11-04-2017, 03:53 PM | #1 |
Join Date: Aug 2004
Location: Buffalo, New York
|
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! |
11-05-2017, 07:42 AM | #2 |
☣
Join Date: Sep 2004
Location: Southeast NC
|
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. |
11-05-2017, 12:39 PM | #3 | |
Join Date: Aug 2004
Location: Buffalo, New York
|
Re: Halfway to Anywhere Article and ASTROSYNTHESIS
Quote:
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. |
|
12-15-2017, 03:40 AM | #4 | |
Join Date: Dec 2014
|
Re: Halfway to Anywhere Article and ASTROSYNTHESIS
Quote:
|
|
12-16-2017, 01:26 PM | #5 | ||
Join Date: Aug 2008
|
Re: Halfway to Anywhere Article and ASTROSYNTHESIS
Quote:
To find when you need to launch, you need to know a two things not generated by GURPS Space:
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:
__________________
Buy My Stuff! Free Stuff: Dungeon Action! Totem Spirits My Blog: Above the Flatline. |
||
12-16-2017, 01:41 PM | #6 | |||
Join Date: Aug 2008
|
Re: Halfway to Anywhere Article and ASTROSYNTHESIS
Quote:
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:
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:
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. |
|||
12-16-2017, 05:40 PM | #7 |
Join Date: Mar 2013
|
Re: Halfway to Anywhere Article and ASTROSYNTHESIS
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! |
12-16-2017, 09:19 PM | #8 |
Join Date: Aug 2008
|
Re: Halfway to Anywhere Article and ASTROSYNTHESIS
Hohmann tranfers only apply to circular orbits, not elliptical ones.
__________________
Buy My Stuff! Free Stuff: Dungeon Action! Totem Spirits My Blog: Above the Flatline. |
12-17-2017, 12:32 AM | #9 |
Join Date: Mar 2013
|
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! |
12-17-2017, 12:06 PM | #10 |
Join Date: Aug 2008
|
Re: Halfway to Anywhere Article and ASTROSYNTHESIS
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. |
Thread Tools | |
Display Modes | |
|
|