Senior Project

A graduation requirement for my high school is the Senior Project. I've had a long interest in astronomy, and worked on asteroids this summer as part of the Summer Science Program (SSP). I wanted to continue working on asteroids as part of my senior project.

What Are Asteroids?

Asteroids are small bodies that orbit the Sun. These bodies are smaller than planets, but larger than meteoroids. Many are located between the orbits of Mars and Jupiter, in a region of the Solar System known as the Asteroid Belt. However, there are numerous asteroids outside of the Asteroid Belt, some even coming close to the Earth, often knocked out of their previous orbits due to the gravity of larger planets. These asteroids can have very eccentric orbits, in contrast to the roughly circular orbits of the asteroids in the Asteroid Belt.

When observing an asteroids through an image from a telescope, there is little distinguishing them from stars. But there is a huge difference when collecting multiple images. After aligning and stacking the images, the stars stay in place, but the asteroids move in relation to the stars. This can be seen in the animation below of asteroid 2000 CO101 from one of my nights of observation. Try to find the asteroid as it moves among the stationary stars from image to image (click for larger view). The exposures are each 30 seconds long, taken one after another, and each pixel is about 2 arc-seconds wide.


The majority of my project is to observe asteroids and determine their orbits. The asteroids that I have focused on are Near Earth Asteroids (NEAs) that are on the critical list. The asteroids are much harder to observe, and/or their orbits are not very well known. I am collecting the asteroids' positions on three days and using the Gaussian method of orbit determination to calculate their orbits.

In addition, I wanted to attempt to determine the rotational period of some asteroids. Many asteroids rotate, and the periods of rotation of most are in the range of 2 to 8 hours. As asteroids rotate, the amount of light from the Sun reflected changes over time, due to uneven shape and structure. The regular change can be used to determine period of rotation.
Wishing Star Observatory

Where I Worked

I worked with Mr. Herbert Peterson at the Wishing Star Observatory in Barrington, RI. Mr. Peterson is now a semi-retired engineer and works in amateur astronomy, and has built the observatory himself.

Choosing Asteroids

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. We did not get great weather for long periods of time, and by the time we did, the asteroid moved to a position where it became 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 has given me a copy of Guide 8 to help me choose my asteroids. It is an astronomy mapping software by Project Pluto. The program lacks some complex visualization features, but that makes it good for our needs. Its user interface is challenging and not very friendly at first, but it gets easier to use as I am using it more often. I ran into a problem when I found that the software is only for Windows, but I have it running on my Mac with CrossOver now.

Observing Asteroids

I observed asteroids with my mentor at his Wishing Star Observatory. On any night, we are able to observe anywhere between 2 to 5 asteroids. At the end of my project, I worked on 2 asteroids for orbit determination, while also observing a few asteroids from the critical list that the Minor Planet Center would especially like further observations on. These are typically newly discovered asteroids.

The exposure time for the images depends on the motion and the brightness of the asteroid. If the asteroid is dim, long exposures are necessary to reveal the asteroid's position. If the asteroid is moving fast, a shorter exposure is better so that the asteroid looks more like a point rather than a streak. Critical list asteroids are tougher because they typically are very fast moving and dim.
Image: Wikipedia

Asteroid Orbits

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). However, asteroids outside the Asteroid Belt can have many types of odd orbits.

All orbits, including those of asteroids, can be described with six orbital elements:
  • Semimajor Axis: Half the length of the longest axis in the ellipse of the orbit.
  • 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.
  • Inclination: How tilted the orbit is from the reference plane, usually the ecliptic plane (plane of the Solar System where the orbits of the planets lie).
  • Longitude of the Ascending Node: How much the orbit (more specifically where the asteroid "ascends" out of the reference plane) is rotated from a reference direction, usually the vernal point.
  • Argument of Periapsis or Perihelion: Where the closest location of the asteroid to the central body (like the Sun) is in reference to the Longitude of the Ascending Node.
  • Mean Anomaly: Where the asteroid is located in the orbit at a certain time.
The graphic from Wikipedia above right helps visualize these elements very well. These orbital elements are calculated when determining the orbit of an asteroid.

Performing Orbit Determination

Carl Friedrich Gauss developed his orbit determination method and demonstrated its power to recover Ceres (a dwarf planet in the Asteroid Belt) in 1801. Ceres had been lost by its discoverer Giuseppe Piazzi after it disappeared behind the Sun. Gauss was able to very easily recover the position of Ceres using his method.

I used the Gaussian method of orbit determination to calculate the orbits of my asteroids. Deriving and understanding this method requires calculus and calculus based physics. Simply, the method determines the six orbital elements from the position and velocity vectors of the asteroid. These vectors themselves are derived from only three observations that only have to have a small time of separation between them. This is one of the reasons why Gauss was successful in finding Ceres. He only needed a few points that Piazzi had been able to collect the few days that he did see Ceres.

The orbits that I calculated are not completely accurate, although they achieve reasonable accuracy during the period of observation. This is due to limitations on my part, such as me not taking into account the movement of the asteroid's effect on light. The Gaussian method itself is also not always very accurate. Gauss was very successful with Ceres because Ceres has a small inclination and is not located very close to the Earth. I have noticed the same thing in my calculations as well; the asteroids with lower inclination values tend to result in more accurate orbits.

Rotation of Asteroids

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. This change can be plotted against time to reveal the rotational period.

My mentor started working with an asteroid that had a very small rotational period of just over 2 hours. He collected data for a whole night and also analyzed it. There wasn't a strong enough pattern to help determine the rotational period. (A detailed explanation is available on my website.)

Presenting at ASSNE

I presented information about my project at a meeting of the Astronomical Society of Southern New England. I was originally supposed to present on April 10,  but my presentation was postponed to May 8 due to good weather1.

Mr presentation primarily focused on how I conducted my orbit determination and performed my observations. I also got the chance to demonstrate the program that I wrote to calculate and visualize orbits of asteroids.

It was great and a lot of fun, and from some comments that I received, such as the following from another ASSNE member, many others enjoyed my talk as well:
I don't know who else was totally blown away by Abhimat's presentation Saturday, but I certainly was! :shock: From the expressions of amazement that I kept hearing from the 'Peanut Gallery' I think many others were, too. I won't even pretend that I understood more than the absolute basics of what was said, but it was obvious to me that we have a budding professional astrophysicist in our midst! What truly impressed me was that this young man was willing to share both his successes - nearly matching the orbital predictions of a supercomputer, for gosh sakes! - as well as a computation that is a work in progress. That shows an amazing level of confidence and competence in what he is attempting, as well as a great level of maturity. Well done, Abhimat, and please be advised that you have raised the bar quite high for any future presenters!

1: In ASSNE, some of the parts of the meeting are postponed if there is good weather so that members have a chance to go outside and observe on a clear night.