The third law states a mathematical relationship between the period of a planet and the radius of its axis. Mathematically it states that, where k is a constant for a specific solar system.
Data Collection:
Period and Distances of Planets in Solar Systems
Data taken from
Data Processing:
Squaring Period and Cubing Axis Radius
Sample Calculations (Mercury):
Squaring Period Cubing Radius
Graph 1-Period Vs Radius
Graph 2-Transformiong Graph to Get Linear Relationship
Experimentally Determined Solar System Constant
K=slope
Actual K Value taken from (Lesson 34: Kepler's Three Laws of Planetary Motion)
Calculating Percent Error
Conclusion:
In conclusion it was found that the orbital constant for the Sun is . When compared to the actual value there is a percent difference of 1.3%. But if both figures were to be rounded to 2 significant digits than the percent difference would be 0%. Using this constant, the period or the axis radius of any stellar object orbiting the Sun can be found.
When looking at Graph 1, it can be seen that the relationship between the period and radius of a planet’s axis is exponential. The further the planet is, the longer its period is.
When looking at Graph 2, it can be seen that there is a y-intercept. This is probably occurred because such large distances were used, and when calculating the data, some figures where rounded down, thus giving a y-intercept. It can also be seen that there is clearly a linear relationship between and , which verifies that Kepler’s 3rd law is indeed true.
Works Cited
"Johannes Kepler." Wikipedia, the free encyclopedia. Web. 28 July 2009.
<http://en.wikipedia.org/wiki/Johannes_Kepler>.
"Kepler's Laws." Test Page for Apache Installation. Web. 28 July 2009.
<http://hyperphysics.phy-astr.gsu.edu/HBASE/Kepler.html>.
"Lesson 34: Kepler's Three Laws of Planetary Motion." Mr. Clintberg's Studyphysics!
Web. 29 July 2009.
<http://www.studyphysics.ca/newnotes/20/unit02_circulargravitation/chp08_s
pace/lesson34.htm>.
