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Astronomy Lab. Problem: How can you calculate the mass of Uranus using 3-5 of its moons? . General information.

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## Astronomy Lab

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### Astronomy Lab

Problem: How can you calculate the mass of Uranus using 3-5 of its moons?

General information
• The planet Uranus is the seventh most distant from the sun and was discovered by William Herschel in 1781. It is a gas giant with a diameter of 50,000km. Nevertheless, its mean distance from the sun of 19.2 astronomical units meant that very little was known about the planet until the Voyager 2 fly-by in January of 1986. Up until then the planet was thought to have only 5 moons. You are given a picture of the moons of Uranus to use to calculate the mass of Uranus.

The formula you will be using is :R3=GM

P24Π2

Where R=radius from the planet using a2 +b2=c2

a is the distance on the x-axis and b is the distance on the y-axis.

P is the rotational period. You are given how many degrees the moon travels per second and need to find how many seconds in 360o.

G is a constant. 6.67x 1011

M or mass is going to be in kg X1025

Helpful Hints and How to do one calculation.

Measure the distance from the center of Uranus to a moon in the North or south direction using it orbital path.

For my example, I got 8.4cm . Measure the distance from the center of Uranus to a moon in the east or west direction using its orbital path. For my example I have 5.9cm.

R therefore = 10.26 cm

Let say the moon moves at 2.23 degrees per second. How many seconds does it take to get around Uranus?

P therefore = 161.4349776 sec

Plug the numbers into the formula: R3=GM

P2 4Π2

7.21E14m3 = 6.67E11m3/s2 x MkgE25

2.61 E4 s2 4Π2

(2.76E10 m3/s2 )(39.48)= 6.67E11m3/s2 xMkgE25

MkgE25 =(1.090719348E12 m3/s2 )/ (6.67E11 m3/s2 )

M= 1.64 E25 (Now do this for four moon. Get an average and then check to see how close you are to the actual mass of Uranus. Do % error only if you are off by magnitude of 10.