I found the duration of a month on Kerbin

[VincentMcConnell]

So, by using the SMA of the Mun, the gravitational parameter of Kerbin and Pi, I calculated the Mun\'s orbital period.

This means I have found the length of a Month (Munth?LOL) on Kerbin.

If my calculations are correct, it lasts:

38.612800340434050698059694445 hours.

We can round this and just say 38.61 hours.

[Selrahc4040]

One and a half small days for man, one giant month for Kerbalkind!

[Vanamonde]

I calculated it by dividing the circumference of its orbit by its stated orbital velocity, which yields 36.696 hours. It works in this instance because Mun\'s orbit is circular; its altitude is a constant 11,400km. I\'ve noticed Minmus\' orbit is inclined a bit, but I haven\'t watched to see if it\'s eliptical.

[VincentMcConnell]

I calculated it by dividing the circumference of its orbit by its stated orbital velocity, which yields 36.696 hours. It works in this instance because Mun\'s orbit is circular; its altitude is a constant 11,400km. I\'ve noticed Minmus\' orbit is inclined a bit, but I haven\'t watched to see if it\'s eliptical.

Sorry to say, but your calculations are off by about two hours.

The most accurate way to find orbital period is the following formula

?(2)?(A^3/U)

? = Pi

A= Semi-Major Axis

U= Gravitational Parameter of Parent Body.

[Vanamonde]

The distance covered (circumference of orbit) divided by the speed has to equal the time required, if the speed is constant, which it would be on a circular orbit. If the figures given by the game\'s map info are correct (and they may not be, I don\'t know), that comes out to 36.676 hours. (I\'m not trying to be argumentative. I just find this stuff interesting.) Your method is the more sophisticated one that works on different kinds of orbits, but in this simple sub-case where the orbit is circular, shouldn\'t my geometry come up with the same answer?

[Zephram Kerman]

This might be one of those times where both answers are correct, because of a discrepancy in the way the game handles these figures. If Mun were in real life, the two methods should coincide exactly. But since we\'re dealing with a simulation, there is bound to be slight error. On the other hand, an error of 5% does seem suspicious...

[Cryphonus]

So, by using the SMA of the Mun, the gravitational parameter of Kerbin and Pi, I calculated the Mun\'s orbital period.

This means I have found the length of a Month (Munth?LOL) on Kerbin.

If my calculations are correct, it lasts:

38.612800340434050698059694445 hours.

We can round this and just say 38.61 hours.

Have you verified this through experiment? Becase Mission Timer shows a day after 24 hours. A month being 38.6 hours doesn\'t sound consistent.

[flaillomanz]

Have you verified this through experiment? Becase Mission Timer shows a day after 24 hours. A month being 38.6 hours doesn\'t sound consistent.

It\'s been transposed to Human time... I mean, Squad ARE obviously channeling radiowaves from the distant Kerbin in order to make this game.

[maltesh]

THe other thing is that using rbital period calculations will give you the sidereal period; the revolution period of the Mun relative to the background stars.

It\'s very unlikely for a civilization to base timekeeping on the sidereal month, they synodic month\'s a lot more obvious to a low-tech civilization.

THe synodic Munar period is the rotation period relative to Kerbol as seen from the surface of Kerbin, which is also the time period for the Mun to go through a full set of phases. In the time that it takes the Mun to complete a sidereal period, Kerbin moves in its orbit, so the Mun has to go around a bit further to get back to the same phase as seen from Kerbin.

Accounting for Kebin\'s rotation around Kerbol, I get 38.62 hours for the sidereal period of the Mun, and 39.22 hours for its Synodic Month.

Similarly, for Minmus, I get 299.39 hours for its sideral period, and 339 hours for its synodic month.

[Tfin]

I\'ve not been here long, but I\'ve seen posted that the Mun, on rails, does not orbit at quite the correct velocity for its given mass and altitude. This was in a thread about multi-body gravitational forces, IIRC. That would mean that the 'more correct' calculation would give an answer that should be accurate, but isn\'t.

[The_Duck]

I suspect some of the confusion in this thread arises from the fact that the altitude the game shows for the Mun is the altitude *from the surface of Kerbin* (just like the altitude meter shows for your ship). But for orbital calculations one must use the altitude from the *center* of Kerbin. If one accounts for this by adding Kerbin\'s 600km radius to the Mun\'s reported altitude, one realizes that the Mun in fact has the correct orbital velocity.

[flaillomanz]

I suspect some of the confusion in this thread arises from the fact that the altitude the game shows for the Mun is the altitude *from the surface of Kerbin* (just like the altitude meter shows for your ship). But for orbital calculations one must use the altitude from the *center* of Kerbin. If one accounts for this by adding Kerbin\'s 600km radius to the Mun\'s reported altitude, one realizes that the Mun in fact has the correct orbital velocity.

Give the man some applause! I like your style.

While the rest of us were puzzling over the discrepancy, you used some good old common sense.

[PakledHostage]

If one accounts for this by adding Kerbin\'s 600km radius to the Mun\'s reported altitude, one realizes that the Mun in fact has the correct orbital velocity.

It does, and it doesn\'t. Adding the 600 km radius cause Vincent\'s and Vanamonde\'s numbers to agree, but the orbital speed of the Mun IS a bit slow in the game. The speed used in the game would be correct if the Mun had insignificant mass relative to Kerbin\'s mass (i.e. like a spacecraft), but when you account for the Mun\'s significant mass, the Mun should be orbiting about 4.9 m/s faster than it is.

That being said, there was an extensive discussion about this back in November where HarvestR pointed out that, even though this isn’t related to 2-body vs. n-body physics, the 542.5 m/s value used in the game is a limitation of Unity and we\'re stuck with it.

[VincentMcConnell]

Have you verified this through experiment? Becase Mission Timer shows a day after 24 hours. A month being 38.6 hours doesn\'t sound consistent.

Yes. These are the same calculations I use to calculate orbital period of all of my spaceflight missions in KSP. This is THE formula for period.

[Endeavour]

The KSP Orbit Mechanic has told me 1 day, 14 hours, 36 minutes and 47 seconds. But good work doing the math.

[Vanamonde]

I did consider several reasons I might be off, including the sidereal/synodic thing, but I confess it never occurred to me that Mun\'s 'altitude' might be measured from Kerbin\'s surface, since that\'s not a useful figure for orbital math. It\'s always the obvious stuff that one overlooks. So is the map\'s altitude surface-to-surface, surface-to-Mun-core, or what? And if I follow Mun at 542.5, will I approach or draw away or just sit there?

[Stevenator1]

As Vincent had said, Kepler\'s laws don\'t change I verified his math, he is absolutely correct.

On the other hand, why the hell is a day on the mission counter 24 hours? A day in kerbal-time is somewhere around the range of 6-7 hours (I\'ve been up for 40 hours, don\'t want to do math, so just observed it on map view).

[PakledHostage]

So is the map\'s altitude surface-to-surface, surface-to-Mun-core, or what? And if I follow Mun at 542.5, will I approach or draw away or just sit there?

I believe it is Kerbin\'s surface to the Mun\'s core. This assumption works in all of my calculations. From what I understood from November\'s discussion, Unity\'s limitations force KSP to calculate the Mun\'s orbital speed as if it were an infinitesimal mass orbiting Kerbin at the Mun\'s orbital radius. If I understood HarvestR\'s comments correctly, then the Mun isn\'t 'on rails' in the game in the sense that its position could be propagated at any arbitrary speed. Instead, it orbits at the same speed as a spacecraft.

Edit: Also for reference, a solar day on Kerbin is 6 hours and 50.8 seconds long. This can be verified by watching Kerbol set from the surface.

[PLB]

As long as we are talking about time, how long SHOULD a kerbal-second be? Let\'s take what a second is on Earth that you can compare anywhere, and proportion it to Kerbin. Then we\'ll work from there!