Help with satellites contracts with "in line sight" restriction

[dimarcinho]

Hi, guys!

I simply love KSP! I already read many things here, but i can't find a good answer to position a satellite. That is my first post around here.

I have this contract, that I must position a satellite in a geostationary orbit around Duna "in line sight x". I can't find a good tutorial or calculator to do this. The orbit is quite simple to achieve, but I must do in a way that when the probe arrives at the apoapsis (in a Hohmann transfer) it must be at the line of sight. That is my problem. I know that should have a balance between the orbit radius and the "ejection angle".

I found tutorials to do this in Kerbin, but i'm quite curious with anything and/or the mathematics. In my example, i'm at 238km and should go to 2880km. I don't know how to calculate where my relative angle to the sight area burning.

Any one could please help?

ps - without mods, pls

 

[bewing]

Those "synchronous orbit with line of sight" contracts are new (with version 1.1). So nobody has had time to write anything about them yet. All I can tell you is how I filled those contracts. I create an almost-synchronous orbit -- where either the Pe or Ap is correct, and the other is just a little bit too high or too low. This means that the "station" on the ground will orbit a little bit faster or slower than the satellite. And then I just wait many orbits for them to line up. When they line up, I do a little burn to fix the Ap or Pe to be correct, and the contract completes.

One other thing to know is that the station on the ground shows the back end of the acceptable position for the satellite. If your satellite is behind that position (even only a few degrees) the contract will not complete. But there is a fairly long distance in front of the position of the station that is acceptable. The station is not in the center of the acceptable range.

To get the contract to complete quickly, you would have to be in a low orbit, and be a little behind the station (just the right distance!), and raise your Ap to the correct value -- so that when you arrived at the Ap, you would be within the acceptable range of positions -- which varies with the number of stars on the contract.

[Streetwind]

Is the point on the surface not shown? I've never attempted such a contract myself, but KSP usually places waypoint markers whenever a point on the surface is relevant to a contract.

Since "geostationary" specifically implies a prograde equatorial orbit (as opposed to just unspecifically geosynchronous), that means it should be easy to do. First, make sure your orbit is equatorial and prograde with respect to Duna's rotation, and find where the waypoint marker is on the surface.

Now, if Duna didn't rotate at all, you would make your burn on the direct opposite side of the planet from where the waypoint is. This would put your apoapsis directly above the waypoint. However, Duna rotates while you are on your way from periapsis to apoapsis, and thus the waypoint will travel away from the apoapsis. So the next order of business is to look up Duna's sidereal rotational period. Alternatively, because Ike is tidally locked, you can also look up Ike's sidereal orbital period, which is exactly the same value. You would do this by focusing on Duna or Ike in map mode, and using the information app in the toolbar. Hopefully, one of these two values will be documented in it. Should you be unable to find this ingame against all expectations, you can definitely find it on the KSP wiki (link at the top of the forums).

Anyway, you will discover that Duna's rotational period is roughly 18 hours (~3 Kerbin days) and 12 minutes. This is great news, because it is a very slow rotation. Much much slower than the time it will take you to travel from a 238 km periapsis to a 2880 km apoapsis. In fact, it is so slow that if you simply made your burn opposite of the waypoint marker, you might even still be in line of sight of the waypoint as you arrive at apoapsis, because the planet just doesn't rotate fast enough.

You can of course increase your chances of being within line of sight if you burn later, after you have passed the opposite of the waypoint. This will put your apoapsis forward with respect to Duna's rotation, so the waypoint first has to catch up and pass it before it has a chance to travel away from it. With a slowly rotating planet, you're probably just fine with eyeballying it, going 20° or 30° past the opposite point. However, if you actually want to calculate it, here is what you do:

Plot a maneuver node to make the geostationary transfer burn, right in front of your vessel, and note the time to apoapsis for the predicted orbit. You know that your destination orbit is circular; and assuming that your departure orbit is also reasonably circular, this time will be roughly the same regardless of where you later choose to make the burn.

Let's just pretend that it would take you 2 hours 30 minutes to get to the apoapsis. You now determine how large a portion of the planet's rotational period this is. Convert both times into seconds. 65,518s for Duna,  9,000s for the trip to apoapsis. Divide the rotational period by 100, and then divide your trip time by that: 9,000 / (65,518 / 100) = ~13,73668... This result is a percentage. Your trip time is about 13.74% of Duna's day. Since one day equals 360 degrees, 13.74% of one day equals 13.74% of 360 degrees: 360 * 0.1374 = 49.464

You now know that you need to burn about 50 degrees past the opposite of the waypoint in order to arrive precisely above the waypoint. But since KSP doesn't have any angle measurement aids, and you only need to be "in line of sight", not directly above, you'd take the easy way out and just pick 45°. This is an easy number to use, because it's half of a right angle. Right angles are easy to eyeball, and thus by definition, this should be easily approximated too. You even know on which side you should err if in doubt, since your ideal angle is slightly above 45°.

 

So, there you go. Now you have all the tools you need to plan your transfer.

 

EDIT:

19 minutes ago, bewing said:

One other thing to know is that the station on the ground shows the back end of the acceptable position for the satellite. If your satellite is behind that position (even only a few degrees) the contract will not complete. But there is a fairly long distance in front of the position of the station that is acceptable. The station is not in the center of the acceptable range.

Wow, that's a nasty little detail I didn't know (since I never did this kind of contract before). Definitely useful to know! That means that just coasting from the opposite point definitely doesn't work, even on bodies with extremely slow rotations. You'll have to develop your own means of adjusting for this - such as adding a flat number of degrees onto your final result, or even already starting some distance past the opposite point as the basis for your calculation.

 

Edited June 16, 2016 by Streetwind

[dimarcinho]

Thanks you two!

I will try it. I think using the method of couting hours and rotations should work, since after I create a node to Ap I can know the time travel to there!

Edited June 17, 2016 by dimarcinho