Simple Orbital Maintenance

[rgrove0172]

Im trying to set up a simple method to determine the speed required to maintain orbit at a given altitude above a world with a given gravity.

Rather than have to grab my calculator during play, I thought perhaps a chart with maybe 10 different orbital altitudes, and the corresponding speeds around a world with 1G gravity would work (using variouis satellite orbital velocities as a reference), then just multiply the result by the actual gravity there.

Example - 35,000 km geostationary orbit requires 188kpm around Earth. If orbiting a world with a gravity of 2G, geostationary orbit would be at 70,000km. Or if you were orbiting at 35,000km you would need just under 400kpm to maintain orbit.

Im not looking for perfect accuracy here, only a working rule to inform my captains what speed they need to maintain given their altitude. Does the mass of the ship come into play at all. Would a simple equation work better?

Anyone see any problems with it?

Oh and is there a simple way to determine the depth of a planet's atmosphere? I know that we consider 'space' to being at about 100km....another world's size, atmospheric density (and lack thereof) would all have an effect so is there a simple way to determine at just what point the atmosphere begins? Its seems kind of important as stutterwarp doesnt function in the atmosphere, nor do some weapons etc.

 

[Strithe]

Im trying to set up a simple method to determine the speed required to maintain orbit at a given altitude above a world with a given gravity.

Rather than have to grab my calculator during play, I thought perhaps a chart with maybe 10 different orbital altitudes, and the corresponding speeds around a world with 1G gravity would work (using variouis satellite orbital velocities as a reference), then just multiply the result by the actual gravity there.

Example - 35,000 km geostationary orbit requires 188kpm around Earth. If orbiting a world with a gravity of 2G, geostationary orbit would be at 70,000km. Or if you were orbiting at 35,000km you would need just under 400kpm to maintain orbit.

Im not looking for perfect accuracy here, only a working rule to inform my captains what speed they need to maintain given their altitude. Does the mass of the ship come into play at all. Would a simple equation work better?

I'd go with a table, it's quicker to just look it up than do a an equation mid-game. I'd also have relatively fewer parameters: maybe three orbit bands (low, high, geosyncrhonous) and four gravity types (micro, low, normal, high) and then just come up with a multiplier for diameter.

Ship mass would only matter if you were trying to come up with an exact thrust number and/or realistic fuel burn. It doesn't sound like you're looking for that here.

Anyone see any problems with it?

None, unless you've got a hard-core planetary science nerd who can't keep his/her mouth shut in your group.

Oh and is there a simple way to determine the depth of a planet's atmosphere? I know that we consider 'space' to being at about 100km....another world's size, atmospheric density (and lack thereof) would all have an effect so is there a simple way to determine at just what point the atmosphere begins? Its seems kind of important as stutterwarp doesnt function in the atmosphere, nor do some weapons etc.

A simple one? It depends on how much realism you're looking for, and how much your players really care about it.

Realistically you've got a variety of pressures with altitude and there really isn't a hard delieation between "atmosphere" and "space." Traveller 5 has some neat tables showing the actual atmosphere type based on altitude, but I think that's a bit more anal-retentive than necessary if your primary goal is to just determine how soon you can kick on your Stutterwarp drive.

I don't know how often it's really going to be useful either, keep in mind even with a very "tall" atmosphere you're still usually going to be well within the 0.1 G zone where rockets work much better than stutterwarp anyway.

If you simply MUST know I'd just keep it simple: come up with a multiplier for planet diameter, and perhaps atmospheric density and make sure it's internally consistent. It's probably going to be a square-root type relationship than linear: the only time you're going to have massively thick atmospheres is on a gas giant, and any 2300ad ship is dead meat if it gets close enough to touch the atmosphere of one.

 

[whartung]

Here's a simple AWK script that can create that table. (AWK!?!? Yea, sue me -- you can port it) Season to taste. This would be trivial in a spreadsheet, of course.

Since Earth is "1g", EarthU is the gravitational constant times the mass of the earth (G * M). So, fractions/multiples of EarthU are fractions and multiples of g.

Radius is in kilometers.

The result is in km/s.

The "meat" of the routine is v = sqrt(u / r)

As an aside, geosynchronous orbit has to do with planet rotation, and nothing to do with the mass of the planet.

P.S. The table feature is very nice, I can not explain the large whitespace gap however.

BEGIN {
    print "<table>"
    earthU = 398600;
    line = "<td>radius\g</td>"
    for(g = 0; g < 8; g++) {
        line = line "<td> " (g + 1) * .5 "</td>";
    }
    print "<tr>" line "</tr>";
    for(r = 0; r < 10; r++) {
        radius = 4000 + (r * 2000);
        line = "<td>" radius "</td>";
        for(g = 0; g < 8; g++) {
            u = (g + 1) * .5 * earthU;
            v = sqrt(u / radius);
            line = line "<td>" v "</td>";
        }
        line = line ;
        print "<tr>" line "</tr>";
    }
    print "</table>"
}

radius\g	0.5	1	1.5	2	2.5	3	3.5	4
4000	7.05868	9.98248	12.226	14.1174	15.7837	17.2902	18.6755	19.965
6000	5.76339	8.15066	9.98248	11.5268	12.8873	14.1174	15.2485	16.3013
8000	4.99124	7.05868	8.64509	9.98248	11.1608	12.226	13.2056	14.1174
10000	4.4643	6.31348	7.7324	8.92861	9.98248	10.9353	11.8114	12.627
12000	4.07533	5.76339	7.05868	8.15066	9.11272	9.98248	10.7823	11.5268
14000	3.77302	5.33586	6.53507	7.54605	8.43674	9.24198	9.98248	10.6717
16000	3.52934	4.99124	6.113	7.05868	7.89185	8.64509	9.33776	9.98248
18000	3.32749	4.70579	5.76339	6.65499	7.4405	8.15066	8.80372	9.41158
20000	3.15674	4.4643	5.46763	6.31348	7.05868	7.7324	8.35195	8.92861
22000	3.00983	4.25655	5.21318	6.01966	6.73019	7.37255	7.96327	8.51309

 

[aramis]

As an aside, geosynchronous orbit has to do with planet rotation, and nothing to do with the mass of the planet.

not exactly true.

The rotation determines the needed orbital period.

The mass affects what altitude that will be.

EG: Mars and Earth both have very nearly identical rotation times, but Mars' Geosynch is about 17,000km, while Earth's is about 35,800km...

 

[McPerth]

Just curious, if you are talking about ships discharging their stutterwarp, and so at the line of 0.1 G gravity, why the need of a geostationary orbit?

I see no problem on having your ship orbiting the world by cycling it, if that is easier to maintain the it at the wanted distance (in this case the 0.1 threshold), leaving geostationary orbits for those facilities that need them (moslty satellites).

 

[McPerth]

P.S. The table feature is very nice, I can not explain the large whitespace gap however.

radius\g	0.5	1	1.5	2	2.5	3	3.5	4
4000	7.05868	9.98248	12.226	14.1174	15.7837	17.2902	18.6755	19.965
6000	5.76339	8.15066	9.98248	11.5268	12.8873	14.1174	15.2485	16.3013
8000	4.99124	7.05868	8.64509	9.98248	11.1608	12.226	13.2056	14.1174
10000	4.4643	6.31348	7.7324	8.92861	9.98248	10.9353	11.8114	12.627
12000	4.07533	5.76339	7.05868	8.15066	9.11272	9.98248	10.7823	11.5268
14000	3.77302	5.33586	6.53507	7.54605	8.43674	9.24198	9.98248	10.6717
16000	3.52934	4.99124	6.113	7.05868	7.89185	8.64509	9.33776	9.98248
18000	3.32749	4.70579	5.76339	6.65499	7.4405	8.15066	8.80372	9.41158
20000	3.15674	4.4643	5.46763	6.31348	7.05868	7.7324	8.35195	8.92861
22000	3.00983	4.25655	5.21318	6.01966	6.73019	7.37255	7.96327	8.51309

The gap is due to putting intro after each table line. What you put among the various cells in the table (incluiding between the lines) is put before the table (in this case some White lines). In the quote of your post, I removed those "end line" intro, and you can see the result (it happened to me the first time I tried to use it, and so I was told about this problem).

I agree the feature is nice, but quite awkward to write.

 

[rgrove0172]

Just curious, if you are talking about ships discharging their stutterwarp, and so at the line of 0.1 G gravity, why the need of a geostationary orbit?

I see no problem on having your ship orbiting the world by cycling it, if that is easier to maintain the it at the wanted distance (in this case the 0.1 threshold), leaving geostationary orbits for those facilities that need them (moslty satellites).

No, I wasnt concerned with the discharge of stutterwarp at all. I just included it as a typical request of altitude from an orbiting captain. Im preparing to give my players a choice when the make orbit, and inform them of the speed required based on it. If they didnt plan ahead they would have to drop out of stutterwarp a bit early, build up the appropriate delta v, then reengage, shutting down as they enter the .1G threshold and coast into the desired orbit. Or such was my thinking. Purely for dramatic flare granted but I like to include as much "color" as I can in the game.

 

[rgrove0172]

As to the table, is the radius from the planet's center or is that altitude above the surface?

And if I chose to just run through the formula quickly,... what is it exactly?

 

[whartung]

As to the table, is the radius from the planet's center or is that altitude above the surface?

And if I chose to just run through the formula quickly,... what is it exactly?

It's the radius from the center of gravity, so, I'd have to think it's the mean surface of the world (since the center of the planet has...no gravity! Negative gravity!?? How deep in the core do you have to be before you start walking on the ceiling?).

Yet...

The gravity at the top of Everest is less than sea level, so..I don't know. Obviously there's a fuzzy space.

I think it's whatever you want it to be, and from a gameplay or story telling aspect it's not going to matter.

 

[SpaceBadger]

Center of gravity is the center of the planet.

 

[shaunhilburn]

And if I chose to just run through the formula quickly,... what is it exactly?

As simple as I can possibly make it:

g planet gravity (gravities, e.g. 1G)
R planet radius (km)
Ro distance from barycenter (km, planet radius+altitude)


for a circular orbit = sqrt(g×R²×0.0098/Ro)

 

[shaunhilburn]

And if I chose to just run through the formula quickly,... what is it exactly?

0.1G altitude km

= sqrt(G/0.1)xRadius-Radius

 

[rgrove0172]

Hmm

taking the lowest altitude you have on the chart - 4000 and a 1G world...

Grav (1) x Radius squared 4000 x 4000 = (16000000) x 0.0098 = 156800, then divide by the altitude and radius of the plant (just 4000 in this case since we didnt initially separate the two) = 39.2... the square root of which is 6.26... not the 9.98 on the chart.

Sorry, dont mean to be a dumbass here but can you help me out?

 

[shaunhilburn]

Hmm

taking the lowest altitude you have on the chart - 4000 and a 1G world...

Grav (1) x Radius squared 4000 x 4000 = (16000000) x 0.0098 = 156800, then divide by the altitude and radius of the plant (just 4000 in this case since we didnt initially separate the two) = 39.2... the square root of which is 6.26... not the 9.98 on the chart.

Sorry, dont mean to be a dumbass here but can you help me out?

Speed required to maintain an orbit e.g. orbital velocity. For a perfectly circular orbit:
sqrt(g×R²×0.0098/Ro) where

g planet gravity (gravities, e.g. 1G)
R planet radius (km)
Ro distance from barycenter (km, planet radius+altitude)

Planet as radius R of 4,000 km, surface gravity 0.5g, and orbit altitude of 300 km:
sqrt(0.5×4000²×.0098/4300) = 4.27 km/s


Planet as radius R of 7,125 km, surface gravity 1.2g, and orbit altitude of 500 km:
sqrt(1.2×7125²×.0098/7625) = 8.85 km/s

 

[rgrove0172]

Got it.. thanks very much. < (thats a smiley guy with a dunce hat!)