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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

Astronomy Lab

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

general information
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.
slide4

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
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

slide6

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.