| MadSci Network: Astronomy |
Sara -
There are a number of tricks astronomers use to find the distances of things, but for objects as close as a passing comet, it is relatively easy to determine it's distance using "stereoscopy", which is exactly how you use your eyes to determine how far away objects are from you. People observing the comet at the same time on different parts of the world can measure very precisely the position in the sky the comet appears to them. They measure the angle the telescope must be at to properly see the comet. When they compare their notes to other people around the world, they can "triangulate"; it goes like this:
If I know where I am exactly (say, Sacramento, California), and I know where you are exactly (say, Minot, North Dakota), I can calculate the exact distance between you and me. Note that this has to be the ABSOLUTE distance, as if we were connected by a long pole that passed right through the Earth; it's not good enough to calculate the distance over land.
First you measure the angle of the comet in the sky, and I do the same thing at the same time. Next, I tell you what my angle was.
The straight line between you and me is the first side of a triangle. The straight line between me and the comet is the second side of the same triangle. And the straight line between you and the comet is the third side of the triangle. Since you know the exact distance to me, and the angles required for each of us to see the comet, you can calculate the exact distance of the comet, using a simple geometry trick. This could even be done on paper if everything is drawn precisely.
Now, if I know exactly how far away it is and how big it LOOKS from here, I can calculate how big it is in a similar way.
To answer your third question is a little more tricky. I won't give you the equations, but I will explain the process. If we know how far the comet is from day to day and plot it's position in the sky, we can see how fast it's going and in what direction. We are fairly sure that the comet is in a kind of orbit around the Sun.
I say "kind of" because we are used to thinking of orbits as perfectly
circular, which they usually are not. Int he case of a comet, it's
orbit is VERY "eccentric", which in this case means long and skinny...
is a narrow ellipse with the Sun near one end. The comet goes way
out away from the Sun and then slows down and begins to fall back in,
speeding by the sun at top speed and then proceeds out away again.
(See this cool
web site on planetary orbits.)
I would also like to point out that it really helps a lot if we know how the Earth moves, for example, the exact angle of it's tilt, it's speed and direction of rotation, it's position relative to the Sun, and the slight eccentricity of IT'S orbit. See, if you want to figure out all this stuff about a comet, you really should already know all this same stuff about the Earth, because you're moving and the comet's moving and none of the math will make any sense if you don't take that into account.
Anyway, if we know the speed and direction, we can predict the shape of the orbit, the speed of the comet at each point inthe orbit, and the time it takes to travel the length of the orbit, which is the time it will take the comet to return.
For more info, check out these web sites:
Hale-Bopp Position Calculator
The Hale-Bopp Locator
I hope that's helpful.
Thank you for your question!