Calculating the Mass of a Planet

Saturn, using Prompt 5 with an Open filter at 1:45 am March 24, 2016.

Of course, we just can’t be picked up a planet and set on a scale!  Planets are too large, waaaaaaaay too large for that.

So how do we get the numbers we see in books and on the ‘net?  How do we calculate the mass of a planet?

My students are working through Skynet, the online program at UNCCH, that’s connected to the robotic telescopes in Chile and Australia.  We are also using Skyglow, a computer program that allows for some editing of the astro-photographs.

First, the students use Afterglow to measure the angular diameter of the planet in one of their images.  Some chose Jupiter, some chose Saturn, as did I.  We are taking two photos every night for two weeks so we have the opportunity to see some moons make complete orbits.

Saturn with moons (from left) Titan, Enceladus, Tethys and Dione, Rhea

Then we measure the apparent orbit of one of the moons in arcsececonds and convert it to the semi-major axis in Astronomical Units (AU).  Next we convert the orbital period from days to years and use the equation

M = | (a/1 AU)3 / (p/ 1 year) 2 | solar masses

to get the mass in the units of ourSun.

Once we convert the answer to Earth masses, students will check their answers against the “correct” answer to see how they did.  According to my sources, Saturn has the mass of 95.2 earths.

So let’s see how close my students and I come to calculating the accepted mass of Saturn.  I plan to post the results here sometime after next week.

Screen Shot 2016-03-30 at 1.41.02 PM
More about this graph in part 2.




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