Just as we are able to calculate how long it
will take our worlds to circle their suns, so we can also calculate
how long it will take our moons to go around our worlds. Will
you have two moons in the sky at once? Three? Let's find out!
Here is the formula
that will help us:
Translation:
T = the Time in hours that it takes
the moon to go around the planet once:
This is one complete orbit.
r = the average distance of the moon
from its world when we use the radius of the earth as 1.
M = the mass of the planet that the
moon is orbiting if we count the mass of the earth as 1.
Mr
Nordley was kind enough to provide the following examples:
Example 1:
Calculate the time that it takes for the earth's
moon to orbit the earth once.
What we know:
The
moon is 60 earth radii away from the earth's center
The
mass of the earth is 1 earth mass =1
Here is our formula:
Let's put in the numbers:
T
= 1.4 * _{
}
T = 1.4
* _{
}
= T = 1.4
* _{
}
=
The square root of 216,000 = 464.7
T
= 1.4 * 464.7 = 650.6 hours
These
are a lot of hours.
Divide
by 24 hours to turn this into days.
T = 650.6 divided by 24 = 27.1 days
The
moon goes around the earth in about 27 days.
It works!
Example 2:
Calculate the time that it takes for
the moon Phobos to orbit Mars once.
What we know:
Phobos is 1.5 earth radii away from
the center of Mars.
The
mass of Mars is 0.11 earth mass = 0.11
Here is our formula:
Let's
put in the numbers
T = 1.4
*
T = 1.4
* =
T = 1.4 *
(3.375
divided by .11) = 30.7 (Round off
the decimals)
T
= 1.4 * _{
}
The square root of 30.7 = 5.5
T
= 1.4 times 5.5 = 7.7 hours
Phobos zips around Mars every 7.7 hours!
Example 3:
Calculate the time that it takes for the moon
Io to orbit Jupiter once.
What we know:
Io is about 66 earth radii away from
the center of Jupiter.
The
mass of Jupiter is about 318 earth masses.
Remember, Jupiter is a huge planet!
Here is our formula:
