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blog:articles:general:orbital_shenanigans [2019/02/16 01:06]
Phil Ide
blog:articles:general:orbital_shenanigans [2019/08/03 12:25] (current)
Phil Ide
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 ====== Orbital Shenanigans ====== ====== Orbital Shenanigans ======
-{{blog:​articles:​mars_map2.png }} +{{blog:​articles:​mars_map2.png|MOLA map of Mars coloured by elevation}}\\ 
-Sometimes when you do some research – actually, quite often – you find out some really interesting stuff and end up changing your mind. In my story, I had some people on the ground on Mars, and wanted a spacecraft in a geostationary orbit above them to give them communications between them at all times. Just for info, when talking about geostationary orbits, the accepted term for Mars is aerostationary. I’ll use geostationary and geosynchronous because it’s my blog and although the aero prefix is accepted, it isn’t mandatory.+Edited: 2019-03-14
  
-Since I’ve written a program ​that can calculate orbits around Mars (see the download section), figuring out the orbital parameters is easy enough for me, but I decided to check my results against published scientific papers. I like to be thorough in my research. This resulted in a delightful piece of serendipity,​ which I’ll talk about in a moment, and turned up some fascinating facts about these peculiar types of orbit that I’d never heard of.+Sometimes when you do some research – actually, quite often – you find out some really interesting stuff and end up changing your mind. In my story, I had some people on the ground on Mars, and wanted a spacecraft in a geostationary orbit above them to give them communications between them at all times. Just for info, when talking about geostationary orbits, the accepted term for Mars is aerostationary. I’ll use geostationary and geosynchronous because it’s my blog and although the aero prefix is accepted, it isn’t mandatory. 
 +=== === 
 +Since I’ve written a [[blog:​articles:​software:​orbital_calculator|program ​to calculate orbits]] (including ​around Mars), figuring out the orbital parameters is easy enough for me, but I decided to check my results against published scientific papers. I like to be thorough in my research. This resulted in a delightful piece of serendipity,​ which I’ll talk about in a moment, and turned up some fascinating facts about these peculiar types of orbit that I’d never heard of.
 === === === ===
 To begin, I should explain the difference between geostationary and geosynchronous. I’ll use Earth as an example to make the explanations easier. The International Space Station lies at an elevation of 250 miles. It completes an orbit once every 92 minutes. The further away from the planet the orbit, the less the gravitational influence, and so the orbital speed is reduced. So the satellite is moving slower, but the circumference of the orbit is getting bigger, hence the orbital period – the time to complete a single orbit – gets longer. Keep moving out, and eventually you reach a point where the period of the orbit equals one day. This equality is a geosynchronous orbit, because the period of the orbit and the rotation of the planet are synchronised. To begin, I should explain the difference between geostationary and geosynchronous. I’ll use Earth as an example to make the explanations easier. The International Space Station lies at an elevation of 250 miles. It completes an orbit once every 92 minutes. The further away from the planet the orbit, the less the gravitational influence, and so the orbital speed is reduced. So the satellite is moving slower, but the circumference of the orbit is getting bigger, hence the orbital period – the time to complete a single orbit – gets longer. Keep moving out, and eventually you reach a point where the period of the orbit equals one day. This equality is a geosynchronous orbit, because the period of the orbit and the rotation of the planet are synchronised.
  
-In theory, this means you stay over the same point of land perpetually. In practice, it’s not that simple, but if you did, then it would be geostationary. Subtle but important difference from geosynchronous.+In theory, this means you stay over the same point of land perpetually,​ but only if the orbit was equatorial. A polar orbit can also be geosynchronous. Subtle but important difference from geosynchronous.
  
 So, why isn’t it simple? With Earth, there are various factors that affect the satellite. The Moon is one of the biggest influences – if it can affect tides on vast bodies of water even further away, it can affect a puny satellite. Venus may have a small effect at various times too, but the biggest factor turns out to be the Earth itself, because it’s not a perfectly smooth sphere. This means that gravity is not uniform all over the planet. So, why isn’t it simple? With Earth, there are various factors that affect the satellite. The Moon is one of the biggest influences – if it can affect tides on vast bodies of water even further away, it can affect a puny satellite. Venus may have a small effect at various times too, but the biggest factor turns out to be the Earth itself, because it’s not a perfectly smooth sphere. This means that gravity is not uniform all over the planet.
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 If you can calculate how much delta-v you need to maintain an orbit, you can plan on having enough fuel on board the craft to give it a decent service lifetime. The lower the delta-v, the more life your satellite has for a given amount of fuel. Since the variations in Earth’s gravity fields are the most significant factor, clever people with letters after their name did some research and found something rather interesting. If you can calculate how much delta-v you need to maintain an orbit, you can plan on having enough fuel on board the craft to give it a decent service lifetime. The lower the delta-v, the more life your satellite has for a given amount of fuel. Since the variations in Earth’s gravity fields are the most significant factor, clever people with letters after their name did some research and found something rather interesting.
  
-There are two points on the Earth where gravity is strongest, and they happen to be opposite each other – one on each side of the world. These two points they named the unstable points. Halfway between them, there were two matching points – again, opposite each other – known as the stable points. The stable points represent the lows in the gravty ​field. If you are at the right altitude for a geostationary orbit, and above one of these four points, your delta-v is going to be lower than anywhere else. If you are between any of these points, then the satellite will tend to drift toward the stable points, increasing delta-v.+There are two points on the Earth where gravity is strongest, and they happen to be opposite each other – one on each side of the world. These two points they named the unstable points. Halfway between them, there were two matching points – again, opposite each other – known as the stable points. The stable points represent the lows in the gravity ​field. If you are at the right altitude for a geostationary orbit, and above one of these four points, your delta-v is going to be lower than anywhere else. If you are between any of these points, then the satellite will tend to drift toward the stable points, increasing delta-v.
  
 It turns out that Mars has this issue too – two stable and two unstable points in the same configuration. Since the delta-v would be lowest at these points, and therefore less effort would be required to maintain station, they would be the go-to places for a geostationary Martian satellite. Mars is quite different from Earth. It doesn’t have a super-massive moon, for starters, and it’s also less spherical than Earth, but the basic issue of delta-v is the same. It turns out that Mars has this issue too – two stable and two unstable points in the same configuration. Since the delta-v would be lowest at these points, and therefore less effort would be required to maintain station, they would be the go-to places for a geostationary Martian satellite. Mars is quite different from Earth. It doesn’t have a super-massive moon, for starters, and it’s also less spherical than Earth, but the basic issue of delta-v is the same.
  
-Back to that delightful piece of serendipity ​mentioned. It turned out that the people on the Martian surface were almost exactly on one of the unstable points. Yippee! +As just said, it is less sphericalbut the gravitational anomalies are much bigger ​in comparison to Earth'​s. There is also the fact that since Mars is so much smallerand that it is far less dense, the geostationary orbit is much closer ​to MarsCloser means those gravitational anomalies have a bigger influence. Aside from the drift away from a stable point toward an unstable point - an east or west drift - there is also a tendency to drift northward which has to be countered.
-Unfortunatelybecause of the wild variance ​in the Martian gravity fieldmaintaining station in a geostationary orbit around Mars turns out to be very difficultIt is simply too easy to begin sliding off-station. It would just be too much effort.+
  
-So, back to the drawing board. Let’s tackle this another way. Another orbit, what you might call a ‘regular’ orbit, doesn’t have this problem. At least, not so much. One suggestion was to use a lower orbit at an elevation ​of 5,000kmConsider ​that at the geostationary orbit (13,​634km), ​the satellite can see 30 degrees ​of the planet either side of the point it is above. That’s ​60 degree spreadAt 5,000km, this reduces, but not by too much. This is important, so hang on to that information.+Back to that delightful piece of serendipity I mentionedIt turned out that the people on the Martian surface were almost exactly on one of the unstable points. Yippee! Unfortunately,​ because ​of the wild variance in the Martian gravity field, maintaining station in geostationary orbit around Mars turns out to be very difficultIt is simply too easy to begin sliding off-station. It would just be too much effort.
  
-A 5,000km orbit has a period of approx 0.26 days (that’s Earth days, not Martian ones, which are about half an hour longer)Using my orbital calculatorI finessed the orbit down to 4,781.361kmThat gives it an orbital period ​of 6hrs 9mins and 53secsIf you do the sums in your headyou’ll ​see that four orbits come to approximately 24hrs 39 mins 35 secs – the same as Martian daySo now we have exactly four orbits per day.+Soback to the drawing boardLet’s tackle this another wayAnother orbitwhat you might call a ‘regular’ ​orbit, ​doesn’t have this problemAt least, not so muchOne suggestion was to use a lower orbit at an elevation ​of 5,000kmConsider that at the geostationary orbit (17,025km), the satellite can see 75 degrees of the planet either side of the point it is above. That’s ​150 degree spreadAt 5,000km, this reduces to 107 degrees.
  
-If the satellite can see approximately 60 degrees ​of the planetthen from the surface within that zonethe satellite is above the horizon60 degrees is exactly 1/6th of a circleand the orbit is approximately ​6hrs longThis means that from a specific point on the ground, the satellite will be above the horizon for about one hour every six hours, or put another way, for one hour four times a day at regular intervals.+A 5,000km orbit has a period ​of approx 0.26 days (that’s Earth daysnot Martian oneswhich are about forty minutes longer)Using my orbital calculatorI finessed ​the orbit down to 4,697km. That gives it an orbital period of 6hrs 9mins and 13secsIf you do the sums in your headyou’ll see that four orbits come to approximately 24hrs 39 mins 53 secs – the same as a Martian day. So now we have exactly ​four orbits per day.
  
-One hour is a pretty decent amount of time to talk to an orbiting crew, and you get four chances a day. Contact, whilst not continuous, is actually pretty good, and the orbit will only require minimal boosting once every few weeks or so. It may not be as glamorous as a geostationary orbit, but technically and logistically it’s an easier one, without sacrificing much communications ability.+At any part of the planet the satellite can see means, from an observer'​s point of view from the ground, the satellite is above the horizon. At 4,697km the satellite can see 29% of the Martian surface, with a spread of 104.45 degrees. However, that is its //visual// footprint. It probably has a radio transceiver aboard to talk to objects/​people on the ground, and that is very likely to have a much smaller //radio// footprint. On Earth, this is typically 60 degrees, and if our satellite had such a radio footprint, it would be high in the sky when radio contact could be established,​ reducing the ill-effects of mountains etc. casting radio shadows. 
 + 
 +The satellite will be above the same point on the ground every 6hrs 9mins and 13secs. The radio footprint is 60 degrees. 60 degrees is exactly one sixth of a circle. This means a ground station will be in the radio footprint for approximately one hour. It will also be in in this footprint four times a day at exactly the same times each day. 
 + 
 +One hour is a pretty decent amount of time to talk to an orbiting crew, and you get four chances a day. Contact, whilst not continuous, is actually pretty good, and the orbit will only require minimal boosting once every few weeks or so, perhaps less, and for a minimal amount of fuel. It may not be as glamorous as a geostationary orbit, but technically and logistically it’s an easier one, without sacrificing much communications ability.
  
 So, yeah. I went with it. So, yeah. I went with it.
 +~~socialite~~
 +~~DISCUSSION~~
 +
blog/articles/general/orbital_shenanigans.1550279194.txt.gz · Last modified: 2019/02/19 12:15 (external edit)

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