How do you calculate the amount of Delta-v required to get into a specific orbit

[Astrofox]

So, I was wondering how you can calculate the amount of Delta-V required to launch from the ground into orbit, since I have been looking all over the internet for an answer.

Here's an example of what I'm talking about:

Calculate the amount of Delta-V required to get into a 200*450km orbit if you launch directly from the ground.

So, is there an equation for such a problem, or is it unsolvable?

Thank you for replying!

[Superfluous J]

It's not "unsolvable" but the divergence between theory and reality is pretty huge. There are a ton of things that can be different from launch to launch, aerodynamics can give you lift but also drag, and dropping stages and changing throttles manually can make differences too.

Personally, I just do a launch or two (or 85) and see how much dV I have at the start and once I'm in orbit. Then I tweak so my launcher has a little bit less than that amount (so it falls back into the atmosphere). Then I do a launch or two (or 85) to make sure the changes I made didn't affect the dV to orbit very much.

[Rosco P. Coltrane]

Are we talking about bodies with an atmosphere or without?

If with atmosphere, there's a thread explaining it, it wasn't hard, but I simply can't find it. In any case, it will change now with the new aerodynamics. If the body is airless, then it's pretty simple and I'd be glad to dig up my calculator history to show you the math.

[Taki117]

Once you spend the ~4500 m/s to get into orbit you don't need much more to change your orbit. We're talking a few hundred m/s max.

[Xavven]

So, I was wondering how you can calculate the amount of Delta-V required to launch from the ground into orbit, since I have been looking all over the internet for an answer.

Here's an example of what I'm talking about:

Calculate the amount of Delta-V required to get into a 200*450km orbit if you launch directly from the ground.

So, is there an equation for such a problem, or is it unsolvable?

Thank you for replying!

Your specific question about getting into orbit from a planet with an atmosphere is very complicated. Just look up the Goddard problem, for example. Let's just say it's not something that was solved with mathematics at the undergraduate college level. It is very dependent on things like your TWR and how it changes as you burn fuel, and when you stage (and how that affects your TWR), as well as how much drag your rocket experiences at each stage and point in time.

Heck, it's hard enough to estimate delta-v needed on airless bodies. Just look at some of the delta-v maps that have been made for KSP. Boy was I in for a surprise when I tried to land on Tylo using the recommended Delta-V on those (hint - they were way off compared to how I built my landers).

[Rosco P. Coltrane]

Heck, it's hard enough to estimate delta-v needed on airless bodies. Just look at some of the delta-v maps that have been made for KSP. Boy was I in for a surprise when I tried to land on Tylo using the recommended Delta-V on those (hint - they were way off compared to how I built my landers).

All dV maps assume that when landing/taking off you a) do it perfectly (ie, optimal ascents, suicide burns) and you land on a point with 0 meters elevation in the equator. Obviously in real life you're not gonna be doing that, so you have to keep that in mind.

[mhoram]

By usual consens in the forum it takes about 4500 m/s to get from Kerbins Spaceport to a 70x70km orbit.

To get from a 70x70km to a 70x450km orbit it takes a single burn with about 236 m/s.

To get from a 70x450km to a 200x450km orbit it takes a single burn at 450km with about 83 m/s.

So in sum you will need about 4500 + 236 + 83 = 4819 m/s of Delta-V to get into a 200x450km orbit.

I used the Vis-Viva equation to calculate the needed Delta-V for the two transferburns.

It might be the case that a direct launch to the target orbit needs a bit less Detla-V but it should be of the same magnitude.