How to Calculate Orbital Period

[VincentMcConnell]

Have you ever been in orbit around Kerbin, Mun or Minmus and thought, I wonder how long this orbit takes? This may be useful to knowing how much time you have until a certain burn or transfer must be made, or even when or where to splash back down in the ocean.

Let\'s find Semi Major Axis First: My own little KSP formula is the following:

A=AP+PE+Pd/2

A: Semi Major Axis

AP: Apoapsis

PE: Periapsis

Pd: Planet diameter

/: divided by (of course!)

So, we can now easily calculate a semi-Major axis. Let’s hypothetically have an orbit of 160x83KM around Kerbin.

The SMA of this orbit is 160+83+1200 divided by 2.

Or: 721.5 kilometers.

Easy enough. Finding the Period is just as simple.

You’ll need two things:

1.) A scientific calculator

2.)The gravitational parameter of the desired body to orbit.

Kerbin’s gravitational parameter is 3530.461km^3/s^2. Ignore the unit, for these calculations, we won’t need it.

The formula is simply

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

?: Pi

A: SMa

U: Gravitational Parameter

I’ll calculate the period of this orbit manually and show you.

First off, our SMa is 721.5Km

Now, we cube that.

=375585663.375

Now we dived by the gravitational parameter (3530.461) of Kerbin.

=106384.3116734613

Now, we do the part of the equation that you’ll need a scientific calculator to complete.

?(2)= 6.283185307

6.283185307?106384.3116734613

In seconds, our orbital period is: 2,049.351406 EXACTLY.

To find this in minutes, simply divide by sixty.

At the altitude I mentioned above, it will take exactly 34.15585677 minutes to complete an orbit.

[Candre]

I personally use 2 ? ?(a^3/u)

Where:

a = semi-major axis

u = gravitational parameter; 65.136 km^3/s^2 for Mun and 3530.461 km^3/s^2 for Kerbin.

? = pi; it looks horrid

For example, orbiting Kerbin @ 100km altitude:

2 ? ?(700km^3/3530.461) = 1958 s = 32.6 minutes

A slight difference from the OP\'s calculation.

The OP\'s method is easier to understand. I really have no idea what I\'m doing here but I know it\'s right because Kepler says so.

[VincentMcConnell]

I rounded a lot of the decimal points. So my calculations might be off by a few minutes or so.

[VincentMcConnell]

Just used your calculations. They worked perfectly the first flight when I went to put my calculations for an SMa orbit of 7.11645KM.

Everyone ignore my OP. I\'ll be updating it to show good calculations.

[maltesh]

Alternatively, (if you\'re running 0.15 or later) on the map screen, hit pause, then hit F2 to hide the UI.

Hover over the markers to discover your Time to Periapsis and your Time to Apoapsis. Subtract the smaller from the larger, and double it. That\'s your orbital period.

[VincentMcConnell]

Didn\'t even think of that... Wow.