Burn time calculation for orbit change

[Ashtar Veres]

Hi all, 

I'm searching for a while how to calculate the duration of a burn required to change orbit both for the Hohmann transfer maneuver and for circularization maneuver.

I'm using KOS in KSP and after launch I have periapsis at about 85km and apoapsis at around -200km. At this point I want to write code for orbit circularization. So from my understanding I should burn until my speed at perigee will be equal to the speed at apogee and this will mean that I have close to 0 eccentricity. I wasn't able to find the calculations needed to get the deltaV needed and the burn time. 

Can anyone help please?

 

Thanks

[Gargamel]

Going to move this over to Game Play Questions. 

[HebaruSan]

The vis viva equation relates speed to altitude of a given orbit:

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

[pincushionman]

Just now, HebaruSan said:

…

Ninja’d!

But anyway, in your case, your a (semi-major axis) is (85,000 + 2 x 600,000 + -200,000) / 2 = 542,500 and your r is 85,000 + 600,000 = 685,000. GM for Kerbin can be found on the wiki.

Put those values in and you’ll get your speed at apoaspsis. Calculate again with both values 685000 and that will be your circular orbit speed; the difference between those numbers is the delta-V of your circularization maneuver.

[Aegolius13]

This page shows the equation to get from delta-v required (determined per above) to burn time, using a rearrangement of the Rocket Equation:

http://www.alternatewars.com/BBOW/Space/Rocket_Equations.htm

But note that that's idealized.  Real-life performance will be slightly worse, mainly because you can't put all of the required impulse down a right at the maneuver node, so some of your potential delta-v will be wasted as cosine losses. 

 

Edited May 4, 2019 by Aegolius13