1. Neptune discovery in physics class: activities and simulations Hezi Yizhaq, Environmental High School, DAT Fulbright Teacher from Israel Email Address: hezi.yizhaq1@gmail.com Matthew Bobrowsky, Department of Physics, University of Marylandhezi.yizhaq1@gmail.com Email Address: msb@umd.edumsb@umd.edu

2. Introduction: Planet Orbits Kepler's laws of planetary motion are three scientific laws describing orbital motion, each giving a description of the motion of planets around the Sun (1619). Kepler's laws are: 1. The orbit of every planet is an ellipse with the Sun at one of the two foci. 2. A line joining a planet and the Sun sweeps out equal areas during equal intervals of time. 3. The square of the orbital period of a planet is directly proportional to the cube of the semi-major axis of its orbit.

3. Newton's law of universal gravitation (1687) explains Kepler’s laws Every point mass attracts every single other point mass by a force pointing along the line intersecting both points. The force is proportional to the product of the two masses and inversely proportional to the square of the distance between them

4. Uranus –A very badly behaved planet Discovered by William Herschel in 1781 Period of revolution 84 years, average distance from the Sun is: 19.22AU. After 1800 discrepancies started to be apparent between the planet position as predicted by theory and as measured in the sky

5. Discrepancies between the observed and the calculated longitudes of Uranus after known causes have subtracted Discrepancies between calculated to observed longitudes

6. An Astronomical Mystery Two possible explanations: 1.Newton's law of gravity might not hold as distances as great as Uranus i.e. the law of gravitation is not universal !!! 2.The law of gravitation is correct but there is another unseen planet far beyond Uranus which perturbed its orbit.

7. Where to look for the new planet? Bode Titus law (1772) An empirical law for the distances of planets from the Sun

8. The Search for the Missing Planet Independently, two astronomers, John Couch Adams in England and Urbain Jean Josef Le Verrier in France, calculated the position of this yet unknown planet. Le Verrier was already a know scientist whereas Adams was a young Cambridge undergraduate, 26 years old, who seems to have taken on a own personal quest to search for an explanation for the apparent misbehavior of Uranus. Urbain Le Verrier John Couch Adams

9. Neptune Discovery Chronology In October 1845, Adams wrote to George Airy, the Astronomer Royal of Greenwich Observatory, claiming that he had solved the problem of Uranus' orbit, and stating the position where the unknown planet could be found. In December 1845 Le Verrier independently published a short manuscript on the orbit of the missing planet. Neptune was ultimately discovered by the German astronomer Johann Galle, on September 29, 1846, using Le Verrier’s predictions.

10. Why Neptune was not discovered in England? In October 1845, Adams wrote to George Airy, the Astronomer Royal of Greenwich Observatory, claiming that he had solved the problem of Uranus' orbit, and stating the position where the unknown planet could be found. Now, if Airy had pointed a telescope at that spot, he might have found Neptune (however, not at the exact spot that Adams had pinpointed). Although, he tried to conceal it, Airy had a strong negative reaction to Adams paper. His altitude later turned out to be of critical importance to the fact that Neptune was not discovered in England. The problem was that Airy was strongly opposed to theoretical investigations and skeptical of the abilities of younger scientists. He was not the sort of man to take a leap into the scientific unknown. “God forgive me for writing in this way – The truth lies on the other side & Adams is the 1 st theoretical discoverer of Neptune. The whole thing was parried [?] and perverted by Airy’s indefensible reticence. On him be the responsibility of the (temporary) transfer of one of the brightest stars in Britain’s Scientific fame to France. “ British Astronomer John Herschel-1846

11. Star Map from the Day of Discovery

12. Who was Neptune’s discover Le Verrier, Adams or Galle?

13. Developed Activities Finding the year of conjunction by performing time numerical derivative of the data

14. MATLAB Numerical Simulations of Planet Orbits Using Feynman’s Method

15. The program can calculate different physical quantities Neptune Uranus

16. Calculation of the perturbation near the conjunction Assuming: Circular orbits, conservation of energy and angular momentum of the system the students will find the perturbed radius of the planet near the conjunction Numerical Solution of the Corrected Orbit of Uranus (unperturbed orbit=19.22AU,R2=38.8AU )

17. The Discovery of Neptune and the Dark Matter in the Universe Rotation Curves in the Solar System Rotation Curves in the Milky Way

18. Thank you for attention