Dependent Variable: the accuracy of the measurements and math.
Control: formulas for the mass, the actual mass of the moons, the orbits of the moons
Materials: Paper, pencil or pen, ruler with cm measurements, information of the orbits of the moons, calculator
Procedure:
- Obtain the picture of the planet Uranus that has all its moons and its orbits
- Measure the radius from the center of Uranus to the moon’s orbit on the x and y direction
- Find the average of the radius in the x and y direction and multiply the answer by 1000 to go from cm to m
- To find the seconds around the planet, divide 360 (orbit) by the period of rotation. The information of the period of rotation should be already given.
-
Find the circumference using the formula C =
- Divide the circumference by the number of seconds to get the period in m’s
-
Use the formula to find out the mass of Uranus by plugging in the information to the formula: R3/P2 = G x M/ 4Π2. G equals 6.67 x 10^11
- Multiply answer by 10^25 to change the answer from meters to km
Data:
Bianca
X= 4.7
Y= 6.4
Radius = = 5.55
5.55 x 1000 = 5550
= 144.58 seconds around the planet
C =
C =5550
C = 34871.678
= 241.19 = p
= 2938734.519
M = 1.74 x 10^-4
1.74 x 10^-4 x 10^25 = 1.74 x 10^21
Miranda
X = 8.3
Y = 12.3
Radius = = 10.3
10.3 x 1000 = 10,300
= 63.83 seconds around the planet
C =
C =
C = 64,716.80866
= 1,013.89 = p
= 1,062,991.997
M= 6.29 x 10^-5
(6.29 x 10^-5) x 10^25 = 6.29 x 10^20
Puck
X = 7
Y = 10.2
Radius = = 8.6
8.6 x 1000 = 8600 = r
= 118.03 seconds around the planet
C =
C =
C = 54035.39
= 457.81 = p
= 3,034,763.17
M = 1.80 x 10^-4
1.80 x 10^-4 x 10^25 = 1.80 x 10^21
Conclusion: I found the mass of a planet from the rotational period and distance from the planet of the moon. The planet used in my scenario was Uranus, and the moons used were listed above.
