Jupiter's moons math question?

Question

Amalthea is a moon of Jupiter. Its period in days and its semi-major axis in kilometers are p (period) = 0.49179 days and a (semi-major axis) = 181,300 km. How do I convert these to years and AUs. Also, how do I calculate the mass of Jupiter in masses of the sun?

Answer 1

Step one.  Look up Amalthea in Wikipedia.  Ignore the nice mythology page.  Check that the period is in Earth days.  Check the hours, minutes and seconds to verify this.  How many Earth days are in an Earth year?  You can find the length of the day and year by looking up the Earth.  Ignore the nice pages about Earth Day.  Then look up the page for Astronomical Units.  Since it doesn't have what you're looking for, follow the link for kilometers.

Wikipedia also has a page for Jupiter.  That will give you it's mass in Earth masses.  How handy.  But you've already looked up the Earth, so you can get it's mass in kilograms.  The wiki page for the Sun has it in Earths, but also kilograms, so you can convert.

So here's how to create an arbitrary conversion for units.  Use dimensional analysis.  I really wish they had taught it in high school.  I didn't get exposure to it until engineering school.  But it's really easy.  You treat your units - km, Earths, etc., like fractions.  You cancel like terms.

So if it's 100 bobs to a frank, and you have 10 bobs,

then 10 bobs * (1 frank / 100 bobs) = 10 franks / 100 = 0.1 franks.  Make sure the bobs cancel, and you'll always get it right.

Wikipedia is your friend.

I'm afraid you're on your own from here.

Answer 2

Suitti gave you good guidance on doing the unit conversion.

If you want to know your weight in ounces, you just multiply your weight in pounds by the number of ounces in one pound.

Likewise if you want your weight in stones (Brits know what I mean) divide your weigh in pounds by the number of pounds in one stone (14 - in case you're wondering).

Now, once you have your units right you can use Kepler's third law P^2 = ka^3

the k is a factor that includes the mass of the planet.

Rearrnage to get mass