totm november 2019 Mysteries of Orbital Inclination

[GungaDin]

I'm in a career game where I am launching from my secret lair in Northwestern China at about 45% longitude.  When I launch I head due East and end up with an inclined orbit.  I'm wondering what the most efficient path is to follow if my ultimate desire is to end up with an equatorial orbit?  (This also makes me wonder how folks in Northern cities get satellite service from a stationary orbit when the earth keeps turning around below the satellite....?)  I.e. how do you park a satellite above Reykjavik? 

 

 

[Streetwind]

First part: there basically isn't a "most efficient path". For any given launch site, the absolute minimum inclination you can directly launch into is the inclination of the launch site. Higher is always possible, lower is never possible. No exceptions. In order to achieve an inclination lower than that of the launch site, you must perform a plane change while already in flight.

Plane changes in low Kerbin orbit are very expensive, and if you're playing Realism Overhaul (it sounds like you are), then that claim counts fourfold. You can discount the cost a little by pushing your apoapsis way out there, doing the plane change at apoapsis, and then bringing the orbit back down... but a.) that takes a lot of time, and b.) it only saves a modicum of dV. It still remains expensive.

You can also decide to fly a "dogleg", that is, change directions mid-ascent. This helps fold part of the cost of the plane change into your orbit insertion, saving some dV.

Finally, you may be able to fold the plane change into the transfer burn towards your destination, if the ascending/descending nodes (the spots where the plane of your current orbit intersects the plane of your desired orbit) happen to line up with your maneuver. This is by far the cheapest method, but only works with bodies in the same SoI in any reliable fashion, because of how transfer windows work.

 

Second part: you don't park satellites above Reykjavik. Your confusion is understandable, because that is indeed physically impossible. You park the satellite in equatorial, geostationary orbit as normal, and then tell the people in Reykjavik to point their satellite dishes relatively flat towards the horizon. As long as there are no obstructions (like tall mountains and other buildings), you can see the geostationary belt from almost all latitudes. It just gets progressively closer to the horizon.

 

Edited October 21, 2019 by Streetwind

[GungaDin]

 

Thanks Street - makes sense.  Actually I'm playing a career in KSRSS so I can afford to be pretty wasteful but I'm still surprised at the limitations imposed on a northerly space base.  Baikonur is at 45 so I'm surprised they can manage that.  How the hell do the Ruskies get satellites into stationary orbits!  Anyway now I know why the Europeans use a South American launch site.

[Harry Rhodan]

There's also this option: https://en.wikipedia.org/wiki/Molniya_orbit

[Streetwind]

@GungaDin - Launch sites at high latitudes do have a small advantage too, not just disadvantages. They are more useful for polar launches. Due to their position, they get less "help" from the planet's rotation... which is a downside when trying to launch into a low inclination orbit... but actually means that polar launches don't have to fight that same rotation.

The US, Russia, and China all operate multiple launch sites, and they use the lower-latitude ones for "straight east" launches and the higher latitude ones for polar launches.

[GungaDin]

Sweet! Thanks. So I'm learning this in phases and the phase I'm on now is rendezvous and docking.   For that I guess I can keep launching at 90 and just ignore the fact that the earth is spinning below me.  But I will need to keep in mind that if I intend to head moonward and marsward I will need to establish equitorial orbits at that point.  I guess if I'm really careful I could time it just right and intercept a planet but at the wrong angle....

Anyway do you folks know of any good, readable books on orbital mechanics?

 

[paul23]

9 hours ago, Streetwind said:

First part: there basically isn't a "most efficient path". For any given launch site, the absolute minimum inclination you can directly launch into is the inclination of the launch site. Higher is always possible, lower is never possible. No exceptions. In order to achieve an inclination lower than that of the launch site, you must perform a plane change while already in flight.

Plane changes in low Kerbin orbit are very expensive, and if you're playing Realism Overhaul (it sounds like you are), then that claim counts fourfold. You can discount the cost a little by pushing your apoapsis way out there, doing the plane change at apoapsis, and then bringing the orbit back down... but a.) that takes a lot of time, and b.) it only saves a modicum of dV. It still remains expensive.

You can also decide to fly a "dogleg", that is, change directions mid-ascent. This helps fold part of the cost of the plane change into your orbit insertion, saving some dV.

Finally, you may be able to fold the plane change into the transfer burn towards your destination, if the ascending/descending nodes (the spots where the plane of your current orbit intersects the plane of your desired orbit) happen to line up with your maneuver. This is by far the cheapest method, but only works with bodies in the same SoI in any reliable fashion, because of how transfer windows work.

 

Second part: you don't park satellites above Reykjavik. Your confusion is understandable, because that is indeed physically impossible. You park the satellite in equatorial, geostationary orbit as normal, and then tell the people in Reykjavik to point their satellite dishes relatively flat towards the horizon. As long as there are no obstructions (like tall mountains and other buildings), you can see the geostationary belt from almost all latitudes. It just gets progressively closer to the horizon.

 

Actually if we would model J2 (and more) behaviour you might be able to park above another non equatorial spot. Because the perturbation moves the longitude of the ascending node.

[Streetwind]

@paul23 That would be a synchronous orbit, true, but not a stationary one. You still can't "park" a satellite in a fixed non-equatorial spot in the sky even with that - you can only ensure that it reliably and periodically returns to that spot. This is not very useful for satellite radio/TV, as it would require the ground receivers to track, and/or the users to accept only intermittent reception.

The Molniya orbit that @Harry Rhodan mentioned also has that issue, but the Russians implemented multiple satellites on the same orbit to ensure continuous coverage. The receiver would be pointed towards the orbit's apoapsis, and receive signals from any satellite in that rough direction. As one started to fall back towards periapsis, another would be coming up on the other side.

[Fierce Wolf]

A curiosity fueled question: On Earth, what is the maximum inclination from the ecuator that a geostationary satellite can have?

[paul23]

A geostationary orbit *by definition* has 0 inclination.

[Pecan]

3 hours ago, Fierce Wolf said:

A curiosity fueled question: On Earth, what is the maximum inclination from the ecuator that a geostationary satellite can have?

As paul23 said, a geostationary satellite needs to have 0 degrees inclination.  A 'geosynchronous' satellite does not, it just needs a 24-hour orbital period, regardless of inclination.  A satellite in a circular geosynchronous distance and say 5 degrees inclination will appear to move up and down in a North-South line between +/- 5 degrees.  With 10 degrees inclination, +/- 10 degrees and so on, until you get to 90 degrees where it's in polar orbit and going backwards and forwards between +/- 90 degrees.

If the orbit is eccentric rather than properly circular a satellite (including the real moon) will appear to move backwards and forward East-West in a similar way.  It will 'fall behind' (whether that's East or West depends on which way around it's orbiting) in its orbit as it climbs and slows from periapsis to apoapsis and will then race ahead as it speeds-up falling back from apoapsis to periapsis.

TL;DR  To appear stationary a satellite must be in a circular equatorial orbit (and, obviously have the same 24-hour-and-a-little-bit orbital period as the Earth's rotation).  Any inclination will make the satellite appear to oscillate North-South, any eccentricity will make it appear to oscillate East-West.  Both together will have it apparently going around in little circles/ovals/whatever.

[Zhetaan]

@GungaDin:

A minor caveat:

If you have axial tilt, then you can launch into the ecliptic (the plane of the planet's orbit but not the plane of the planet's equator) from any latitude up to the equivalent of the tilt.  It requires you to launch at one of the nodes and in a deviant direction, but it does work.  For higher latitudes than the axial tilt, you cannot launch into the ecliptic, but proper timing can save a lot of the inclination change.  This won't help you with geostationary orbits but it will provide some assistance when you decide to visit other planets, since you mentioned going that way.

[AHHans]

On 10/22/2019 at 2:50 PM, Fierce Wolf said:

A curiosity fueled question: On Earth, what is the maximum inclination from the ecuator that a geostationary satellite can have?

I think @Pecan already said everything relevant about the orbital mechanics.

But as a senior antenna wrangler I want to add this: the advantage of a geostationary orbit is that you can point a high gain (= very directional!) antenna at a one point in the sky and have it pointing at the satellite all the time. That way you can have cheap satellite dishes on fixed mounts to distribute TV to the masses (or whatever you want to do). But every antenna has a certain beam-width, the opening angle for which it has nearly full sensitivity. (... does some math ... gets surprised ... queries online antenna calculator ...) O.K. turns out that the beam-width of a typical TV-antenna is only about 1 degree (0.5 degrees from the center). But that still means, that as long as the satellite stays within the +/- 0.5 degrees of the ideal position then you will be able to receive it.

Well, I had planned to write that the satellite companies have some leeway when managing the orbits, it turns out that they don't have that much. In order to allow everyone who had their TV dish installed by a ham-fisted amateur on a long pole that swings around in a good breeze to keep receiving their signal, they have to pretty much keep their satellites spot-on. Well, you learn something new every day...

Edited October 24, 2019 by AHHans
fixed typo

[paul23]

6 hours ago, AHHans said:

I think @Pecan already said everything relevant about the orbital mechanics.

But as a senior antenna wrangler I want to add this: the advantage of a geostationary orbit is that you can point a high gain (= very directional!) antenna at a one point in the sky and have it pointing at the satellite all the time. That way you can have cheap satellite dishes on fixed mounts to distribute TV to the masses (or whatever you want to do). But every antenna has a certain beam-width, the opening angle for which it has nearly full sensitivity. (... does some math ... gets surprised ... queries online antenna calculator ...) O.K. turns out that the beam-width of a typical TV-antenna is only about 1 degree (0.5 degrees from the center). But that still means, that as long as the satellite stays within the +/- 0.5 degrees of the ideal position then you will be able to receive it.

Well, I had planned to write that the satellite companies have some leeway when managing the orbits, it turns out that they don't have that much. In order to allow everyone who had their TV dish installed by a ham-fisted amateur on a long pole that swings around in a good breeze to keep receiving their signal, they have to pretty much keep their satellites spot-on. Well, you learn something new every day...

Well they could just decrease the gain, and at the same time increase the power of the (receiving or transmitting) antenna, it's just a square relationship. So to get 10 times as much gain (5 degrees, would be enough for a molniya orbit without any form of tracking), you'll need 100 times as much power.

A normal dish uses 50 watt (though high latitude could mean this also multiplies several times to reduce atmospheric noise)? Then a 5 degree one would use 5 kW, not impossible but quite high. (About what a modern sq. meter solar panel produces in ideal situation at sea level with sun directly above). Or about the same power of a single pit on an electric furnace at medium settings.

Edited October 24, 2019 by paul23

[AHHans]

8 hours ago, paul23 said:

Well they could just decrease the gain, and at the same time increase the power of the (receiving or transmitting) antenna, it's just a square relationship. So to get 10 times as much gain (5 degrees, would be enough for a molniya orbit without any form of tracking), you'll need 100 times as much power.

A normal dish uses 50 watt (though high latitude could mean this also multiplies several times to reduce atmospheric noise)? Then a 5 degree one would use 5 kW, not impossible but quite high. (About what a modern sq. meter solar panel produces in ideal situation at sea level with sun directly above). Or about the same power of a single pit on an electric furnace at medium settings.

You are completely right as far as the technical side is concerned. But think through the consequences: instead of selling a satcom system that has essentially negligible power requirements, you'll have to convince your customers to buy something that will double their power bill. And you'll also need 100 times the power on your satellite, that means 100 times as much solar panels, batteries, and cooling capacity. And you'll need to lift all that extra weight into orbit.

So I think that for geostationary applications it is only worth it, if having a smaller dish size is a major selling point. Like going from a 1.2 meter dish to a 0.6 meter dish (which is a factor of 2 not of 10) that kind of made the transition from "needs to be installed by a professional" to "can be sold at a store and installed by everyone". You cannot even relax your station-keeping on the satellite (and maybe save on RCS fuel), because that would kick out everyone who has a bigger dish.

It makes more sense for systems that use a Molniya orbit as you say.

[paul23]

7 hours ago, AHHans said:

You are completely right as far as the technical side is concerned. But think through the consequences: instead of selling a satcom system that has essentially negligible power requirements, you'll have to convince your customers to buy something that will double their power bill. And you'll also need 100 times the power on your satellite, that means 100 times as much solar panels, batteries, and cooling capacity. And you'll need to lift all that extra weight into orbit.

So I think that for geostationary applications it is only worth it, if having a smaller dish size is a major selling point. Like going from a 1.2 meter dish to a 0.6 meter dish (which is a factor of 2 not of 10) that kind of made the transition from "needs to be installed by a professional" to "can be sold at a store and installed by everyone". You cannot even relax your station-keeping on the satellite (and maybe save on RCS fuel), because that would kick out everyone who has a bigger dish.

It makes more sense for systems that use a Molniya orbit as you say.

Yet geostat is due to thermal interference in the atmosphere hard to get from norway up. So you're discriminating against where people live, which luckily the EU no longer allows unless for good reasons. 

 

Station keeping on geostationary is expensive, due to j2,2 effect geostationary satellites tend to drift east or westwards constantly. Just a simple controller inside a movable dish that finds "local maximum" would be enough. (Btw a 2 times as small radius is 4 times as small gain).

 

Making heavy equipment on *earth* is free compared to doing stuff in orbit.

[James Kerman]

Congratulations @GungaDin and all the contributors here, you have been awarded thread of the month.