Molniya Orbit

[inigma]

I need help figuring out altitudes for a Molniya Orbit in KSP with a period of 1/2 a sidereal day. Any ideas?

I think the orbital inclination is 63.4 degrees, apogee I think is at geostationary orbit alt of 2868.75km, but I need to figure out the perigee. Am I on the right track? I want this spy...er "weather" satellite to have a consistent orbit of a long hang time over the huge land continent on the other side of the planet from the KSC.

Tips or tricks for getting into such an orbit would be appreciated.

Edited June 12, 2013 by inigma

[Mr Shifty]

1) The Molniya orbits have that exact inclination to cancel out orbital perturbations caused by Earth's slight non-spherical shape. This isn't an issue for Kerbin, as it is perfectly spherical. You should choose an inclination that matches the latitude of the area you're interested in surveying.

2) To get 1/2 a sidereal day, you need an orbit that has a semimajor axis of:

a = ((T/(2*pi))²*G*M)^1/3

So for a period of 3 hours, or 10,800 seconds, you get;

a = ((10,800 s/(2*pi))²*3.5316000×10¹² m³/s²)^1/3

a = 2,185.176km

Edit: I had Kerbin radius here before. Should be diameter.

This means that your (apoapsis + periapsis + Kerbin diameter) / 2 = 2,185.176km

You want apokee as far out as possible so that it takes up as much of the orbit as possible, so I'd put your perikee at 75km, which is about as low as it can go. Then your apokee would be (2,185.176 km * 2) - (75 km) - (1,200 km) = 3,095.352 km

The best way to do this would be to put your perikee where you want it and then burn until your orbital period (as shown in e.g. MechJeb) is 3 hours. You don't have to look at distance at all.

Edited June 11, 2013 by Mr Shifty

[inigma]

Thanks for the math!

I updated the SpySat II mission:

http://wiki.kerbalspaceprogram.com/wiki/Campaign:_Age_of_Satellites#KerbSat_II_.28aka_SpySat_II.29

Edited June 11, 2013 by inigma

[purpletarget]

Unfortunately because of the thickness of the atmosphere around Kerbin relative to the Radius, we can't actually get the eccentricity that you would see on the Molniya orbits...they end up looking a lot more like Tundra orbits instead.

[Mr Shifty]

Unfortunately because of the thickness of the atmosphere around Kerbin relative to the Radius, we can't actually get the eccentricity that you would see on the Molniya orbits...they end up looking a lot more like Tundra orbits instead.

Typical Earth Molniya eccentricity: ~0.7

Eccentricity of the scheme I outlined: 0.691

Molniya orbits aren't defined by their eccentricities, just that they should be high to maximize the time near apoapsis.

Here's one at 0.722: http://www.n2yo.com/satellite/?s=7276

Here's one at 0.718: http://www.n2yo.com/satellite/?s=9941

Here's one at 0.700: http://www.n2yo.com/satellite/?s=13875

Tundra orbits have an orbital period of 1 day, and thus are conceptually different than Molniya orbits. In addition, since Tunda orbits are longer than Molniya orbits, they can have higher eccentricities. A Tundra orbit around Kerbin with a perikee at 75km would have an eccentricity of 0.836.

Edited June 11, 2013 by Mr Shifty

[purpletarget]

Typical Earth Molniya eccentricity: ~0.7

Eccentricity of the scheme I outlined: 0.691

Molniya orbits aren't defined by their eccentricities, just that they should be high to maximize the time near apoapsis.

Here's one at 0.722: http://www.n2yo.com/satellite/?s=7276

Here's one at 0.718: http://www.n2yo.com/satellite/?s=9941

Here's one at 0.700: http://www.n2yo.com/satellite/?s=13875

Yes, and that was my point...the max eccentricity you can get on a semi-sync orbit around kerbin is around 0.693 before scrapping atmo.

The Pe for Molniya's in terms of the IRL eccentricities we see is:

e 0.70, Pe 55.5km

e 0.72, Pe 11.8km

e 0.74, Pe -31.8km These ones usually have the loopback over the target area, but around Kerbin they would require a long underground tunnel

ie: It doesn't take much change in eccentricity to make significant differences.

[Mr Shifty]

Yes, and that was my point...the max eccentricity you can get on a semi-sync orbit around kerbin is around 0.693 before scrapping atmo.

The Pe for Molniya's in terms of the IRL eccentricities we see is:

e 0.70, Pe 55.5km

e 0.72, Pe 11.8km

e 0.74, Pe -31.8km These ones usually have the loopback over the target area, but around Kerbin they would require a long underground tunnel

ie: It doesn't take much change in eccentricity to make significant differences.

An eccentricity of 0.691 is nearly as good as 0.74. The point of the Molniya orbit is to give good high elevation observation angles of an entire hemisphere at high latitudes. What you want is for the satellite to be at as high an elevation angle as possible over your latitude of interest for as long as possible during its orbit. Assume that an elevation angle of 45 degrees is sufficient (and ignoring the planet's radius), you can calculate how much time will be spent going from a true anomaly of 135 degrees (relative to perikee) to 225 degrees.

For an eccentricity of 0.691: 29% of the total period

For an eccentricity of 0.74: 32% of the total period

So sure, you get an improvement at higher eccentricities, but the difference isn't that large. You'd probably still set up the same 3-satellite network for continuous coverage that is used IRL.

Edited June 11, 2013 by Mr Shifty

[purpletarget]

You do realize at this point we're really just arguing the minutia...

[Konraden]

You do realize at this point we're really just arguing the minutia...

Translation: "I lost, shut up already."

I was looking for the same information earlier for Remote-Tech. I didn't feel like dumping a bunch of satellites into orbit for global coverage, so I figure these Molniya and Tundra orbits would be fantastic.

[intidragon]

Would anybody be so kind as to provide visual data here? I've been trying it out, but I'm not sure if my orbits "look" right.

[purpletarget]

If you want to see the Tundra and Molniya in action you can check the vid here:

http://forum.kerbalspaceprogram.com/showthread.php/24623-Tutorial-Video-Krash-Test-Kerbals-How-to-science%21?p=303586&viewfull=1#post303586

Check around 18:40...

[CameronLeroux]

This is going to be useful, thank you fellow KSP Veteran.