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Old 11-08-2017, 07:04 PM   #11
Anthony
 
Join Date: Feb 2005
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Default Re: Question regarding GURPS SPACESHIPS formulas

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Originally Posted by cvannrederode View Post
Yup, this is the heart of the matter. As a somewhat avid player of Kerbal Space Program, I can say transfer orbits are very much beyond a simple spreadsheet.
Well, a Hohmann transfer orbit between circular orbits (or orbits that are close enough to circular) isn't, and even the orbital insertion isn't too bad as long as you have a high thrust drive (there is some loss due to spiraling. This is mostly ignorable as long as drive thrust exceeds planetary gravity)

Orbital velocity is roughly 30 km/s * sqrt( 2/r - 1/a ), where r is your actual distance from the sun and a is your semi-major axis. The semi-major axis of a transfer orbit is equal to (r1+r2)/2. Thus, for an Earth to Mars, we get:
Earth orbital velocity: r = a = 1, v = 30 km/s
Mars orbital velocity: r = a = 1.52; v = 24.3 km/s
Transfer orbit at Earth: r = 1, a = 1.26, v = 33 km/s. Delta-V at Earth: 3 km/s
Transfer orbit at Mars: r = 1.52, a = 1.52, v = 21.7 km/s. Delta-V at Mars: 2.6 km/s.

Now, for the orbital insertion effect, the velocity required is sqrt( escape velocity ^ 2 + transfer velocity ^2 ) - current orbital velocity (if in orbit). Thus, Earth Surface->Mars Transfer requires total sqrt( 11.2^2 + 3^2 ) = 11.6 km/s, Earth Low Orbit requires 11.6-7.9 = 3.7 km/s. Earth Transfer->Mars Surface is sqrt( 5^2 + 2.6^2 ) = 5.6 km/s, Earth Transfer->Mars Low Orbit is 5.6 - 3.5 = 2.1 km/s.

The orbital period of your transfer orbit is SMA^3/2 or 1.41 years in this case, a transfer takes half a period. The interval between solutions is y1*y2 / abs(y1-y2) = 1.88/0.88 = 2.14 years. All of this can be done in a spreadsheet.
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Old 11-08-2017, 08:21 PM   #12
cvannrederode
 
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Default Re: Question regarding GURPS SPACESHIPS formulas

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Originally Posted by Anthony View Post
Well, a Hohmann transfer orbit between circular orbits (or orbits that are close enough to circular) isn't, and even the orbital insertion isn't too bad as long as you have a high thrust drive (there is some loss due to spiraling. This is mostly ignorable as long as drive thrust exceeds planetary gravity)
Yes, it can be done in Excel and the like, but it's not simple. Plus, Mars has an eccentricity of 0.0934, which barely qualifies as "circular". But try Mercury with e=0.205 and an inclination of over 7 degrees.

Long story short, yes you can create a spreadsheet that will approximate a transfer orbit, but does a game really need that level of detail?
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Old 11-08-2017, 08:31 PM   #13
Fred Brackin
 
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Default Re: Question regarding GURPS SPACESHIPS formulas

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Originally Posted by cvannrederode View Post
Long story short, yes you can create a spreadsheet that will approximate a transfer orbit, but does a game really need that level of detail?
If you can build workable interplanetary ships whose delta-v margins are small enough that you don't just gloss over all the details you'll discover that their operation is significantly less flexible than railroad trains.

A gameworld nation's railroad system is usually not something even the most detail-oriented among us try and simulate precisely. Normally the PC's are told "The train goes from city X to city Y and it will take Z units of time.". This is the way really, really hard science spaceships work too.
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Old 11-09-2017, 04:58 PM   #14
sir_pudding
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Default Re: Question regarding GURPS SPACESHIPS formulas

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Originally Posted by Fred Brackin View Post
A gameworld nation's railroad system is usually not something even the most detail-oriented among us try and simulate precisely. Normally the PC's are told "The train goes from city X to city Y and it will take Z units of time.". This is the way really, really hard science spaceships work too.
Also "The train from X to Z leaves tomorrow at P hours" which is also what you have with low delta-v transfer orbits.
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