Plotting an Asteroid Light Curve

Summary

Investigate how fast an asteroid is rotating.

Goals

Students will plot and analyze observational data collected by members of the public using Asteroid Tracker, and aim to measure the rotational period of the asteroid.

Learning Objectives

Become familiar with asteroids and near-Earth objects
Participate in the Asteroid Tracker citizen science project and contribute to furthering our understanding of the Solar System
Plot a photometric curve using observational data
Interpret graphs and recognize the periodicity in a set of data
Understand how and why astronomers study asteroid rotation

Planning

Materials

A Computer with spreadsheet software and access to the Internet
Observational data of asteroids taken using Asteroid Tracker, e.g. 2002 KL6 (.txt)
Optional: 2002 KL6 Activity Spreadsheet

Background

Asteroids are rocky objects that orbit the Sun, but are too small to be considered planets. In fact, they're commonly known as 'Minor Planets'.

The majority of the asteroids in our Solar System are located in the asteroid belt, between Mars and Jupiter. However, there are some that have left this region after being influenced by the gravitational forces exerted by the planets, and are on paths that bring them near to Earth. If they approach the Earth at a distance of less than 1.3 AU (1 AU is the distance between the Earth and the Sun), they are considered to be Near Earth Objects, or NEOs. Observations of near-Earth objects can reveal information about their size, shape, composition, orbital path and rotation.

As asteroids are such small bodies that reside far from the Earth, they often look just like ordinary stars (small dots of light). The difference is, since asteroids are orbiting around the Sun they appear to move in respect to the fixed stars on the background -- this is how we spot asteroids. We can observe them in detail by taking a series of short exposure observations. An asteroid’s path can be determined across the sky by measuring with precision the position of the asteroid at different times. This will allow the determination of the asteroid’s orbit around the Sun, and therefore its path on the sky in subsequent days, months or years.

Find out more with Space Book.

Instructions

If you’d like to plot your own data, visit the Asteroid Tracker website to carry out your observations in advance.

Some data is already available from Asteroid Tracker for asteroid 2002 KL6. You can download the raw data as a text (.txt) file or download the data in a pre-made excel spreadsheet.

If you download the excel spreadsheet, jump to Step 4. If you downloaded your data as a text file (.txt or .dat) you will need to open it in your spreadsheet software (this guide is based on Microsoft Excel) and separate the data into columns. Do this by selecting data>text to columns>delimited
The data will need to be separated into seven columns (A-H), labelled as shown below:

A: NEO designation (various lengths, numbers and txt)

B: Observation date (year, month)

C: Observation time (day and seconds)

D: Celestial coordinates: RA (normally a 6 figure number to 2 decimal places) and Dec (normally +/- and a 6 figure number to 1 decimal place)

F: Magnitude (generally a 1 or 2 figure number to several decimal places).

G: Filter (denoted by a letter such as 'V' which stands for 'visible').

H: Telescope code (a code made up of a varying number of letters and numbers).

3. Order your spreadsheet by Telescope Code. Delete all rows that do not have the telescope code 'Z21', this will leave us with data collected by a 0.4-metre LCO telescope at Teide Observatory in Tenerife, Canary Islands.

4. In this activity we will be plotting the change in the asteroid's magnitude (brightness) over time. To do this, make a scatter plot of the date (day) and magnitude. You can highlight both columns by pressing CMD on a Mac, or CTRL on a Windows device, then select Chart > Marked scatter plot.

screen_shot_2017-02-24_at_12.39.57-737x364.png

You’ll notice that there are gaps in the data, like those seen in the image above, giving us a series of partial light curves. The next step is to combine your data and create a full light curve, do this by following the steps below.

5. If you are using the pre-made spreadsheet, go to the second tab labelled '2002_KL6 (2)'. If you have created your own spreadsheet, open a new excel tab and copy your data over. You can do this by right-clicking on the sheet tab and selecting Move or Copy then ticking Create a copy. **Do not delete your first sheet or light curve**.

6. We now need to enter the rotation period of the asteroid. The rotation period will be entered into a column named 'Period'. If you would like to know the rotation period, highlight the following text:

4.61 hours

Otherwise, you must enter a rotation period at random, then infer how accurately the value is based on the lightcurve you will plot in Step 9. As a starting point we will tell you that the period for 200 KL6 is between 4.5 hours and 5 hours. If you enter the correct rotation period, you should see a series of stacked lightcurves. If the value is incorrect, the data will appear confused and random. Simply change the figure in the Period column until you are happy with the lightcurve.

7. You now need to convert your rotation period into a fraction of a day. In a column called Rotation, use the following equation to enter the correct value into each row;

period(hrs)/24(hrs)

8. We will now use the rotation period and the date, to calculate the Phase. In a column called Phase, use the following equation where INT will turn the second quantity into an integer.

(date/rotation)-INT(date/rotation)

9. Fill in the Phase for each row.

10. We will now create a new scatter plot to show the asteroid’s magnitude changing over time. This time create the plot using the Phase and Magnitude values. You should notice that the light curves are now stacked and the gaps have been removed, creating a clearer, more complete light curve. If this is not the case, try playing with the Period value until you get something similar to the graph below.

11. Lower magnitude values mean an object is brighter, and the peaks are clearly following a downward slope. Click on the magnitude axis and select Values in reverse order to show this clearly.

12. Now, revisit the first light curve you made. Do you notice that the asteroid appears to brighten over time? What do you think caused this brightening? Highlight the following text to see the answer:

The asteroid was travelling closer to the Earth!

This brightening is the reason your most recent plot has several peaks stacked directly above one another. To overlay these peaks, we will have to compensate for the brightening by changing our magnitude values by eye. Create a new column for the revised magnitudes and continue reading.

How to compensate for asteroid brightening

Looking back at your old plot, you'll notice that while the asteroid brightened over time, some of the peaks are similar in magnitude. On the example below you can see my data points can be separated into three groups with other peaks of the same magnitude. Let's call them Group 1, Group 2 and Group 3 (moving left to right).

As there are more data points in Group 2, I will reduce the magnitude of the Group 1, and increase the magnitude of the Group 3 to match. The data points in Group 2 will remain unchanged.

Looking at my plot, I can see the the data points in Group 1 fall between 8-10 June and peak at 16 mag, +0.25 mag compared to Group 2. To align these peaks, I need to lower to all data points between 8-10 June by 0.25 magnitude. This can be done by calculating =SUM(magnitude-0.25)

The final peak seems to take place around the 22 June, and peaks -0.35 compared to first peaks. This means you will need to add 0.35 to all values around 22 June.

Copy the magnitude for Group 2 directly from the magnitude column and create a new scatter plot showing Altered Magniude and Phase. If necessary, keep adjusting your values in this way, until you have aligned the peaks on your plot (see image below).

You should now have a solid light curve showing the change in brightness of this asteroid over time. Congratulations!

What is the rotation period for your asteroid? __________ hours
Did any of your classmates use a different period? Compare your final plots. Who do you think was closer to the correct answer?

Evaluation

Now, answer the questions below to demonstrate your understanding of the how astronomers measure asteroid rotation periods.

What does this light curve show us?
What causes the asteroid brightness to vary?
Would the light curve look the same if the asteroid were spherical?
How long it takes your asteroid to rotate using only your final light curve?
1. How did you measure the rotation period?
Did the overall magnitude grow progressively lower or higher over time?

a) Why might this happen?

Activity