Descriptions of invited papers from the 2012 AAPT Winter Meeting Session on “Using the Riches of Astronomy to Teach Physics”
Using Black Holes and Extrasolar Planets to Teach Kepler’s Laws
Tue 02/07, 8:00AM – 8:30AM
by Seth Hornstein
Two popular topics in an introductory astronomy course are supermassive black holes and extrasolar planets. In this talk, I will discuss two labs/recitation activities that can be used to harness this interest to teach orbital properties. In the first activity, students are provided with a Lego Orrery (as designed by the Kepler Mission Education team) and, using a light sensor and computer, develop a relationship between orbital radius and period as well as a relationship between extrasolar planet radius and detected light intensity drop. In a second activity, students are given a plot of the orbits of stars around the supermassive black hole (SMBH) at the Galactic Center. Using the actual orbital elements, students use Newton’s version of Kepler’s third law to determine the mass of the SMBH. In both cases, students have reported enjoying the activities due to their portrayal of actual scientific methods and use of research-based data.
Solar Coronal Loops: Faraday Constrained
Tue 02/07, 8:30AM – 9:00AM
by Gordon Emslie
Images of solar coronal loops in ultraviolet and X-ray radiation are used to motivate a discussion of Faraday’s law of induction. Even though the resistivity of the solar atmosphere is similar to that of copper, the huge (~100,000 km) extent of a solar active region makes the overall resistance very small. Further, there is a limit to how much current can flow ? the limiting current density is given by the charge density times the local sound speed. This combination of low resistance and finite current severely restricts the voltage differences that can exist, and hence, by Faraday’s law, the speed at which a current element in the solar atmosphere can cross magnetic field lines. As a result, the gas is effectively “frozen-in” to the magnetic field, resulting in the dramatic (and beautiful) manner in which radiating material delineates the loop-like magnetic field geometry of a solar active region.
Measurement of Spherical Balloon Circumference Using Eratosthenes’ Method
Tue 02/07, 9:00AM – 9:10AM
by Seiji Takemae
We present an activity, based on Eratosthenes’ method of estimating Earth’s circumference, of measuring the circumference of an inflated rubber balloon. Suction-cup darts are attached to the surface of the balloon along a meridian. The experimental circumference is obtained from multiple measurements of shadows cast by the darts. This measurement is then compared with the circumference obtained using a cloth measuring tape. An assessment of uncertainties is given. The activity presented is suitable for astronomy, physics, or math classes or laboratories.
Kepler’s Second Law and Conservation of Angular Momentum
Tue 02/07, 9:10AM – 9:20AM
by Pari Spolter
Kepler’s second law is calculated for 18 planets and asteroids. It is shown that equal areas are swept in equal intervals of time only near the perihelion (P) and the aphelion (A). A highly significant relation between the ratio of the area swept at the average of P and A to the area swept at semimajor (S) in the same interval of time and the eccentricity is presented. The equation is ratio = a.eb+c with a = -0.617, b = 2, and c = 1.00. The correlation coefficient is 0.9975. The ratio is equal to the square root of one minus e square , which is equal to sin theta, where theta is the smaller angle between the two vectors v and r. Angular momentum is a vector perpendicular to the plane formed by v and r and is conserved, indicating that there is no torque in the direction vertical to the plane of the orbits.