Overview Lesson Demonstration Presentation

Luminosity and the Transit Method

Overview

When we look into the night skies, one can see the moon, the clouds, and with some luck, the stars. But while the moon is brigt with details, the stars but appear as dots in the skies, all despite their true nature as gargantuan balls hot gas and plasma. But nevertheless there are many things we can find from what we can see. Examples include how far away a star is, how "bright" it is, and perhaps most exciting of all, if there are exoplanets orbiting the star!

A good way to find a star's distance or brightness is by making use of how a star's distance, intrisic luminosity and apparant luminosity are related. As for exoplanets, one way to determine their presence is to use the transit method of finding exoplanets, which can also provide some information of the planet itself. We will demonstrate this using a faux star and planets, and measuring the intensity of light from the faux star with different arrangements. The goal is to make the above concepts as simple and approachable as possible, such that by end of the presentation the students may think that they too, are capable of finding planets.

Lesson

The lesson will be split into two parts, the first discussing the luminosity of stars and the intensity of their light, and the second discussing the transit method. The key demonstration for both parts will likewise be different - demonstrating the two distinct concepts.

Intensity & Luminosity

In the first part we will discuss how a star's distance, intrisic luminosity and apparant luminosity are related. The star's intrinsic luminosity refers to how much energy a star is emmiting per second - a star's power. This is what a star's luminosity actually refers to. The star's apparant luminosity refers to how much power we measure coming from the star per unit area - the intensity of the light coming from the star. The three are related through the relation

$$ I = {L \over {4 \pi d^2}}.$$

where I is the intensity, L the star's luminosity, and d the star's distance. For this part the demonstration will consist of moving the faux star to different distances. relative to the light sensor and showing the change in intensity measured (The background light will have to be taken into consideration).

Transit Method

In the second part we will discuss the transit method of finding stars. The key point lies in identifying a periodic dip in the measured intensity coming from the star. This dip is caused by an object, in this case a planet, coming between us and the star, and blocking part of the light coming from the star. From the decrease in intensity we can also infer some properties of the planet. The radius of the planet can be determined using the equation

$$ {{I_{unblocked} - I_{blocked}} \over I_{unblocked}} = {R_{planet}^2 \over R_{star}^2}$$

We can also determine the orbital period of the planet using the periodicity of the dips - one cycle in the dips corresponds to one orbital period. For this part the demonstration will consist of fixing a ball on a rotating table to simulate an orbiting planet. The ball, much like a planet, will go between the light sensor and the faux star, creating dips in the measured intensity.

Demonstration

Materials & Equipment

Arrangement

There will be two set-ups for the demo – one with the base, and one with the rotating table. The light source will be connected to the base for the first half such that it is easy to move around. And then for the second half about the transit method, the light source will be connected to the rotating table. In our case, the table was repurposed from a Coriolis effect demo.

The light source that is connected to the base will consist if the two metal bars, one of the clamps, the bosshead, clamp holder, halogen light bulb, and the glass light diffuser. The metal bars will be connected using the clamp holder, and the bosshead will be placed on the thinner of the two bars. The halogen light bulb will be placed inside the light diffuser such that the luminosity is uniform on the diffuser’s surface. We will hang the light source by wrapping the wire around the bosshead and connecting it to the extension cord, which wire would run along the metal bar and then hang off the clamp holder. The set up with the base should look like this:

Part 1 Arrangement

For the rotating table, a power source will be connected to the motor at the bottom of the table and will be placed at the opposite end of the table from the light sensor. The rotating table itself should be placed on a set of four tables put together into a square. The black cloth (which should have as little gloss as possible) will placed on the rotating table, over which the clamp will be placed, on the edge of the round, rotating part of the table. The copper wire will then be placed in the clamp, and the wire will itself be connected to either the ping-pong ball or the plastic ball. The copper wire will be bent such that it runs along a “longitudinal line” of the balls, and then bent such that it wraps around the ball along a “latitudinal line”. Tape will be placed on the first bent section to keep the ball in place, and this taped side will be placed such that it faces inward towards the light source. The wire would be bent somewhat like so:

Wirebending

The ball will therefore rotate along with the table, with the copper wire blocking a small amount of light, but small enough compared to what either of the “planets” will block. Another clamp will be placed on one of the desks on which the rotating table is be standing on such that it is to the side of the table relative to the light sensor (not on the opposite side of the table from the light sensor). The light source will be placed on this clamp, and the set up with the light source should look like this:

Part 2 Arrangement

As for the measurement side, the light sensor will be placed on a small stand on top of a desk a distance away from the light source, with a few more books or such placed below it so that it is level with the light source. The light sensor will be connected to the LabPro via one of its four channel ports. The LabPro will then be connected to the computer with double USB connection. The LoggerPro software will need to be installed to make used of the LabPro on the computer. Using this setup, we will be able to plot an intensity vs time graph in real time which will be projected for the students to see.

Presentation