The Summer Science Program in Astrophysics
Asteroid Orbit Determination
Near-earth asteroids, also known as “minor planets,” orbit the sun at roughly the same distance as Earth. Collisions with them are catastrophic – just ask the dinosaurs – so being able to predict their future position is an important application of vector calculus.
On the first day of SSP, participants are taught the celestial coordinate system, and how to interpret an ephemeris to select a near-earth asteroid to study. Each team of three then writes an “observing proposal” similar to what an astronomer would submit to an observatory. On the third night, weather permitting, teams begin scheduled observing runs, accompanied by a Teaching Assistant.
After each observing run, the team locates the asteroid’s faint dot among the background stars (not always easy to do), then precisely measures its position relative to surrounding stars. Once they have at least three or four observations taken on different nights, they write software in Python to calculate the asteroid’s position and velocity vectors, then transform them into the six orbital elements that characterize the asteroid’s orbital ellipse, using numerical differentiation.
Each team performs every step themselves: choosing their asteroid, pointing the telescope, taking images, reducing the data, calculating the orbit. Some go on to improve the accuracy of their calculated orbits using additional observations to make differential corrections. Another option is to use Visual Python to make an animation of their asteroid orbiting the sun!
Each team’s observations are submitted to the Minor Planet Center of the International Astronomical Union, and used to improve future predictions of the asteroid’s position.
Topics covered typically include:
- Astronomy: celestial coordinates, digital observational techniques, astrometry; brief introductions to planetary science, cosmology
- Physics: gravitation, celestial mechanics; brief introductions to the electromagnetic spectrum, relativity, quantum mechanics
- Mathematics: interpolation, coordinate transformations, differential and integral vector calculus, numerical methods, differential equations
- Scientific Programming in Python