ORGANIZATION AND HIERARCHY ACTIVITY

ORGANIZATION AND HIERARCHY ACTIVITY

Report and personal reflection

In this activity we can put into practice the Kepler third law, with a problem formulated by Galileo in 1610.

1. Galileo discovered the Moons of Jupiter, measure the size of their orbits using only the diameter of Jupiter as a unit of measurement; discovered that Ío, one of its moons, has a period of 1.8 Earth-days, and was 4.2 units from the center of Jupiter, Callisto, the fourth moon of Jupiter, had a period of 16.7 days, using the same units that Galileo, predicts the distance of Callisto to Jupiter.

T₁= 16.7 days (period of Jupiter)

T₂= 1.8 days (period of Ío)

r₁= 4.2 units (distance from the center of Jupiter to Ío)

r= ?

K=T^2/r^3

r^(3= ) 〖16.7〗^2/(300.46x〖10〗^(-21) )

r^3= 〖9.282100779x10〗^20

r= ∛(█(〖9.282100779x10〗^20@))

r= 9754733.894 m

2. With the help of your teammates and using the third Law of planetary motion of Kepler, calculate the distance (in units diameter-Jupiter) from Jupiter to Callisto.

3. Search in different texts or in internet the following data: Jupiter’s diameter, distance of Ío to Jupiter and the distance from Callisto to Jupiter, and record it on the following table.

4. After having obtained the above information, calculate how much measured in kilometers a unit, as Galileo it used. Perform the necessary mathematical operations and check if the result you got in step 3 correspond to the actual distance of Jupiter moons that you got in the investigation, and register on the following table.

5. Make up a word document (or follow the instructions of your teacher) organizes all the information that you investigated, obtained and the table, you should include in the repor the equivalence that you used in step 4, as well as the mathematical operations.

TO B C D E F

Distances by calculations Conversion factor and the operation Research of the diferents distances Conversion factor and the operation Difference between columns B and D

Diameter of Jupiter 139.822 KM 117.4 KM NOT FOUND 117.4 km Column B is more accurate

Distance of Ío to Jupiter 421.6 km 421.6 km Not found 421.6 km They are similar

Distance of Callisto to Jupiter. 1882.7 km 1882.7 km Not found 1882.7 km They are the same

REFLECTION

In this activity i learned to put into practice the Kepler's third law thanks to a problem of Galileo formulated in 1610. In addition to Galileo discovered the moons of Jupiter, but not only that but also he was the one who could measure the orbits of Jupiter using only its diameter of the planet as measurement. I learned that thanks to that Galileo discovered that Io was one of the moons of Jupiter and that can have a period of 1.8 Earth-days and that was to 4.2 units of the center of Jupiter and Callisto

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