Determining the distance to an Asteroid using Parallax
                                                                              7/4/00
Most of the asteroids (or "minor planets") orbit the sun in a belt (coplanar with the planetary orbits) which is located between 2.3 and 3.3 au from the Sun. This places them somewhere between Mars and Jupiter but very close to the earth relative to the distant stars. In general asteroids are large chunks of rock having masses less than 1021 kg. For comparison, Earth’s mass is 6 x 1024 kg. You will be measuring the distance to an asteroid called 1992 JB using the parallax method.

The two images we have available for this purpose were taken on May 23, 1992, from two different locations. The image called Astrd1.fts was taken at the Foggy Bottom Observatory at Colgate University, Hamilton, New York. Astrd2.fts was taken at National Undergraduate Research Observatory, Anderson Mesa, Flagstaff, Arizona. These two calculations provide a baseline of approximately 2900 km.

acquiring the images

A) Access the two asteroid images by going to http://192.154.43.167/ph110read/hou/

B)  Download the two asteroid images to your local hard drive (T: drive in the EFC or your own M: drive):

In Netscape: hold down Shift + left click with mouse

In Internet Explorer: right click and choose Save As…


   determining the distance to the asteroid

1) Open images Astrd1.fts and Astrd2.fts. Adjust the contrast/brightness settings so you can see the brightest objects in each image very clearly. Change the sizes of the two windows so that you can put the images side by side.

2) Study the two images, and try to decide which one object has shifted position. Check with the teacher when you have a convincing method/reason.

3) The plate scales of the two telescopes are different. The plate scale relates angular separation in the sky between two points (in " = seconds of arc) to their separation in pixels.  Astrd1.fts has a plate scale of 0.99" per pixel. Use the Resize option under Manipulation to make Astrd2.fts have the same scale. Show all work (including relevant diagrams) in the lab book. If you don't know what to do, please ask.

4) You can assume that the other "stars" in the images are so far away as to be fixed in position. Choose one bright star near the asteroid to use as a reference star for the rest of your measurements.

5) Now devise a plan for determining the angle (in arc seconds) that asteroid 1992 JB has shifted between the two images. Write out your plan; you are encouraged to check its feasibility with me. You might find the Translate option under Manipulation useful, but there are a number of correct ways to do this.

6) How does the angle determined in (5) differ from the parallax angle for stars? How does the angle relate to the distance to the asteroid?

7) Carry out your plan and determine the distance to the asteroid. Express your final distance to the asteroid in meters and in AU.