Calculating Delta-V required when not in space?

[qoonpooka]

Search came up with nothing so...

I have a satellite mission with a specific equatorial orbit around Kerbin. No big deal, really, but I'd like to be efficient about it. How can I calculate the delta-v needed to move from my 80km parking LKO to the target orbit without launching and reverting? I know how to do it with a maneuver node, but I'd like to build once, launch once, and get it right.

EDIT: The Vis-Viva equation was exactly what I'm looking for, and KSP gives us the GM part of it in the show-info on a given body. Yay!

Edited October 28, 2015 by qoonpooka

[Superfluous J]

Actually it'd be far more efficient to launch directly into the target orbit's inclination. Time warp until the launchpad is directly under the target orbit, and launch that direction. The total cost of this will be (normal cost to orbit) + (a trifling amount). Really. A couple hundred dV at most, and dependent on how far off of equatorial the launch is.

You can find out surface orbital speed by going into orbit mode (click "surface" on the navball) on a landed vessel. It's somewhere around 200m/s IIRC. That's the "boost" you get when launching east. To launch North, (so you get no boost) it should cost you that much more dV to get to orbit. To launch west, you need 2x that amount more. So your 3500m/s booster will need 3700 to launch into a polar orbit, or 3900 to launch retrograde.

I won't have time to write this up right now, sorry again. That's what I get for trying to post at work. It suddenly gets busy!

Edited October 28, 2015 by 5thHorseman

[Red Iron Crown]

Assuming you launch into the plane of the desired orbit, all you need is the Vis-Viva equation.

1. Calculate your speed in your parking orbit.

2. Calculate your speed at Pe of an orbit with pe equal to your parking orbit and Ap at the Pe of the desired orbit.

3. Subtract result of step 1 from result of step 2. That's your first burn.

4. Calculate speed at Ap of the interim orbit.

5. Calculate speed at Pe of the desired orbit.

6. Subtract the result of step 4 from the result of step 5. That's your second burn.

7. Add the results of steps 3 and 6 to get total dV required for the transfer.

[Snark]

Search came up with nothing so...

I have a satellite mission with a specific equatorial orbit around Kerbin. No big deal, really, but I'd like to be efficient about it. How can I calculate the delta-v needed to move from my 80km parking LKO to the target orbit without launching and reverting? I know how to do it with a maneuver node, but I'd like to build once, launch once, and get it right.

You want the vis-viva equation:

https://en.m.wikipedia.org/wiki/Vis-viva_equation

Conveniently, if you focus on a planet in map view and open the info panel for it, KSP gives you the value for GM right there, which you can plug straight into the equation.

[Empiro]

The exact delta-V value can be found here:

https://en.wikipedia.org/wiki/Hohmann_transfer_orbit

The practical answer is "very little" if the target orbit is relatively close to Kerbin (up to 1000 km), and if you look at the maximum delta-V on the wikipedia page, it caps out around 53% of your initial orbital velocity (i.e. 1200 m/s will get you anywhere within Kerbin SOI).

[paul23]

Using a hohman transfer is simple enough. Basically you calculate the transfer orbit and the speed in the apogee/perigee. Then at the apogee you do another burn to get to the correct orbit: which is simple enough.

It's a simple equation to get the speed at a certain position, one should simply use the vis-viva equation:

With G*M being the standard gravitational parameter, which is 3.5316000 * 10^12 M^3/s^2. r is the distance from the center (Kerbin). And "a" is the semi-major axis of the orbits (radius in case of a circular, difference between peri-apoapsis divided by two in case of an ellipse). Notice that the left hand is the speed squared, so take the root of the right side for the speed.

So steps are as following, all using above equation:

1) Calculate speed at the LKO (r = 600+80km, a = 600+80km)

2) Calculate speed for the transfer orbit at periapsis (r = 600+80 km, a = (600+80km + touching_point)/2)

3) Difference in speed is delta-V_1

4) Calculate speed at apoapsis of transfer orbit. (r = ...., a = ...) notice that a is the same as in step 2, but since r isn't, the speed isn't either

5) Calculate speed at this position for the final orbit (r = ..., a = ...)

6) Difference between 4 & 5 is delta-V_2

7) Sum up the delta-Vs

Edited October 28, 2015 by paul23

[qoonpooka]

Awesome! That's the formula I needed. Thank you guys!

[Red Iron Crown]

One thing when running the Vis-Viva equation: It's true radius from planet center for r, not altitude from sea level. So you have to add 600km (around Kerbin) to all those values for Ap and Pe for the formula to work properly.