Steve Jackson Games - Site Navigation
Home General Info Follow Us Search Illuminator Store Forums What's New Other Games Ogre GURPS Munchkin Our Games: Home

Go Back   Steve Jackson Games Forums > Roleplaying > GURPS

Reply
 
Thread Tools Display Modes
Old 11-04-2017, 03:53 PM   #1
hal
 
Join Date: Aug 2004
Location: Buffalo, New York
Default Halfway to Anywhere Article and ASTROSYNTHESIS

For those who might be interested, ASTROSYNTHESIS has a function that shows the orbits of various planets around any given star. You can use the ability to show where worlds will be on any given date simply by allowing each second that passes real time to equal any given ratio of time in the display. Thus, you can watch Earth, Mars, Venus, and Mercury whip about the system at an accelerated pace.

When entering the planetary data by hand, one would need to enter in the following variables such as:

Distance from Sun (orbital radius in kilometers)
Eccentricity of orbit
Inclination of orbit
Ascending Node (degrees)
Periapsis Angle (degrees)
Time Past Periapsis (Days)
Rotation in hours
Axial Tilt (degrees)

At one point in time, I began to experiment with trying to get the Solar System diagram to match that of TRANSHUMAN SPACE for the year 2100 AD. I got it to look very close to the paper drawn map. :)

I could easily enough, by altering the value in days for Time Past Periaspsis, get the worlds to be more or less as shown on the map. But this bit of information in PYRAMID 3/79, under HALFWAY TO ANYWHERE, said the following that got my interest...

"Launch Windows
Both Hohmann transfers and bi-elliptic transfers require
the calculation of launch windows – times when the angle
between the destination through the primary to the point of
origin is such that the spaceship catches up to and stops at
its intended target. While the calculation of this angle is not
particularly difficult, the rules for generating star systems in
Space don’t provide the requisite information, thus boiling
the entire exercise down to GM arbitration.
"

What would it take to generate that specific information for the dermination of launch windows? Is the information above sufficient (for Astrosysnthesis with ascending node and days past periapsis) for the calculations?

Just curious. I'm digging in deeper to that article to see if it has any information pertaining to how one calculates "drift" times when leaving a world's orbit, and heading to a destination world's orbit using newtonian physics.

I SOOO want to merge/meld worlds generated using GURPS SPACE into ASTROSYNETHESIS. Just using ASTROSYNTHESIS to keep track of planetary locations with the solar system for a TL 9 campaign looks nice!
hal is offline   Reply With Quote
Old 11-05-2017, 07:42 AM   #2
RyanW
 
RyanW's Avatar
 
Join Date: Sep 2004
Location: Southeast NC
Default Re: Halfway to Anywhere Article and ASTROSYNTHESIS

The ascending node and periapsis angle tell you how the orbits line up, and the days past periapsis tells you where along their orbits the planets start. Without that information, you can find an average of the frequency and delta-v of transfers, but not the details of any specific transfer.
__________________
RyanW
- Actually one normal sized guy in three tiny trenchcoats.
RyanW is offline   Reply With Quote
Old 11-05-2017, 12:39 PM   #3
hal
 
Join Date: Aug 2004
Location: Buffalo, New York
Default Re: Halfway to Anywhere Article and ASTROSYNTHESIS

Quote:
Originally Posted by RyanW View Post
The ascending node and periapsis angle tell you how the orbits line up, and the days past periapsis tells you where along their orbits the planets start. Without that information, you can find an average of the frequency and delta-v of transfers, but not the details of any specific transfer.
So, if you had how many days past Periapsis, and you had a means of measuring the locations of any given planet along its orbit, could you then determine where the launch windows would be and when?

I'm wondering how possible it would be to find someone who can point me to where I can find formulas for describing how far along the orbit any given planet is/was. For example? I recall from my high school days, that the distance travelled in a given time unit along the oribit - will create a triangle between the two points on the orbit and the star - that will equal the area of two points on the orbital track of the same time duration. Thus, at further distances and seemingly slower movement, the triangle formed by those three points will equal the triangle formed by the two points along the orbit closer to the sun that seemingly traversed a larger distance along the orbit (ie faster movement).

While I can get a formula to describe an ellipse of a given eccentricity - determining how to figure out planetary motion along the orbit has eluded me. Being able to know where planets are, relative distances between any given point along an orbit, and even something like reactionless or Newtonian movement might prove to be interesting.

But, if nothing else, Astrosynthesis does seemingly allow you to set the planet along a given point in its orbit, and then track planetary motion to the point where it can do time lapse movement and even export the information to a movie file. Being able to set the planets in relative positions that ape that found in TRANSHUMAN SPACE map is particularly nice.
hal is offline   Reply With Quote
Old 12-15-2017, 03:40 AM   #4
loofou
 
Join Date: Dec 2014
Default Re: Halfway to Anywhere Article and ASTROSYNTHESIS

Quote:
At one point in time, I began to experiment with trying to get the Solar System diagram to match that of TRANSHUMAN SPACE for the year 2100 AD. I got it to look very close to the paper drawn map. :)
I know this is very late, but do you still have this file around? I am trying to do the same thing (getting a proper map for THS in digital form). I played around in Astrosynthesis for a while, then tested SpaceEngine, and now I try to go back to AstroSynthesis because it's cleaner and easier to use. I found this page and am wondering if you might want to share your file for the THS system.
loofou is offline   Reply With Quote
Old 12-16-2017, 01:26 PM   #5
Humabout
 
Humabout's Avatar
 
Join Date: Aug 2008
Default Re: Halfway to Anywhere Article and ASTROSYNTHESIS

Quote:
Originally Posted by hal View Post
What would it take to generate that specific information for the dermination of launch windows? Is the information above sufficient (for Astrosysnthesis with ascending node and days past periapsis) for the calculations?
A Hohhman transfer will intercept the destination orbit 180 degrees (pi radians) from your origin (opposite sides of their orbits). Bi-elliptics are far more complicated and actually let you adjust your launch window based on the two ellipses used.

To find when you need to launch, you need to know a two things not generated by GURPS Space:
  • Mean Anomaly* of the Origin: MA_o
  • Mean Anomaly* of the Destination: MA_d
You also need a few things you should already have from Space:
  • Mass of the primary: m_p
  • The orbital radius of the origin: a_o
  • The orbital radius of the destination: a_d
Then you need to calculate a couple of things:
  • Orbital Speed of the Origin: v_o = sqrt[G x m_p/ a_o]
  • Orbital Speed of the Destination: v_d = sqrt[G x m_p / a_d]
  • Angular Velocity of the Destination: w = 1 / sqrt[(r_d^3) / (G x m_p)]
  • Time of Flight (see below for where you find this calculation in the article)
Once you have this information, you can find the phase angle for your transfer: Y = (v_d - v_o) - w x (T)

You can launch when MA_d - MA_o = Y. Make sure you use SI units (meters, seconds, and kilograms). Your answer will be in radians. This alignment will occur once per synodic period (see p. 26 for the calculation in GURPS units).

* Note that Mean Anomaly equals True Anomaly in the case of circular orbits, so there's no reason to dive down the rabbit hold of calculating True Anomaly.

Quote:
Originally Posted by hal View Post
I'm digging in deeper to that article to see if it has any information pertaining to how one calculates "drift" times when leaving a world's orbit, and heading to a destination world's orbit using newtonian physics.
The time it takes to complete a transfer is given by solving for T under each transfer type:
  • Hohhman: p. 26-27
  • Bi-Elliptic: p. 27
  • Brachistochrone: p. 27-28
They are also given under Index of Formulae (p. 28) and in SI units under Formulae by the Numbers (p. 29).
__________________
Buy My Stuff!

Free Stuff:
Dungeon Action!
Totem Spirits

My Blog: Above the Flatline.
Humabout is offline   Reply With Quote
Old 12-16-2017, 01:41 PM   #6
Humabout
 
Humabout's Avatar
 
Join Date: Aug 2008
Default Re: Halfway to Anywhere Article and ASTROSYNTHESIS

Quote:
Originally Posted by hal View Post
So, if you had how many days past Periapsis, and you had a means of measuring the locations of any given planet along its orbit, could you then determine where the launch windows would be and when?
You need to take your Mean Anomaly at a specific time so you have a reference point. Remember that literally everything is moving. That's why my above launch window calculation gives you a phase angle - the position of the destination with respect to the origin, in this case. You can't know when that angle will occur unless you have a starting point to work from. Also, were I to arbitrarily choose such a starting point, it'd be at an alignment so I could literally just count forward by synodic periods to find every alignment in the future.

If I were setting up an entire solar system, I'd probably take my datum with all of the planets lined up in a row on one side of the primary, so that every one is halfway through its synodic period with any other planet. That would make calculating launch windows much simpler; I'd just need to know the synodic period between any two planets and then just count forward.


Quote:
Originally Posted by hal View Post
I'm wondering how possible it would be to find someone who can point me to where I can find formulas for describing how far along the orbit any given planet is/was.
This is actually pretty simple:

1) Find Angular Velocity: w = 1 / sqrt[(a^3) / (G x m_p)]
2) Multiply Angular Velocity by the time elapsed from when you took your datum. This is the Angular Displacement from your datum the body has moved in that time.
3) Divide the Angular Displacement by (2 x pi) to find how far around the orbit your body is from its starting point.

Note that all calculations above should use SI units and give angles in radians.

Quote:
Originally Posted by hal View Post
Thus, at further distances and seemingly slower movement, the triangle formed by those three points will equal the triangle formed by the two points along the orbit closer to the sun that seemingly traversed a larger distance along the orbit (ie faster movement).
If you're using Keplerian orbits, you shouldn't be using Hohhman transfers. Those only work for circular orbits. If you can assume your orbits are circular, the planets won't be speeding up at any point in their orbit.

Quote:
Originally Posted by hal View Post
While I can get a formula to describe an ellipse of a given eccentricity - determining how to figure out planetary motion along the orbit has eluded me.
I have a MATLAB script I wrote that will do this, if you want me to send it to you. Otherwise, for Keplerian orbits, you're in for a world of hurt. You will need to use an iterative method (bisection, Newton-Raphson, secant method, etc.) to solve a transendental equation to find the True Anomaly as many times as you want the planet's position. Computers are the way to go here, for sure.
__________________
Buy My Stuff!

Free Stuff:
Dungeon Action!
Totem Spirits

My Blog: Above the Flatline.
Humabout is offline   Reply With Quote
Old 12-16-2017, 05:40 PM   #7
Nemoricus
 
Join Date: Mar 2013
Default Re: Halfway to Anywhere Article and ASTROSYNTHESIS

Quote:
Originally Posted by Humabout View Post
If you're using Keplerian orbits, you shouldn't be using Hohhman transfers. Those only work for circular orbits. If you can assume your orbits are circular, the planets won't be speeding up at any point in their orbit.
Huh? Kepler's laws explicitly apply to all elliptical orbits. It's right there in the first law stating that all orbits are ellipses.
__________________
For GURPS reviews and Psi-Wars inspired content, check out my blog at Libris Ludorum!
Nemoricus is offline   Reply With Quote
Old 12-16-2017, 09:19 PM   #8
Humabout
 
Humabout's Avatar
 
Join Date: Aug 2008
Default Re: Halfway to Anywhere Article and ASTROSYNTHESIS

Quote:
Originally Posted by Nemoricus View Post
Huh? Kepler's laws explicitly apply to all elliptical orbits. It's right there in the first law stating that all orbits are ellipses.
Hohmann tranfers only apply to circular orbits, not elliptical ones.
__________________
Buy My Stuff!

Free Stuff:
Dungeon Action!
Totem Spirits

My Blog: Above the Flatline.
Humabout is offline   Reply With Quote
Old 12-17-2017, 12:32 AM   #9
Nemoricus
 
Join Date: Mar 2013
Default Re: Halfway to Anywhere Article and ASTROSYNTHESIS

Ah, my apologies. I misunderstood what you were saying.
__________________
For GURPS reviews and Psi-Wars inspired content, check out my blog at Libris Ludorum!
Nemoricus is offline   Reply With Quote
Old 12-17-2017, 12:06 PM   #10
Humabout
 
Humabout's Avatar
 
Join Date: Aug 2008
Default Re: Halfway to Anywhere Article and ASTROSYNTHESIS

Quote:
Originally Posted by Nemoricus View Post
Ah, my apologies. I misunderstood what you were saying.
All good. I make mistakes, so point them out if you see them.
__________________
Buy My Stuff!

Free Stuff:
Dungeon Action!
Totem Spirits

My Blog: Above the Flatline.
Humabout is offline   Reply With Quote
Reply

Thread Tools
Display Modes

Posting Rules
You may not post new threads
You may not post replies
You may not post attachments
You may not edit your posts

BB code is On
Fnords are Off
[IMG] code is Off
HTML code is Off

Forum Jump


All times are GMT -6. The time now is 07:05 AM.


Powered by vBulletin® Version 3.8.9
Copyright ©2000 - 2024, vBulletin Solutions, Inc.