# Measuring the speed of asteroids

#### Aug 14, 2001

Your goal in this project will be to measure the orbital speed of an asteroid. In order to do that, you will have to carry out the following steps:

1. choose an asteroid to observe
2. determine where it will be at a given time
3. make a finding chart
4. learn how to measure positions and brightnesses of objects in astronomical images
5. take two pictures of the asteroid through a telescope, over an interval of 30-60 minutes
6. reduce the pictures (remove instrumental defects)
7. find the asteroid in the pictures
8. measure the angular distance it moves
9. measure its brightness in "magnitudes"
10. find the distance of the asteroid from the Earth and Sun
11. convert the angular motion into linear motion
Each pair of students will work on a different asteroid. After all groups have finished their work, you may compare the velocities you have calculated, and look for some pattern.

#### Day one: preparing for an observing run

During the first day, you must get everything ready for the night's work at the RIT Observatory. Without a good plan, you'll just waste time and energy. Here's what you need to do:

• First, pick the right asteroid

There are thousands of known asteroids. Astronomers assign both a name and a number to each asteroid with a well-defined orbit. Your first task is to pick an asteroid which will be

• more than 25 degrees above the horizon tonight at 10:00 PM
• bright enough for us to detect: its magnitude must be LESS than 13 (astronomers measure brightness in "magnitudes", which are backwards: small numbers mean "bright", large numbers mean "faint")
Each group should consider asteroids from one of the following range of numbers:
```                1-10
170-179
230-239
240-249
250-259
340-349
400-409
```

You can use the JPL Horizons Ephemeris web site

http://ssd.jpl.nasa.gov/cgi-bin/eph
to look up the name for an asteroid, given its number. You can also look up its position at 10:00 PM tonight, in two ways. Azimuth and elevation tell you in which direction of the compass (North-East-South-West) and how far above the horizon an object will appear; you need to find an asteroid which will be more than 25 degrees above the horizon. Right Ascension and Declination are the celestial equivalents of longitude and latitude; you can use them to create finding charts, and to point a telescope at a particular object.

• Make a naked-eye finding chart

Where will the asteroid be in the sky? Which constellation? Which direction? To find out, use the Azimuth and Elevation of your asteroid. Go to this WWW site, which provides an applet which displays a view of the entire night sky from Rochester (the URL below has been split in half so you can read it -- it really ought to be typed all together):

http://www.wunderground.com/sky/ShowSky.asp? TheLat=43.08230209&TheLon=-77.63246918&TimeZone=5&TimeZoneCode=1

Set the date and time of this tool for tonight at around 10:00 PM. On the map, you'll see two sets of red numbers. The numbers ranging from 0 to 350 degrees in a circle around the sky are values of Azimuth. The numbers ranging from 90 (at the zenith, overhead) to 0 (on the horizon) are Elevation. Where will your asteroid be? Should you look North, South, East, or West? Find a constellation nearby which you can recognize. It may help to click on the appropriate "Direction" button to show a better view of the portion of the sky containing your target.

• Next, make a zoomed-in finding chart.

A finding chart shows the stars which ought to appear around a target; when you take a picture at night, you can compare the image to the chart, and verify that you are pointing in the proper direction. Without a chart, you could spend a whole night taking pictures of the wrong part of the sky!

There are two tools you can use to make charts. Both require that you enter the Right Ascension and Declination of an object. The tools are:

Both tools will provide you with a picture of some portion of the sky. The CCD camera we will use creates images which are about one quarter of a degree on a side: that's about 15 arcminutes. Make a chart showing the field around the asteroid you have chosen, at 10:00 PM tonight. Print out the picture. You might find it easier to read a printed copy if you reverse the color scheme, so that black stars appear on a white background.

• Figure out how bright the asteroid ought to be

It will help you to find the asteroid if you know how bright it should be, compared to stars in the field around it. The magnitude of the asteroid is one of the bits of information in the big tables returned by the JPL Horizons Ephemeris -- it should be a number between 9 and 13. What is the magnitude of your asteroid?

The Aladin tool has a facility called "Vizier", which allows you to superimpose information from stellar catalogs on top of finding charts. You can use it to look up the magnitude of stars in your finding chart. Pick the USNO2 catalog, which will provide two magnitude values (one for measurements through a blue filter, the other for measurements through a red filter). Use the second magnitude value. Try to find several stars on your finding chart which are roughly the same magnitude as the asteroid ought to be.

You should also use the Aladin tool to measure the distance between a pair of bright stars. Aladin will give you the distance in "arcminutes"; each arcminute is 1/60 of a degree. You'll need this distance tomorrow to calculate the plate scale of the CCD images we'll take tonight.

• Practice using the SIP image processing tool

Tomorrow, you will have to perform several operations on the raw CCD images of your asteroid. You will use a Java applet called SIP

http://www.phys.vt.edu/~jhs/SIP/
to do these tasks. Spend some time practicing with it today. It operates on images in a format called FITS which is used only by astronomers. You can download FITS copies of your finding charts and use SIP to measure the relative brightness of several stars. Try picking stars for which you looked up magnitudes in the previous step -- measure their magnitudes from images using SIP; check to see that the difference in magnitude between two stars is roughly the same, based on the catalog values and the values you measure from the image.

At night, we'll go to the RIT Observatory and use the 10-inch telescope and CCD camera to take pictures of your asteroids. We will take one picture of each asteroid, then go back and take a second picture of each one. Each group should end up with two pictures of their chosen field, taken 30-60 minutes apart. The asteroid will move a perceptible distance from one image to the other, which should make it easy to find.

You must be ready to provide your field's Right Ascension and Declination, which we will use to point the telescope. You should also be ready to compare the image which will appear on the computer's screen with your finding chart, so that you can verify that we are indeed pointing at the proper spot in the sky.

We will save all the images in FITS format and transfer them back to computer on campus for processing on Day Two.

#### Day Two: reduce and analyze the images

On the second day, you must first process your images to remove several types of instrumental defects, and then analyze them to measure properties of your asteroid.

Describe its appearance. Are there any annoying features? Can you match the raw image to your finding chart? Is it easy to see faint stars?

2. Remove the dark current

CCD cameras suffer from noise in their electronics; the warmer they are, the worse the noise becomes. Most CCD cameras are cooled far below room temperature to reduce this noise as much as possible. Our camera was cooled only to -5 degrees Celsius, which leaves lots of "hot pixels". We can get rid of them by taking a dark image, which is simply a picture with the shutter closed. Since no light enters the camera, only the noise appears. If we subtract this dark image from a raw image, we should remove much of the electronic noise.

3. Correct for flat field variations

Another problem with CCD cameras is that they aren't uniformly sensitive across their extent: the silicon in one corner of the chip might be slightly more or less sensitive than that in the center, for example. That can cause stars in one portion of the image to appear improperly brighter or fainter than stars in another portion of the image.

You may notice "donuts" in your images; these are caused by small particles of dust on the filters or other pieces of glass in the telescope and camera. The particles in essence cast shadows on the chip, making circular areas appear fainter than they ought to (the real phenomenon is called diffraction, which you may learn about in college).

In order to remove both the "donuts" and variations in sensitivity, you can divide your images by a flat-field frame. A flatfield frame is simply a picture taken of a uniform light source, such as an evenly lit white sheet of paper, or a blank section of the sky at sunset, before any stars appear.

You know roughly how bright your asteroid should be. Simply look for an object of the right brightness which appears in your images, but not on the finding chart. If you have trouble finding it, try blinking your two images.

Measure the magnitude of the asteroid, and of two or three stars of known magnitude. Use the difference between your values for the asteroid and the stars to calculate the magnitude of the asteroid. Does it match the predicted magnitude, to within 0.4 mag or so?

6. Determine the angular distance your asteroid moved

Yesterday, you should have found the distance between two bright stars in your field, in units of "arcminutes". Now, use SIP to measure the distance between these same stars in "pixels" (you will probably need to use the Pythagorean theorem). Find the conversion factor

```             distance in pixels
K   =  ----------------------
distance in arcminutes
```
This should be a small number, much less than one.

Measure the distance the asteroid moves between your two pictures, in pixels. Then convert that distance to arcminutes, using your value for K.

Finally, convert the distance to degrees: remember that one arcminute is 1/60 of a degree. You should find that the asteroid moved a small fraction of a degree in the interval between the two pictures.

7. Calculate the linear distance your asteroid moved

You will need to know the distance from the Earth to the asteroid at the time we took the pictures. You can find it in the JPL Horizons Ephemeris information.

8. Calculate the speed of your asteroid in kilometers per second

This speed is actually a combination of the motion of the asteroid and the motion of the Earth, but we'll ignore the latter for now.

At this point, different groups can compare the speeds of their asteroids. There might be some connection between the orbital speed of an asteroid and its distance from the Sun. Do your results show any obvious pattern?