transfer orbit to
travel between planets, and this orbit depends on the amount and du-
ration of the spaceship's acceleration, the orbital speed of the planets,
their gravitational influences, and so on.

True, but as you say, it's a game, the extra effort is not required (seems wasted even), especially (iirc) when the reaction drives in question are undoubtedly NOT realistic in any real sense

Traveller reaction drives (again iirc) do effectively make it a straight line flight with little change in the distance over the very short time traveled.

 

[rust]

Traveller reaction drives (again iirc) do effectively make it a straight line flight with little change in the distance over the very short time traveled.

This depends a bit on what you consider a "little change in the distance".

For example, with a reaction drive with enough fuel to accelerate all the
time at 2 G (full acceleration to the mid point, turn around and full dece-
leration to the destination) a voyage of 5 AU takes approximately 4 1/2
days.
Provided the destination planet is Earth, it has an orbital velocity of about
18.5 miles per second, so it will have moved approximately 7 million miles
during these 4 1/2 days of the voyage, roughly 30 times the average dis-
tance between Earth and Moon.

 

[far-trader]

...and that 7 million miles will change that to what? About (just a guess) plus or minus half a day? Not insignificant but not a lot either.

EDIT: Ah, but on re-reading you probably mean the straight line part I'm guessing. Still pretty much effectively a straight line shot I think. My gut says it can't be many degrees off... but I've been wrong before

 

[rust]

It has the potential to become a nasty can of worms when
the spaceship does not carry enough fuel for a permanent
acceleration with its reaction drive, and therefore has to
spend some time coasting, leading to longer voyage times
and greater consequences of the planets' orbital velocities.

But, as mentioned, I would happily ignore that level of rea-
lism as well as the precise locations and distances of the pla-
nets. For interplanetary voyages in my settings I simply use
the orbital radius of the further planet as the travel distance,
so Jupiter is always approximately 5.2 AU from Earth.

Beyond that, mathematics would begin in earnest ... :shock:

 

[AndrewW]

Celestia will tell you the distance between objects (say between Jupiter and Mars for example):

http://www.shatters.net/celestia/

 

[zero]

Far-Trader, trig would be great and thanks for the help, but I am awful at that whole level of math, I really need something more layman or at least explained to me that I can use my windows calculator to sort out a total

I'm playing Cstars, which uses the T-Drive; like a mini Jump drive it pushes the ship forward in a straight line a distance of 1.25AU in a week, into to coasting speed of 1 AU per 5.83 days. The M-Drive can make any turn needed that the astrogator missed out when plotting the T-Drive usage.
Then a deccel is needed for the T-Drive that means another 1.25AU is travelled in a straight line to the destination.

So, say we have a journey from Earth to Neptune with a distance of 29 AU between them, the ship leaves Earth and the T-Drive pushes the ship 1.25 AU straight in the first week, then it travels more freely for 26.5 AU (154.5 days - just over five months coasting) - then the T-Drive deccels the last 1.25 AU in a straight line over the last week to Neptune space.

6 months from Earth to Neptune when closest and the astrogator is going to need to know where Jupiter will be six months from the current date to plan the correct course.

The Cstars book has a min/max time for the closest and furthest planets are, but I wondered if it was mathematically ok to do the inbetween positions?

 

[BP]

You have a two-burn sequence? Sounds like a classic Hohman Transfer orbit. Well, except the 'straight line' bit - which cannot happen without overcoming the initial orbital motion (if one started somewhere in system) and the pull of the system's sun. If you are aiming for even pseudo realism it is important to understand that fundamentally reality works on curves (a straight line being just a special case of a curve)

If you really want to do this, even just superficially, you can't be afraid of a little math or you will not succeed. Crude approximations can be way, way off - however they can provide a starting point.

Dealing with 'realistic' transits is actually easier than with Traveller's constant acceleration model - in that a lot of RW info exists (earth orbital transits are similiar to interplanetary). A quick google of 'transfer orbits' will yield plenty of goodness. Try these:

http://en.wikipedia.org/wiki/Hohmann_transfer_orbit
http://www.braeunig.us/space/orbmech.htm
http://www.physicsforums.com/showthread.php?t=29524

I quickly skimmed them and they don't look too bad.

Look up real world space probes - most, of course, use flybys for gravitational assists (though ion drive probes, like Dawn, don't need to and can even pause for to orbit things - they are more akin to Traveller ships, though with markedly lower acceleration). Sometimes its worthwhile to get a gravity assist from the world one is departing from - ala the Juno probe (I got to hold an actual instrument on this one ) - sometimes, even multiple times - like Rosetta (dad fab-ed Alice instrument ).

Good luck - and stick with it. The experience can be quite worthwhile (even if you never get to plot transfer orbits for real spacecraft).

 

[zero]

Thanks, BP! I already know the math behind coasting speeds and accel/deccel as a seasoned Traveller player, I actually managed to get pretty far totalling things out, but now I have got to a point that is far too complex for myself alone!

Perhaps I worded it a little wrong, but what I meant to say in my previous post was when the T-Drive is activated, the ship cannot be turned by a pilot and goes where the thrusters push it. How accel/deccel of the ship affects the direction the ship goes in, well thats the difficult bit.

The exact acceleration it does in space (as in Cstars the law dictates a minimum distance from a planet to fire it up due to it's dangerous exhaust) is pretty unknown.

But I managed to figure out through (alot of) mathematics (and science) that it pushes 1.25 AU in a week to put the ship's coasting speed to 296,991.137793025 m/s (something I totalled as the fluff of 150,000 m/s was far too slow for the journeys presented in the crunch when I tried to do the math to calculate trips).

But with a coasting speed that low, the accel/deccel is less than a consistent 1G, yet the crew need to be put in Grav-Couches in the crunch when the T-Drive runs.

So... it must work as a pulse drive mechanism, acceling/decceling the ship a high number of Gs every now and then, slowly making the ship accel/deccel faster and faster.

If its 9G increments, 3,365 (rounded) seconds would be spent on acceling/decceling, which would be approximately 20 seconds for each hour in the week the T-Drive is active.

Further help would be much appreciated!

 

[Mithras]

Go here, problem solved:

http://orbit-downloader.brothersoft.com/orbit-downloader2.2.1

 

[Mithras]

Of course you need to know delta V...

 

[zero]

Luckily I know how to calculate delta-v and similar mechanics thanks to the Project Rho Atomic Rockets site, but instead I'm speaking more about Torchships and the use of orrerys to total the distance between the min and max distance two planets have on a specific date (something beyond even Project Rho's math and formulaes).

I already have the Solar System Live website in my favourites list for this purpose, but it is only any good if I want to go to or leave Earth. I don't want to be that restricted in an ongoing game.

 

[rust]

You should find all the data you need in the Astronomical
Almanac, and it should not be difficult to calculate the dis-
tances between any planets at any moment in time once
you have their precise locations:

http://asa.usno.navy.mil/

 

[zero]

The thing is that I am finding it difficult, to the point I may think I have mathematical dyslexia (I'm not being funny, I genuinely have trouble with numbers alot of the time).

If I could find out how to work out how many AU are between worlds based on the info given about them (Ascension, Declination, Altitude and Azimuth) I'd be ok.

Saying that, is there anyone who has this info that could do a working example to show how many AU are between worlds that do not involve Earth?

 

[saundby]

Here's a quick and dirty way to get a WAG that may be good enough for you:

Add the average orbital distances of the two bodies. That's your transfer orbit diameter (d).
You'll travel half its circumference, pretend it's a circle, not an ellipse: 1/2*PI*d.

Trim it a tad if you like, maybe use 3 instead of Pi. So it becomes 1.5*d.

Example:
Mercury to Venus:
d=.39+.72=1.11AU
1/2PI(d)=1.74AU (method 1)
or 1.5*d=1.67AU (method 2)

Jupiter to Saturn:
d=5.20+9.54=14.74
so 23.2 or 22.1 AU.

 

[Yatima]

There's a relatively simple system to do what you require in the Normal Space Tasks appendix of the Megatraveller Starship Operator's Manual. It takes the task of calculating the distance between two worlds and reduces it to a page and a half of diagrams tables and a few simple sums. It works like this:

1. Determine the relative positions of the two points in the system - reduced to six points on each of two concentric circles so you can roll D6 to see which of the six points a planet is in on the inner orbit and the same for the outer orbit.
2. Determine which of three types of trajectory are required to move between the two points on the inner and outer orbits - each trajectory is a Hohmann Transfer orbit, a segment of a circle linking the points on the inner and outer orbits.
3. This all reduces to a sum that determines the distance to be covered, you can then work out how much deltaV you need to move between the orbits.

There's a bit of math here, but not as much as if you tried to work out a real-world orbital mechanics solution - it's all abstracted away into a very simple model that feels good enough for the purposes of game play without turning play sessions into a Nasa seminar.

J