keplers third law

Name: Denisse Perez Cruz _____ Date: ______November 1, 2023  Which way do the planets move around the Sun - clockwise or counter-clockwise? The planets move around the Sun counterclockwise direction.  Are there any exceptions? Only if you see the solar system from the North pole, it is traveling clockwise.  Does Kepler’s Second law seem to hold true, at least qualitatively, from the way the planets move? In other words, which planets would you expect to move fastest or slowest? What is the general rule about how fast planets move around the Sun compared to how far they are from the Sun? Is this what you see? Due to Kepler’s 2 nd the line coming together with the planet and sun equals the area of space be- tween the interval time of the planet around the sun. I would expect the planets to travel fastest due to the timing on them. The rule is the closer the planet is to the sun, the fastest it will travel.  What is the date? 8.8 days  Now what is the date? 9.1. Table 1 Planet Start Date End Date Orbital Period, T (days) Mercury 2.5 3.5 20 Venus 3.5 4.5 30 Earth 4.5 5.5 40 Mars 5.5 6.5 50 Jupiter 6.5 7.5 60 Saturn 7.5 8.5 70 Uranus 8.5 9.5 80 Neptune 9.5 10.5 90 11/15/2023 1 Planet Orbital Radius (R) (AU) Orbital Period (T) (years) R 3 (AU 3 ) T 2 (years 2 ) Mercury 0125.2 20 5 9 Venus 0.526 52 10 6 Earth 0.869 65 85 6 Mars 0.854 45 54 7 Jupiter 1.1552 52 26 8 Saturn 0.1534 60 26 9 Uranus 1542.6 70 8 10 Neptune 01.255 80 9 11

Table 2 Table 3  Are they all close to? Yes they are close to 1. ´ M =_________________89______________. Now we need to calculate how far each value of M is from ´ M . For each value of M, we call this difference “ ΔM .” Calculate this number for each planet and fill in Table 4 on the next page. Table 4 Planet ΔM = M − ´ M Mercury 12 Venus 16 19 Mars 25 Jupiter 63 Saturn 25 Uranus 61 Neptune 10  What is your standard deviation, σ ? ___________55995_____________________. Remember, the closer the standard deviation is to zero, the more all your values are M are nearly the same. If the expected value of M (in this case, 1), is within one standard deviation of your average value, then we can say that they are, for all intents and purposes, equal. In other words, if ´ M − 1 is less than σ , then you’ve proved Kepler correct!  Was Kepler correct, according to your data? No, he wasn’t for the most part it was a low numerator 11/15/2023 2 Planet M (=R 3 /T 2 ) Mercury 0.25 Venus 0.84 Earth 1.25 Mars 152.3 Jupiter 14.23 Saturn 0.156 Uranus 1.256 Neptune 2.546