Optimal launch schedual for Solar relay network

[peewee69]

I wanted a deep space relay network and so went through various calculations, working out that I would need a constellation of 5 relays in a circular 17.7 Gm Solar orbit.

So I decided that the best way to get them to their appropriate orbit would be to launch them 1 at a time in intervals equal to 1/5 of Kerbin's orbital period. I calculated this to be aprox every 85 days (given that it take 426 days to orbit Kerbol). As long as I followed the same trajectories for each launch, they should all end up at aprox 72° apart from one another, right? 

WRONG!

Instead, they have ended up at about half the intended distance to one another (around 30° or so).

Why?

[Rauko]

Well, it doesnt work that way. Both kerbin and your already launched relays are movong, so launching in 1/5 years interval wont work.

To solve this, you could launch a relay an place it in your desired orbit. Take note of final position relative to kerbin and time spent to get there (t). For the second launch you will have to figure out where will your first relay and kerbin be "t" days into the future, and where will your second relay finish. 

[mystifeid]

Kepler has always been my all-time favorite historical person.

In his day, it was widely known that the position of the stars and planets influenced destiny. To call oneself a scientist meant that you understood the movement of celestial bodies and could forecast their positions say in five years time. Even Kepler supported himself by casting horoscopes. Unfortunately, when people looked at their horoscope in five years time, the planets were never in the right places and so scientist and like terms were synonymous with charlatan.

I think Kepler became the first person ever able to cast accurate horoscopes although I think the third law was not winnowed from his writings until something like a hundred years after his death.

Edited May 27, 2018 by mystifeid

[Gargamel]

Another option is to do a 'satellite mothership'.  All your satellites are attached to one vessel and get deployed one at a time. 

You launch it once and set it up on a resonant diving orbit, releasing each satellite at the apoapsis or periapsis (depending on the orbit you set up) and having it circularize.  The mother ship dives in it's orbit again, and when reaching apo/peri again, it is 1/5 the way around the intended orbit. 

A good tool for this: https://meyerweb.com/eric/ksp/resonant-orbits/

 

1 hour ago, mystifeid said:

*snip*.

What do horoscopes have to do with the question at hand?

[Geonovast]

6 minutes ago, Gargamel said:

The mother ship dives in it's orbit again, and when reaching apo/peri again, it is 1/5 the way around the intended orbit

 

Make sure to select Kerbol

Your number of satellites

Orbital Altitude is 13599840256 if you want it in Kerbin's orbit.  (I recommend adjusting this... unless you want to use Kerbin itself as the 5th satellite, which would be best if you have the extra groundstations enabled)

Select Dive Orbit.

Edited May 27, 2018 by Geonovast

[mystifeid]

1 hour ago, Gargamel said:

What do horoscopes have to do with the question at hand?

 

Quote

A horoscope is an astrological chart or diagram representing the positions of the Sun, Moon, planets, astrological aspects and sensitive angles at the time of an event...

wikipedia

[Gargamel]

55 minutes ago, mystifeid said:

 

wikipedia

Well don't stop there, you actually make it sound useful with that partial definition.  

[mystifeid]

2 hours ago, Gargamel said:

Well don't stop there, you actually make it sound useful with that partial definition.

Yeah, I think you're missing the point with the horoscopes.

I was sort of hoping someone who was slick at arithmetic might happen by because this could get embarrassing - well never mind.

If all the satellites are leaving on the same trajectory, they're all taking the same amount of time to reach the new orbit so you need to know how much the first satellite has traveled around in its orbit by the time the second one gets there.  To know that it would be helpful to know the period of the first satellite around Kerbol.

Kepler's third law says that the square of the period of a body is proportional to the cube of its semi-major axis. Or:

P² = ka³  or  P²/a³ = k

The constant k is the same for all bodies so

P²_(kerbin)/a³_(kerbin) = P²_(sat)/a³_(sat) = k

If we set Kerbin's period as 1 year and the semi-major axis as 1 AU then (forgetting about units)

P²_(sat)/a³_(sat) = 1

The OP wants the satellite to orbit at 17.7Gm which is roughly the same as saying 1.3 AU so the period is

P = sqrt(1.3³) years

or 1.48 years or 630 days. So it should orbit Kerbol at around 0.57 degrees per day. If the Op launches 85 days apart and teleports them to orbit then the second satellite should hit orbit at a time when the first satellite has already traveled 48 degrees in its orbit - narrowing the lead of the second satellite from 72 degrees to 24 degrees.

Not sure why the OP has them arriving 30 degrees apart - maybe it's because the first satellite has not made orbit yet by the time the second one launches and/or I'm ignoring rotational differences in outbound trajectories -  anyway, I'm sure that person who is slick at arithmetic is still coming...that'll be me, cringing, over there.

Edited May 27, 2018 by mystifeid

[Gargamel]

1 hour ago, mystifeid said:

Yeah, I think you're missing the point with the horoscopes.

I was sort of hoping someone who was slick at arithmetic might happen by because this could get embarrassing - well never mind.

If all the satellites are leaving on the same trajectory, they're all taking the same amount of time to reach the new orbit so you need to know how much the first satellite has traveled around in its orbit by the time the second one gets there.  To know that it would be helpful to know the period of the first satellite around Kerbol.

Kepler's third law says that the square of the period of a body is proportional to the cube of its semi-major axis. Or:

P² = ka³  or  P²/a³ = k

The constant k is the same for all bodies so

P²_(kerbin)/a³_(kerbin) = P²_(sat)/a³_(sat) = k

If we set Kerbin's period as 1 year and the semi-major axis as 1 AU then (forgetting about units)

P²_(sat)/a³_(sat) = 1

The OP wants the satellite to orbit at 17.7Gm which is roughly the same as saying 1.3 AU so the period is

P = sqrt(1.3³) years

or 1.48 years or 630 days. So it should orbit Kerbol at around 0.57 degrees per day. If the Op launches 85 days apart and teleports them to orbit then the second satellite should hit orbit at a time when the first satellite has already traveled 48 degrees in its orbit - narrowing the lead of the second satellite from 72 degrees to 24 degrees.

Not sure why the OP has them arriving 30 degrees apart - maybe it's because the first satellite has not made orbit yet by the time the second one launches and/or I'm ignoring rotational differences in outbound trajectories -  anyway, I'm sure that person who is slick at arithmetic is still coming...that'll be me, cringing, over there.

See, now that is a good answer.  I haven't checked your math, or the theory, but it is at least helpful (I think). 

[peewee69]

On ‎5‎/‎27‎/‎2018 at 6:34 AM, mystifeid said:

Not sure why the OP has them arriving 30 degrees apart 

Actually, this only applied to the distance between the first and second satellites due to a slight launch timing error of about 10 days. Given that your maths calculates the travel time around Kerbol of 0.57° per day, then this should lead to an error of about 5.7° degrees, which should make up the difference between your calculated value of 24° and the measured value of 30°.

When the 3rd satellite arrived into it's designated orbit, it was indeed about 24° from the 2nd.

Thanks so much for the reply, I can now sleep at night!

On ‎5‎/‎27‎/‎2018 at 2:31 AM, Gargamel said:

Another option is to do a 'satellite mothership'.  All your satellites are attached to one vessel and get deployed one at a time. 

You launch it once and set it up on a resonant diving orbit, releasing each satellite at the apoapsis or periapsis (depending on the orbit you set up) and having it circularize.  The mother ship dives in it's orbit again, and when reaching apo/peri again, it is 1/5 the way around the intended orbit. 

This is what I usually do for local satellites. However, I didn't much like the thought of doing this for the deep space satellites as it would involve waiting for many years before the constellation was fully operable, and I have a contract which will need the deep space coms up and running in no more than 4 years.

[mystifeid]

2 hours ago, peewee69 said:

Actually, this only applied to the distance between the first and second satellites due to a slight launch timing error of about 10 days. Given that your maths calculates the travel time around Kerbol of 0.57° per day, then this should lead to an error of about 5.7° degrees, which should make up the difference between your calculated value of 24° and the measured value of 30°.

If it was true that the outbound trips could be ignored and the teleportation example used - and the oldtimers disease is making my head hurt thinking about it - then launching 10 days early should give a separation of around 20 degrees while launching 10 days late gives 26 degrees. Nice to hear you got one at 24 degrees though.

[Gargamel]

On 5/27/2018 at 1:34 AM, mystifeid said:

If the Op launches 85 days apart and teleports them to orbit then the second satellite should hit orbit at a time when the first satellite has already traveled 48 degrees in its orbit - narrowing the lead of the second satellite from 72 degrees to 24 degrees.

Same idea, without the math, I think.  Launch the first one, immediately send it on it's way to the desired orbit.  Once it does it's circularization burn, launch the next.  You may end up with something like a 5/2 resonant launch pattern, but I think that may give the appropriate spread.    Just a guess there....

[mystifeid]

2 hours ago, mystifeid said:

If it was true that the outbound trips could be ignored and the teleportation example used

Easy enough to try. If true the burn windows should be around 263 days apart. Each probe was taking about 40-45 days longer than that to reach the circularization burn in orbit so that might help to explain the discrepancy below. Either that or it was me eye-balling the burns. The first probe is at the top and the fifth probe is to it's right. Anyway, as an approximation (in this case), it turned out to be not that terrible.

Edited May 29, 2018 by mystifeid

[CrashyMcCrashFace]

Launch all at the same time (1 right after the other) and put them into an elliptical solar orbit 4/5 the final orbital period. Then every time the group comes around to target orbit, circularize one of them. Seems like this would take a LONG time.