Escape Velocites and Orbital Heights

[shadragon]

Yes, noob question, sorry.

I have take-off and recoveries under (relative) control, now I want to go higher and hit orbit, then eventually get to Mun, Minmus.and beyond.

I'm looking for a reference chart (or Excel spreadsheet sort of thing) showing all the various bodies in the game with their escape velocities and orbit heights. Should make planning missions a lot easier. Is there such a thing?

Cheers.

Edit: Last minute Google search produced this table for Kerbin: http://gaming.stackexchange.com/questions/80423/can-i-escape-kerbins-gravitational-pull

Is there one doc with all system planets and moons listed? I want to print it off and have it as a handy reference instead of alt-tabbing to the wiki all the time.

Edited August 24, 2016 by shadragon

[mhoram]

For mission planning Delta-V charts can help a lot:

There are many Delta-V Maps available.

They help you to estimate the Delta-V you need to get from Kerbin to the other planetary bodies (and back).

For planning missions between other bodies, these two webapplications can help:

- http://alexmoon.github.io/ksp/
- http://ksp.olex.biz/

Also there is a mod for this.

I have never seen a chart of escape velocities, but it is quite easy to compile one by yourself by using the formula found on Wikipedia and inserting the mass of the planet.

 

Edited August 24, 2016 by mhoram

[OhioBob]

Both orbital velocity and escape velocity vary depending on the radius of the orbit.  If you want a table, you may have to compute it yourself.

For a circular orbit, orbital velocity is

v = (μ/r)^1/2

and escape velocity is,

v = (2μ/r)^1/2

where v is the velocity, μ is the planet's gravitational parameter, and r is the orbital radius (radius of planet + orbital altitude).

The gravitational parameters and radii for all of KSP's celestial bodies are:

	μ (m3/s2)	ro (m)
Sun	1.17233277E+18	261,600,000
Moho	1.68609375E+11	250,000
Eve	8.17173000E+12	700,000
Gilly	8.28945000E+06	13,000
Kerbin	3.53160000E+12	600,000
Mun	6.51384000E+10	200,000
Minmus	1.76580000E+09	60,000
Duna	3.01363200E+11	320,000
Ike	1.85683680E+10	130,000
Dres	2.14844886E+10	138,000
Jool	2.82528000E+14	6,000,000
Laythe	1.96200000E+12	500,000
Vall	2.07481500E+11	300,000
Tylo	2.82528000E+12	600,000
Bop	2.48683500E+09	65,000
Pol	7.21702080E+08	44,000
Eeloo	7.44108120E+10	210,000

 

Edited August 24, 2016 by OhioBob

[shadragon]

Mhoram & OhioBob, I took your responses (THANKS!) and turned them into a spreadsheet for orbital and escape velocities of each major body in the game. Should be self-explanatory. "(My calc)" columns are ones I calculated from the data provided and the "(Wiki)" column is copied from the Wiki to validate the calculations accuracy. If you don't want to download my copy of the spreadsheet, for whatever reason, you should be able to recreate this pretty quickly.

I hope this is of use to someone. Next project is to add a delta v table from each body to all others. Tips on how to proceed welcome. 

Screenshot of spreadsheet here: 

Excel 2010 file download here (xlsx): https://www.mediafire.com/?g2246rxpjm8epj2

Note: While I have scanned this Excel file with decent anti-virus and anti-malware software to ensure it is clean, downloading third party files from the Internet is always problematic. Please keep this in mind and vet any downloads with your own scanning software before opening them. 

[foamyesque]

Those look like they're 0-altitude orbital velocities to me, which are interesting but not super useful.

[GoSlash27]

shadragon,

 Assuming you're in a circular orbit, escape velocity is simply orbital velocity x sqrt(2).

Recommended orbital altitudes are given in the DV maps, but feel free to set your own based on terrain, atmosphere, and time warp limitations.

Best,
-Slashy

[mhoram]

A few comments on your post:

Now that I think about it, Escape velocities do not provide essential information for mission planning:

The most commonly used method for going interplanetary to a different planet is to burn in low Kerbin orbit in order to get an intercept with another planet (There are a few alternatives but lets keep this for this argumentation simple). In order to calculate this ejection burn, your table does not provide substantial information besides that the ejecteion burn is larger than "escape velocity - orbital velocity".
Your table offers information about the Delta-V needed in order to leave Kerbins SOI (from a circular orbit at altitude 0). Such a maneuver brings you into a Solar orbit very near to Kerbins orbit. This target destination is only useful in very few occasions, so please don't be disappointed, if your table receives less feedback than you expected.

Kudos for diving into the calculations!

Also you might want to switch to a different file hoster: See here

17 hours ago, shadragon said:

Next project is to add a delta v table from each body to all others. Tips on how to proceed welcome.

If you were to compile such a table, then I would recommend to look at the values you find in the Community Delta-V Map. These should provide you with information about important aspects of mission planning.

[shadragon]

Hey Guys,

It's a Work in progress. If I need to add altitude parameters, point me in the way of the formulas and I'll include it. I was surprised to get such a close correlation between my initial calcs and the Wiki. The end goal is to have a reference sheet for quick info look-ups. As stated, I'm approaching this with wide eyed optimism so if I screw up or don't take something into account, do tell me. My experience in orbital mechanics is about five days old at the moment.

Cheers.

 

[GoSlash27]

2 hours ago, mhoram said:

Now that I think about it, Escape velocities do not provide essential information for mission planning:

mhoram,

 Actually, they do. We calculate burns across SoI boundaries using the excess velocity (vis-viva in the solar frame), escape velocity, and orbital velocity. 

DV=sqrt(Vexcess^2+Vescape^2)-Vorbit

Best,
-Slashy

*edit* as an example...

Suppose you want to burn directly from low Kerbin orbit to Duna. 

First thing you need to do is figure out what a Hohmann transfer would cost from Kerbin to Duna. There's lots of good tutorials on vis-viva, but it goes like this.

Kerbin's orbital velocity is 9,297 m/sec.

If we were in an elliptical orbit with a periapsis at Kerbin and an apoapsis at Duna, our velocity at periapsis would be 10,216 m/sec. Our hypothetical DV on this burn would be 10,216-9,297= 919 m/sec.

Of course, we are not actually doing this burn, but it is the excess velocity required to set up a Duna transfer, so we use it in the above equation.

Vxs= 919 m/sec

We're chillin' in LKO at 70 km altitude, so

Vorb=2,296 m/sec

Escape velocity is orbital velocity x sqrt(2)

Vesc= 3,247 m/sec

So using the equation above...

DV= sqrt(3,247^2+919^2)-2,296

DV=1,079 m/sec

Best,
-Slashy

 

 

 

 

 

 

Edited August 26, 2016 by GoSlash27

[mhoram]

51 minutes ago, GoSlash27 said:

DV=sqrt(Vexcess^2+Vescape^2)-Vorbit

Cool, I was not aware that the escape velocity could be used for this.

My approach for the escape-burn-DV calculation was to apply the Vis-Viva formula twice without using the escape velocity. (first to calculate the semi-major axis of the hyperbolic Kerbin-escape orbit and second to calculate the velocity at the periapsis)

[OhioBob]

3 hours ago, shadragon said:

If I need to add altitude parameters, point me in the way of the formulas and I'll include it.

The formulas are the same, you just change the value of r.  That is,

r = r_o + z

where z is your altitude.

Let's say you want to know orbital velocity in a 80 km orbit around Kerbin,

r = 600000+80000 = 680000 m

v = SQRT(3.5316E+12/680000) = 2279 m/s

[GoSlash27]

^ In addition to what OhioBob said, "low orbit" is whatever you personally decide is appropriate. For bodies with atmospheres, "orbit" doesn't include altitudes where you encounter drag, but you may decide to raise it far above the atmosphere for higher time warp multipliers. For airless bodies, the lower limit is terrain avoidance and again... higher altitudes allow for higher warp.

It's your chart, so you decide what constitutes "low orbit".

Best,
-Slashy