KSP celestial slide rule table

[Rodhern]

Welcome to “Kerbin G 113”, a krash kourse in gravitaional mathematics.

Disclaimer: This lesson is valid only in KSP version 1.1.3.

 

It has come to our attention that even our most trusted slide rule jockeys occasionally are caught using those 'modern' electronic calculators. The so-called results obtained in this fashion are of course tedious, hence this mandatory back-to-basics krash kourse.

First thing first, here is your approved course materials.

Spoiler

 

Body	R, km	M, mill. kg	GM
Kerbol	261'600	17'565'669'685'832'900'000'000	1.17233279E+018
Moho	250	2'526'361'681'967'480	1.68609379E+011
Eve	700	122'441'268'043'315'000	8.17173023E+012
Gilly	13	124'205'121'587	8.28944981E+006
Kerbin	600	52'915'792'628'109'100	3.53160000E+012
Mun	200	976'002'360'215'474	6.51383975E+010
Minmus	60	26'457'896'708'308	1.76580003E+009
Duna	320	4'515'481'150'361'070	3.01363212E+011
Ike	130	278'219'487'161'283	1.85683686E+010
Dres	138	321'913'224'453'102	2.14844886E+010
Jool	6'000	4'233'263'473'329'270'000	2.82528004E+014
Laythe	500	29'397'663'009'231'000	1.96200003E+012
Vall	300	3'108'802'809'016'350	2.07481499E+011
Tylo	600	42'332'634'733'292'700	2.82528004E+012
Bop	65	37'261'536'476'100	2.48683494E+009
Pol	44	10'813'636'200'180	7.21702080E+008
Eeloo	210	1'114'935'788'538'350	7.44108145E+010

 

 

First lesson

When I say the g₀ mark of your slide rule line up perfectly with the 9.81 mark, then the result is 9.81 and not a decimal more! Understood? Now go do the exercise; you are to divide the Kerbin GM by Kerbin R and then divide by Kerbin R again.

Spoiler

3.53160000E+012 / 600E+03 / 600E+03 = 35316E+08 / 36E+10 = 35316 / 36 / 100 = 9.81

 

Second lesson

Repeat after me: “If I want to find a universal G, I will take GM and divide by M. I will choose one of the celestial bodies listed in the course material to look up GM and M. There are no other options than those listed”. That is good, now, just for the fun of it, calculate a universal G.

Spoiler

 

Body	GM / M
Kerbol	6.674000E-11
Moho	6.674000E-11
Eve	6.674000E-11
Gilly	6.674000E-11
Kerbin	6.674000E-11
Mun	6.674000E-11
Minmus	6.674000E-11
Duna	6.674000E-11
Ike	6.674000E-11
Dres	6.674000E-11
Jool	6.674000E-11
Laythe	6.674000E-11
Vall	6.674000E-11
Tylo	6.674000E-11
Bop	6.674000E-11
Pol	6.674000E-11
Eeloo	6.674000E-11

 

 

 

Thank you. You did well today. Let us hope you all make it to “Kerbin G 12”, our advanced course where participants are entitled to extra decimals.

 

Request

I have a request for one of you badS talented artists. Could you please make an image of a Kerbal classroom with a black board. Maybe with a Kerbal professor and Kerbal students in it. On the blackboard it says at the top “KSP ver. 1.1.3” and it says “g₀ = 35316 / 36 / 100 = 9.81 m/s²” with the 9.81 part rather over-sized. Preferably a reusable image, so that we may get a new one saying “KSP ver. 1.2” and “g₀ = 9.80665 m/s²” once we get confirmation of that in version 1.2. The idea is that the two images can go side by side and help remind people of the version changes, if for instance they are building a Keo-stationary comms-network in the upcomming release.

 

Edit: I hoped it would be obvious that the above post was meant to be entertaining.

Edited October 20, 2016 by Rodhern

[Rodhern]

Welcome to “Kerbin G 12”.

Note: Exercises valid for KSP version 1.2 only.

First thing first, let us look at the updated course materials.

Spoiler

Version 1.2 parameters

	GM, m3/s2	M, 1012 kg	R, km	SMA	p (rotation)
Kerbol	1.17193245692600E+018	17'559'460'733'554'300	261'600	-	-
Moho	1.68551800528262E+011	2'525'468'687	250	5.263138304 Gm	56d 0h 06m 40.000000s
Eve	8.16893967913260E+012	122'397'988'624	700	9.832684544 Gm	3d 4h 21m 40.000000s
Gilly	8.28661906478000E+006	124'161	13	31'500 km	1d 1h 50m 55.000000s
Kerbin	3.53039400000000E+012	52'897'088'438	600	13.599840256 Gm	0d 5h 59m 09.433799s
Mun	6.51161535216273E+010	975'657'372	200	12'000 km	6d 2h 36m 48.113422s
Minmus	1.76519702630349E+009	26'448'545	60	47'000 km	1d 5h 13m 20.000000s
Duna	3.01260299971008E+011	4'513'885'059	320	20.726155264 Gm	3d 0h 11m 57.859375s
Ike	1.85620276929483E+010	278'121'145	130	3'200 km	3d 0h 12m 09.051792s
Dres	2.14771518990000E+010	321'799'438	138	40.839348203 Gm	1d 3h 40m 00.000000s
Jool	2.82431524208558E+014	4'231'767'138'071	6'000	68.773560320 Gm	1d 4h 00m 00.000000s
Laythe	1.96133002922609E+012	29'387'271'792	500	27'184 km	2d 2h 43m 09.927551s
Vall	2.07410646973931E+011	3'107'703'938	300	43'152 km	4d 5h 26m 20.185935s
Tylo	2.82431524208558E+012	42'317'671'381	600	68'500 km	9d 4h 52m 42.552475s
Bop	2.48598571943389E+009	37'248'366	65	128'500 km	25d 1h 16m 40.423787s
Pol	7.21455627200000E+008	10'809'814	44	179'890 km	41d 4h 34m 16.657569s
Eeloo	7.43854041061866E+010	1'114'541'691	210	90.118820000 Gm	0d 5h 24m 20.000000s

This time a cheat sheet is provided too.

Spoiler

Cheat sheet showing 'surface' gravity in Kerbal Gees. With this table we may perform calculations with great accuracy without the need for a lot of decimals. This table is not used in the exercises below.

KSP ver. 1.2 surface gravity

Body	Gees, g0	R, km
Kerbol	(6.985)*	(130'800)*
Moho	0.275	250
Eve	1.700	700
Gilly	0.005	13
Kerbin	1.000	600
Mun	0.166	200
Minmus	0.050	60
Duna	0.300	320
Ike	0.112	130
Dres	0.115	138
Jool	0.800	6'000
Laythe	0.800	500
Vall	0.235	300
Tylo	0.800	600
Bop	0.060	65
Pol	0.038	44
Eeloo	0.172	210

For Kerbol, in this cheat sheet, R is replaced by an artifical value that is half the radius of Kerbol and the Gees parameter is adjusted accordingly. This is done for convenience.

 

First exercise

Determine the Kerbin sea level gravity acceleration, g₀, better known as "1 Gee".

Spoiler

GM_Kerbin / R_Kerbin / R_Kerbin = 3.530394E+012 / (600E3 * 600E3) = 3.530394 / 0.36 = 9.806650 m/s²

 

Second exercise

Find a suitable universal gravitational constant, G, by examining the mass of the celestial bodies.

Spoiler

GM / M = 66.740800E-12 m³/s²/kg

 

Third exercise

Use the table values to determine the Keo-stationary orbit altitude above Kerbin's equator.

Spoiler

(p*GM^1/2/2/pi)^2/3 - R
 = ((5*3600+59*60+09.433799)*3.530394E+012^(1/2)/2/pi)^(2/3) - 600E3
 = 2'862'940.71 m

 

P.S. If you spot errors in the tables please post a comment about it.

Edited October 21, 2016 by Rodhern
Added cheat sheet

[Rodhern]

So, we arrived at “Kerbin G 121”.

Note: Data valid for KSP version 1.2.1.

Let us run through which of our parameters have changed from version 1.2 to version 1.2.1.

• Radius of all bodies unchanged.
• Periapsis, apoapsis and inclination of orbits unchanged.
• Gravity changed (increased by a factor of 9.81/9.80665 for all bodies).
• Rotation period was changed for Kerbin and all moons except Gilly and Minmus.

 

First lesson

The g₀-value, representing the surface gravity at Kerbin, is (again) exactly 9.81 m/s².

  Hide contents

Refer to the first lesson of version 1.1.3 above; the GM parameter is again 3.53160000E+012.

3.53160000E+012 / 600E+03 / 600E+03 = 9.81

 

Second lesson

The new Kerbinational standard unit for gravitational acceleration is one Gee, which is 9.80665 m/s². This means that the (sea level) surface gravity on Kerbin is more than one Gee.

Spoiler

The Kerbin surface Gee value can be checked at the Tracking Station; it is:

3.53160000E+012 / 600E+03 / 600E+03 / 9.80665 = approx. 1.000342 Gee.

 

Further lessons

I haven't added any tables this time. If anyone misses the course material tables, leave a comment, and I might just add a table or two.