## Archive for the ‘**EDUCATION**’ Category

## Unveiling the Higgs mechanism to students

**Giovanni Organtini**

In this paper we give the outline of a lecture given to undergraduate students aiming at understanding why physicists are so much interested in the Higgs boson. The lecture has been conceived for students not yet familiar with advanced physics and is suitable for several disciplines, other than physics. The Higgs mechanism is introduced by semi-classical arguments mimicking the basic field theory concepts, assuming the validity of a symmetry principle in the expression of the energy of particles in a classical field. The lecture is divided in two parts: the first, suitable even to high–school students, shows how the mass of a particle results as a dynamical effect due to the interaction between a massless particle and a field (as in the Higgs mechanism). The audience of the second part, much more technical, consists mainly of teachers and university students of disciplines other than physics….

Read more: http://arxiv.org/pdf/1207.2146v1.pdf

## Measuring the eccentricity of the Earth orbit with a nail

## … and a piece of plywood

**Thierry Lahaye**

I describe how to obtain a rather good experimental determination of the eccentricity of the Earth orbit, as well as the obliquity of the Earth rotation axis, by measuring, over the course of a year, the elevation of the Sun as a function of time during a day. With a very simple “instrument” consisting of an elementary sundial, first-year students can carry out an appealing measurement programme, learn important concepts in experimental physics, see concrete applications of kinematics and changes of reference frames, and benefit from a hands-on introduction to astronomy.

**1. Introduction**

One of the cornerstones of introductory courses in classical mechanics is the derivation of Kepler’s laws. In particular, the derivation of Kepler’s ﬁrst law, stating that the trajectory of a planet is an ellipse with the Sun located at one of the foci, is an important application of Newton’s laws to a multidimensional problem. However, very few students are aware of the fact that the eccentricities of the planets of the Solar system are actually quite small, with trajectories very close to a circle, which makes Kepler’s achievement (based on Tycho Brahe’s measurements) even more remarkable.

Here, I describe a simple measurement programme, suitable for ﬁrst-year university students, consisting in measuring the elevation of the Sun as a function of time during a day, and in repeating this typically once a week over a full year. By measuring the maximal elevation hmax of the Sun, and the time tmax at which this maximum occurs (i.e. the true local noon), students can readily check that these quantities vary a lot over the year. The change in hmax is essentially related to the obliquity ε of the Earth over the ecliptic, and thus allows for quite an accurate determination of ε (as well as that of the latitude of οbservation).

The change of tmax over a year gives an experimental determination of the equation of time E(t), i.e. the difference between the mean local noon and the true local noon, and allows for a determination of the eccentricity e of the Earth orbit [1]. This is a rewarding result for students to realize that with such simple measurements they can obtain good experimental values for the above quantities, and that with careful observations one can perform ‘**science without instruments**’ as did the astronomers of various antique civilizations [2, 3].

This article is organized as follows. I ﬁrst describe how to measure in a simple way the elevation of the Sun versus time over a day, with an accuracy of about 1^{o} .

Then I give the results I obtained for hmax(t) and E(t) by repeating the measurement about once a week for one year, starting in August 2010. I show how one can extract the obliquity ε of the Earth’s axis and the eccentricity e of its orbit by ﬁtting the experimental data with simple, analytic expressions. Finally, possible extensions of the work are proposed. Appendix A contains a brief reminder on basic notions of spherical astronomy, and should be read ﬁrst by readers not familiar with these notions. In the remaining appendices, the derivation of the analytic expressions used for ﬁtting the data is given, so that the article is self-contained…….

Read more: http://arxiv.org/pdf/1207.0982v1.pdf

## An Introduction to the Study of Stellar Structure

## by **Subrahmanyan Chandrasekhar**

Read more: books.google.gr/books

## Teaching General Relativity To Undergraduates

**Here’s an article in this month’s Physics Today** on what is needed to teach General Relativity in an undergraduate physics curriculum. Not sure how effective it is, but it is certainly worth an attempt, I suppose. This is in line with **Hartle’s earlier paper in AJP** on teaching this same subject to the same group of people.

## Computing Accurate Age and Distance Factors in Cosmology

**Jodi Christiansen, Andy Siver**

As the universe expands astronomical observables such as brightness and angular size on the sky change in ways that differ from our simple Cartesian expectation. We show how observed quantities depend on the expansion of space and demonstrate how to calculate such quantities using the Friedmann equations. The general solution to the Friedmann equations requires a numerical solution which is easily coded in any computing language (including EXCEL). We use these numerical calculations in four student projects that help to build their understanding of high-redshift phenomena and cosmology. Instructions for these projects are available as supplementary materials…

Read more: http://arxiv.orgpdf

## Foundations of analog and digital Electronics Circuits

**Anant Agarwal**

## How Simple Ideas Lead to Scientific Discoveries

Adam Savage walks through two spectacular examples of profound scientific discoveries that came from simple, creative methods anyone could have followed — Eratosthenes’ calculation of the Earth’s circumference around 200 BC and Hippolyte Fizeau’s measurement of the speed of light in 1849. (Launching a series on Inventions that Shaped History)

“How Simple Ideas Lead to Scientific Discoveries” was animated by the TED-Ed Animation Team (Jeremiah Dickey, Biljana Labovic, Celeste Lai, Kari Mulholland and Franz Palomares)

http://youtu.be/F8UFGu2M2gM

## Getting the Swing of Surface Gravity

**Brian C. Thomas & Matthew Quick**

Sports are a popular and effective way to illustrate physics principles.

Baseball in particular presents a number of opportunities to motivate student interest and teach concepts.

Several articles have appeared in this journal on this topic, illustrating a wide variety of areas of physics.

In addition, several websites and an entire book are available.

In this paper we describe a student-designed project that illustrates the relative surface gravity on the Earth, Sun and other solar-system bodies using baseball.

We describe the project and its results here as an example of a simple, fun, and student-driven use of baseball to illustrate an important physics principle.

This project was completed to satisfy a course requirement in an introductory astronomy course at Washburn University (a Masters-level university) in Topeka, Kansas.

The assignment was an open-ended, independent project designed and executed by the student. The requirements were that the project must be self-designed and related to astronomy, with creativity emphasized.

The project described here asks the question “What would it be like to play baseball on other

planets?” Two quantities were chosen for comparison: “hang time” of the baseball and distance from home plate to the center field fence.

These values are affected by the surface gravity of the planet or other body.

Surface gravity means the gravitational acceleration at the surface of the body, which depends on both the body’s mass and the distance from the center to the surface.

We realize that one would not actually be able to stand (let alone play baseball!) on the surface of a planet such as Jupiter; the idea is to help students understand surface gravity. This concept may be difficult for some students, since it involves variation of two parameters simultaneously.

Therefore, we hope this exercise will be both engaging and useful in helping students understand the counter-intuitive fact that even a planet with greater mass than the Earth (for instance, Neptune) may have a smaller surface gravity, or vice versa…..

Read more: arxiv.org/ftp/arxiv/pdf