What's the true mass of Kerbin? [SOLVED]

[Jupiter3927]

I was trying to phase shift one of my satellites but the listed mass for Kerbin seems to be wrong and it's throwing off my math.

The game lists kerbin's mass as 5.292*10^22.
The ksp wiki (maybe outdated) says Kerbin's mass is 5.2915134*10^22.
I checked both values for my current orbital period of 1 hour 17 minutes and 17 seconds and my math says I'm orbiting at 1,243,637 meters.
Problem is my satellite is orbiting at 500km above the surface or 1,100,000 meters.

I used my equation, r = ((G*m*T^2)/(4*pi^2))^(1/3), to solve for the mass of Kerbin and got 3.6165479157*10^22 kg.

My question is: is Kerbin 5.292*10^22 kg like the game says or 3.617*10^22 kg like my math says?

[Stickmiin]

So, i guess it's better if we walk through this from the start.

The main things we know for sure for Kerbin are equatorial radius (at 600km) and gravitational acceleration at sea level (roughly 9.81m/s^2). What can we use these for?

Well, for a start, we can use the equation F = G*((m1*m2)/r^2) to give us a value for our mass (m1 will stand for Kerbin's mass and m2 will be representing any object that you can think of).
What we can take from that formula is that it can give us a value for our weight (W) when we are standing right on the surface, so we use the formula W = m2 * g to help us out with our masses, now F = W and we can get our third, and final, equation.

m2 * g = G * ( ( m1 * m2 ) / r^2 )

from here, we remove m2 and shift things around to get a better view of our mass.

m1 = g * ( r^2 ) / G

plug the numbers

m1 = 9.81 * ( ( 6 * 10^5) ^2) / (6.67 * 10^-11)
m1 = 9.81 * 36 * 10 ^10 / (6.67 * 10^-11)
m1 = (10^21) * ( ( 9.81 * 36 ) / 6.67)

m1 = 52.947526236881565 * 10^21

which we can convert to a simple

m1 = 5.2947526236881565 * 10^22 kg

now, i'm not sure where you went wrong with your calculations, since i just saw the question and did this to get the value, but i hope i've helped you.

[Jupiter3927]

Maybe I entered something in my calculator wrong?
I'm using Kepler's thrid law for my calculation.
T^2 = (4*pi^2*r^3)/(G*m)

When rearranged to solve for for m, you get...
m = (4*pi^2*r^3)/(G*T^2).
r = 1100000 meters.
T = 4637 seconds or 1 hour, 17 minutes, 17 seconds.

m came out to 3.6638506865 * 10^22 this time.

Such a mystery...

[Jupiter3927]

Calculated the mass of Kerbin from the Mun...
Using the same formula from above but changing 2 variables...
r = 12,000,000
T = (2*pi*12,000,000)/542.5

The mass of Kerbin came out to 4.07839433148*10^19.

Is mass not constant anymore?

[Manwith Noname]

What happens if you use the orbital period and distance of Kerbin around the sun?

[Jupiter3927]

So kerbin around Kerbol...
r would be 13,599,840,256.
T would be (2*pi*r)/9284.5.

Kerbol's mass comes out to 1.61763363811*10^35.
KSP wiki has the mass of Kerbol listed at 1.756459*10^28.

There's definetly some unknown variable.
That or I'm wrong and no one caught my error.

[Stickmiin]

Alright, i took some time to re-check everything and did what you did with the Mun.
So let me just show how i worked it out.

First, i looked at the formula in it's basic form, ( (T^2/R^3) = (4*pi^2) / (G*M) ). From that, i decided that it was easier for me to work on the left side of it first, them move things around after that.

T^2 = 138984*138984 = 19316552256 and R^3 = 1.728 * 10^24

from that, we get that T^2/R^3 = 1.117856 * 10^-14 = U (im using U just to simplify things)

now we can work on the rest, multiply that by G and we get

U*6.67*10^-11 = 7.4560997 * 10^-25 = Y (same as the reason i used U)

for our next part, we move things around so we have

(4*pi^2) / Y = M

throw the numbers in

39.4784176 / 7.4560997 * 10^-25 = M

and finally

5.29478134584995 * 10^25 g

[Stickmiin]

Personally, i would avoid using the modified third law to do this because it really isnt optimal. It is an aproximation (since we just kinda discard our sattelite's mass) and compared to the simplicity of using the gravitational force makes it very bad at giving us what we want.
As for other stuff on the wiki, most of the numbers there are given to us by the game and it's been a long time since things changed drastically. I think the only really big change to numbers was on atmospheres, which are all mostly irrelevant for most things other than when you are in them.

[Jupiter3927]

I found my error in my Kerbol mass calculation...

Originally posted by Jupiter3927:

So kerbin around Kerbol...
r would be 13,599,840,256.
T would be (2*pi*r)/9284.5.

Kerbol's mass comes out to 1.61763363811*10^35.
KSP wiki has the mass of Kerbol listed at 1.756459*10^28.

I forgot to square the period and came out with about 1.758*10^28kg.

One mystery solved at least.


Back to Kerbin...
About the 3rd law approximation, the satellite mass when compared to Kerbin is so low, it's negligeable.
All the planets are 'on rails' too so they won't move even if you put something massive enough to affect the orbit of a planet near the planet.

The wiki is updated frequently enough that I doubt it would be out of date for more than an hour after a new version of KSP comes out.

I redid my Mun calculation with...

M=(4*pi^2*12000000^3)/(G*((2*pi*12000000)/542.5)^2)

...and M came out to 5.29486506747*10^22


I hate it when problems resolve themselves like that.

Chalking this one up to calculator input error.
Thanks for helping.

[Manwith Noname]

So, here's something weird...I'm doing things the lazy way because "pen and paper math" is something I gave up years ago....

http://www.ajdesigner.com/phpgravity/keplers_law_equation_mass.php

Using that with values for the Mun I get the right mass for Kerbin, with the craft information from the OP, I get the wrong value for Kerbin.

*throws spanner in the works*

[Stickmiin]

The third law thing is more of a personal dislike with approximations of formulas than actual practical use, so it's up to you if you feel like you can use it or not.
Anyway, glad i could be of help, hope whatever you needed these for will work out.

[Stickmiin]

Originally posted by Manwith Noname:

So, here's something weird...I'm doing things the lazy way because "pen and paper math" is something I gave up years ago....

http://www.ajdesigner.com/phpgravity/keplers_law_equation_mass.php

Using that with values for the Mun I get the right mass for Kerbin, with the craft information from the OP, I get the wrong value for Kerbin.

*throws spanner in the works*

So, for the website, if you use OP's first value for the radius (1,243,637 meters) the value comes out right, but if you use the second one (1100000 meters) it comes out higher. I think it's because it's possibly the value of the pe and not the mean value between ap and pe.

[Jupiter3927]

I guess throwing a manuever node directly behind the ship and zooming in all the way and moving the node until it say 0 seconds isn't a valid way to get orbital period information.

The orbit was circular enough to have both the Pe and the Ap say 500,000 meters.

[Jupiter3927]

One more mystery solved...
I did 2*pi*1100000(m)/1791.8(m/s) and got 3857.3s ish for my period.

I guess manuever nodes account for the rotation of the planet around Kerbol.

[Stickmiin]

There's a way to get that easily. Let's say that you are going towards your pe and it will take you X amount of time to get there and Y time to get to your ap. What you do is T = 2 * ( Y - X).