Tutorial - Evenly Spacing Satellites for a Communications Relay Network - Kerbal Space Program 

Very nice. Although I would suggest one minor change. The change is get the orbit of your drop ship tuned prior to deploying any of the satellites. This modification means that you're only interested in adjusting the orbit of a single vessel at any given time and that you have plenty of time to tweak the drop ship's periapsis and apoapsis to as precise a value as desired. Once the drop ship's orbit is tweaked, you then no longer have to adjust its orbit for the rest of the deployment. Now, each time the drop ship reaches its periapsis, you detach the next satellite and circularize its orbit. Heck, if you want your timing to be nice and relaxed, you can have the drop ship doing a retrograde hold attitude during the orbit and have the satellite separate a minute or two before reaching periapsis. After separation have the satellite also go into retrograde hold and perform the circularization burn as the satellite reaches periapsis. Advantages? At no time are you needing to perform maneuvers with two vessels at the same time. Also, you don't have a tight time constraint on adjusting the orbit of the drop ship (which you do with your method).

Is it normal to play ksp with a notepad/calculator nearby? Because I'm about to break them out.

What i do is I just enter a circular (pretty much perfect circular) orbit with "eyeballed" altitude, take the orbital period time (from kerbal engineer redux), - convert it all into seconds, multiply those by 1.3 (to increase it by 1/3 coz i usually deploy 3 comm relay sats), - convert back to D/H/M/S (from just seconds) and then burn prograde with my "drop ship" until my engy redux shows that orbital period..... Simple as that... Then drop the relays 1 by 1 at a predesignated spot (Pa, since i burned prograde to increase orbital period by 1/3 - works other way round too.....) and burn retrograde with each sat until my orbital period is the same as original, eyeballed one..... Use RCS to adjust orbital period down to millisecond and voila! new fully functional comm relay is there..

For what it's worth, the most important thing i took away from this video (you smart boi) :D, is (which I totally forgot) the thrust limiter, to increase the accuracy of the engine controls to get a more exact orbit. Always fumbling around with really short presses to get the orbit right :D.

Great vid man! I like how you animate the equations. Clean and simple. Keep it up !

Pretty good video, it explains the math quite well. I was following your equations by doing them in my notepad and I put a little extra feature into them, which is accounting for the atmosphere. According to my 2 am math, it only has to be accounted for when you're calculating the minimum height. My equation for that came to be (p+a)/sin(π/2 - π/n) - p (where p is the planet radius, a the atmosphere height and n the number of satellites). After finishing, I decided I really don't want to be doing these calculations myself or alternatively having to write them into wolfram all the time, so I made a dorky little C++ program that just asks for the parameters and for some reason speaks like a cowboy. It totally didn't take me 3 hours because of some weird type shenanigans (especially with the power function). So it may or may not be 5 am right now... But hey, the numbers it's spouting out now are correct and it's gonna be really useful as I send my drone army around the Kerbol system! Anyway, thanks a lot, mate!

Thank you for this explanation! Now I'm not just launching satellites haphazardly

You Sir are a gentleman and a scholar.

You could save some dV by having your dropship have a lower orbit than your final satellite orbit. For example, suppose you are going for keo-stationary oribts starting from a 100km circular orbit of kerbin. To get your apoapsis from 100km up to 2863km, you need 651 m/s of dV. Then if you put yourself in an orbit with 2/3 the synchronous orbital period, you only need an additional 253 m/s of dV. Then you release your satellites and they circularize at 2863km, which requires another 171 m/s of dV. Overall each of your satellites needs 171 m/s of dV and your ship (once in orbit) needs 904 m/s of dV. However, if you set up your dropship with an orbit as shown in the video, where the orbital period of the dropship is 4/3 the synchronous period (rather than 1/3) then the following would be true. To get from 100 km to the apoapsis of the higher orbit (4327 km) would require 726 m/s of dV. Then to raise the periapsis from 100km to 2863 km would require 346 m/s of dV. Then once the satellites are released, each satellite would need to lower its orbit requiring 84 m/s of dV. Here your dropship would need 1073 m/s of dV (after reaching a 100km circular orbit). Overall if you use a higher dropship orbit, then your satellites need less dV, but your dropship (carrying all that mass of the satellites) requires MORE dV as compared to using a lower dropship orbit. NOTE: This is all specifically for a Kerbin network. A network around any other body would be the exact opposite, where higher dropship orbits are less dV expensive because for those bodies you start with a hyperbolic orbit rather than an elliptical orbit.

Fantastic job sir! I love how you did this as well as explaining in detail how it all works and why. Very very cool and a much better done video than the one I attempted 4 years ago ;)

This is so great! Thank You!

Fantastic tutorial, thank you so much for making this!

Thanks for working this out. And thanks for the math. I followed most of it. And I love the spreadsheet. One question, though, how did you build the launcher with multiple satellites? I paused the video and looked at the parts, but haven't managed to sort it out yet. Did you happen to make a build video for this or something similar? Thanks.

When should you be circularizing the orbit? ASAP? At PP or AP? That's the only thing I have issue with. Besides that I'm good on this for sure.

In the end, you should've played "The Dark Side of the Mun" by Pink Kerman.

This video is amazing thank you so much

Guys, if this is too much maths for you, don't worry. Just burn prograde with your dropshit until it is roughly one third behind your first satellite. Drop the sattelite, circularize and repeat.

Great video and presentation style.

I've spent more than 2h30 understanding the first 5 minutes.... :c

Satellite spacing doesn't last. The game engine always does something to one orbit or the other and your perfectly designed pentagram on the map screen turns into a cat's cradle.

just eyeball it ; )

After watching this the only thing I want to say is that I feel dumb.. 😔

You are over-complicating the problem. (1) get to the desired orbit (2) divide the current orbital period by the amount of satellites and add this number to the orbital period to get your second orbital period and burn prograde until it's achieved (3) release a satellite right before the PE where both orbits intersect (4) burn retrograde with the sat until the first orbital period is achieved, and let the dropship continue on the second orbital period (5) repeat with the other sats (6) fine tune the orbits when all sats are in place

i say less explanation of stuff like the math/science