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Verification Of Kepler's 3rd law

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Introduction

Challenge 9- Verification of Kepler’s 3rd law using a database.

Design

Research Question: Is it possible to verify Kepler’s 3rd law using a database?

Hypothesis: I believe that it is possible to verify Kepler’s 3rd law using a database due to the nature of the law. Kepler’s law states that the square of the time of one orbital period is directly proportional to the cube of its average orbital radius. Mathematically this looks like:

image00.png

Where T is the orbital period and R is the orbital radius. As a result we can see that:

image01.png

In order to verify this law we have to draw a table using the database given and then draw a graph.

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Middle

Name of Planet

Distance from the Sun relative to Earth

Time for 1 orbit/ years

Constant (T2/R3)

Average K

Mercury

0,4

0,2

0,6

1,0

Venus

0,7

0,6

1,0

1,0

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Conclusion

2/R3 = K. This means that we can use the period of the earth and its distance to the sun to find periods of other planets and/or their distance from the sun regarding that we know one of the two.

Thinking about why the constant wasn’t precisely accurate, I believe that the numbers in the database are rounded up or are not fully accurate and therefore cannot give a 100% accurate result for the constant. As a result, the graphs are also not perfect, especially the second but the fact that there is a linear correlation in the graphs is sufficient enough to verify Kepler’s law due to the fact that the numbers in the database are not 100% accurate.  

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