High School Senior Project

The Senior Project was a graduation requirement at my high school. I performed research on asteroids and other minor planets, focusing mainly on orbits, during my senior year (2009-2010).

For orbit determination work, I selected asteroids from the Minor Planet Center's critical list. The list contains asteroids whose orbits are not very well known, and/or are difficult to observe. It may also include those close to the Earth, crossing the orbit of the Earth, where they may in the future pose a threat. Because of this, most asteroids on the list are either too faint, requiring a long exposure which can result in a streaked image that is impossible to measure, or moving too fast, also resulting in a streaked image.

After observing many asteroids from the list, we found that we were unable to get three good observations of the asteroids. The weather was typically not favorable for long enough periods of time, and when it was, most asteroids had moved to a position where they were too dim to be detected. Because of this, we started to choose asteroids that were still on the critical list, but with uncertainty levels that were lower. After switching, we were able to get three good observations with a sufficient separation time.

Our tactic for choosing asteroids for calculating rotation period was different. At first, as we tried out the process, I wanted to choose an asteroid whose rotational period is known and short (about 2-3 hours), and that is also fairly bright (so that we have little problem measuring the required change in magnitude). The short period ensures that we can observe the asteroid in one night, with multiple periods. Afterwards, the plan was to work on an asteroid whose rotational period is not known. However, we were not successful with finding the period of our first asteroid, and dropped our plans of working on other asteroids.

My mentor gave me a copy of Guide 8 to help me choose my asteroids. It is an astronomy mapping software by Project Pluto. I imported orbital data of the asteroids from the Minor Planet Center to display the position of the asteroids. The program lacks some complex visualization features, but that made it better for our needs. Its user interface is challenging and not very friendly at first, but it got easier to use as I used it more often. I ran into a problem when I found that software is only for Windows, but I have it running on my Mac with CrossOver.

I performed my observations at the Wishing Star Observatory, above in a picture taken by me during one of my observations. It is an observatory my mentor, Mr. Herbert Peterson, built in his backyard.

On the side are a few pictures of me working at the observatory, along with some of the equipment I was using.

I was usually able to observe three to five asteroids a night. When observing we collect a series of images, taking the position of the asteroid and time of observation for each picture. From that, one image can become an observation used for orbit determination, requiring two additional observations.

When viewing an asteroid, it usually doesn’t appear any different than the numerous stars (white dots) on the image. That’s why we collect multiple images. After aligning and replaying the images in sequence, there is one (sometimes multiple if there is more than one asteroid) white dot that is moving, the asteroid, while the other white dots are stars. Here's an example for asteroid 2000 CO101. Try to spot it in the animation below.

Orbit determination is the process of calculating an orbit of an object.

I conducted orbit determination using a program I wrote in Python and VPython while at the Summer Science Program (SSP) in the summer of 2009. For my Senior Project, I slightly modified my program to improve it. I was able to successfully work on two different asteroids during my project.

My project uses the Gaussian Method of Orbit Determination. Gauss developed this method in the early 1800s, and demonstrated its power by recovering the asteroid (also known as a dwarf planet now) Ceres. Ceres had been observed for a few days by its discoverer Giuseppe Piazzi, but it was lost after it disappeared behind the Sun. Gauss used thes relatively few observation points to calculate the orbit of Ceres and recover it.

When conducting orbit determination, the goal is to determine the six orbital elements. This is done by calculating the position vector of the body (in this case the position of the asteroid relative to the Sun) and the velocity vector of the body. There is only one orbit that satisfies these. These are calculated using three observation points (during each observation we collect the position of the asteroid in the sky (R.A. and Dec., which is later converted to the position from the Sun), and exact time). The cool thing about this method is that the observations don’t have to be spread out throughout the whole orbit (which would be common sense), but can be essentially from any three points in the orbit. This is one reason why Gauss was so successful.

Like the planets, asteroids orbit around the Sun, and have elliptical orbits where the Sun is one of the two foci of the ellipse. Asteroids in the Asteroid Belt have orbits that are roughly circular (meaning that their orbits’ eccentricities are almost equal to 1), and with low inclinations. However, asteroids outside the Asteroid Belt can have many types of odd orbits.

All orbits, including those of asteroids, can be described uniquely by the six orbital elements (the above image from Wikipedia is greatly helpful in visualizing these):

1. Semimajor Axis: Half the length of the longest axis in the ellipse of the orbit.
2. Eccentricity: Shape of the ellipse. Values closer to 0 result in shapes that are more squished, while values closer to 1 are shapes that are more circular.
3. Inclination: How tilted the orbit is from the reference plane. This reference plane when working with asteroids is usually the ecliptic plane (plane of the Solar System where the orbits of the planets lie).
4. Longitude of the Ascending Node: How much the orbit is rotated from the reference direction, usually the vernal point. In other words, it is where the asteroid “ascends” out of the reference plane in its orbit.
5. Argument of Periapsis or Perihelion: Where the closest location of the asteroid to the central body (i.e. the Sun) is in reference to the Longitude of the Ascending Node.
6. Mean Anomaly: Where the asteroid is located in the orbit at a certain time.

These orbital elements are calculated when determining the orbit of an asteroid.

Asteroid 163132

Asteroid 163132 is a Near Earth Asteroid. This is a picture of the orbit I calculated using my program. My orbit is in orange, while the accepted one calculated by JPL is in red. The shape of the orbit very closely matches the actual orbit during the observation time, where the red object and the blue Earth are located. Also notice that the asteroid is not in the correct location. This is a problem in my calculation of one of the six orbital elements (Mean Anomaly) that I was unable to figure out.

Asteroid 2000 CO101

Asteroid 2000 CO101 is also a Near Earth Asteroid. Here is a picture of the orbit I calculated with my program. As you can see, the shape of the orbit more closely matches that of the accepted. Again, my asteroid is not in the correct location due to an error in my calculation of the Mean Anomaly.

I also researched some causes for the discrepancy in the shape of the orbits from the actual orbit. Likely, the best fix would be to collect more observations in an effort to improve the orbit. I'm also not accounting for some phenomena like the asteroid’s velocity and its effect on the light it reflects.

Perhaps the differing results may be due to the Gaussian method itself. I’ve read that the Gaussian method works best at low inclinations, a reason why Gauss was very successful with Ceres, since it is in the Asteroid Belt. This may account for the vast differences in the accuracy for the above two asteroids. 163132 has a high inclination, whereas 2000 CO101 does not.

Alongside orbit determination, I planned to determine the rotational period of asteroids. As asteroids rotate, the light reflected from the Sun can change in magnitude, due to the uneven shape of asteroids which reflect light at different levels at different times. This change can be plotted against time to reveal the rotational period.

My plan was to first test out our methods on a relatively easy asteroid, and then move onto an asteroid that has an unknown rotational period. My mentor started working with asteroid 3554 Amun that had a very small rotational period of 2.53 hours He collected data for a whole night and also analyzed it. This is what we found.

The first plot is of the brightness (measured in magnitude) over time. Initially there appears to be a pattern that could correspond to the period of what we were looking for. But we can’t be too confident in the results. For one, the changes in between consecutive images are too large. This could be very easily due to noise, not the asteroid itself.

When my mentor conducted a rolling 9 measurement average, shown in the second plot, the period ended up being too short. In the end, we decided that our results are not accurate enough, and we cannot find rotational period with accuracy using our equipment. We had to give up on further plans to determine rotational period of more asteroids.

I presented my work to a meeting of the Astronomical Society of Southern New England (ASSNE) on May 9. ASSNE is a group of amateur astronomers who like to perform astronomical outreach in the area. The monthly meetings are open to the public. I discussed the orbit determination portion of my project in great detail, while also sharing how I conducted observation. I also demonstrated the programs that I wrote to calculate and visualize orbits of asteroids.