I have been asked by friends and family how we get probes and satellites through the asteroid belt that lies between Mars and Jupiter. The simple answer is that, contrary to Star Wars and other science fiction portrayals of them, asteroid fields are rather... empty.
Now, we don't know exactly how many objects are in the asteroid belt. It isn't particularly important for this demonstration, so lets err on the side of caution and say there are 10 million asteroids more than half a mile across in the asteroid belt. How likely are you to run into one passing through the asteroid belt?
The middle of the asteroid belt is around 2.8 astronomical units from the sun. One astronomical unit is 92,955,887.6 miles, the distance between the Earth and the sun. Some quick math (circumference tells us that the circumference of a circle with a diameter of 2.8 astronomical units is 1.64 * 10^9 miles. Written out, that is a circle 1,640,000,000 miles around. If there were 10 million objects larger than half a mile across, there would be 164 miles between each one. And this is if every object was arranged on a ring. The real asteroid belt is a 'donut', a full astronomical unit across, and it isn't completely flat. There is just so much space and so little of everything else that actually running into -anything- is very unlikely.
The odds of succesfully navigating the asteroid belt are significantly better than 3720 to 1, in any case.
Tuesday, February 16, 2010
Wednesday, February 10, 2010
Parsecs Part Two: Parallax
This a continuation of the original post here.
Now that we have an understanding of how arc is measured, we can talk about parallax. Parallax is the phenomenon that astronomers use to determine how far away an object is. Although parallax sounds impressive, it is actually something that people deal with every day without thinking about it.
If you've ever looked out the window while riding in a car, you probably noticed that close things appear to be going by faster than things that are further away. The reason why is obvious, if something is 10 feet away and you move 5 feet, you've made a major change in the distance between you. Conversely, if something is a mile away, that same 5 feet doesn't change much at all.
This same principle works for stars as well. Most stars are so far away that it doesn't matter what we do, they don't seem to move at all relative to one another. This is like looking at 2 objects, one which is 10 miles away and 1 which is 11 miles away. Moving ten feet doesn't change the relative position of the two objects at all. They look just as close to one another as they did originally.
However, some stars are close enough that we can see them move ever so slightly. Astronomers take an observation of a star's position in the sky, then wait six months. In six months, the Earth will have moved to the other side of the Sun along its orbit, giving us the greatest change in perspective possible. This turns out to be just enough for us to see nearby stars move relative to the 'background stars'. The picture below is exaggerated, but it illustrates the point.
First, an Astronomical Unit is defined as the distance from the Earth to the Sun. Although not useful for interstellar distances, AUs are convenient for expressing distances within the solar system, such as the distance between planets. In a form that might be more familiar to you, 1 AU is 92, 955, 886.6 miles.
So the 'baseline', or the distance between the two observations is over 180 million miles. This is quite a step up from moving 5 feet to get a different perspective! However, the distances we are comparing this shift to also increased many times over. Proxima Centauri, the closest star to us after the Sun, is about 4.2 lightyears away. A quick refresher, a lightyear is the distance that light will travel in a year. Since light travels at 186 thousand miles a second, the distance it covers over the course of a year is hard to visualize. Without going into scientific notation, a single lightyear is around 5,880,000,000,000 (or rather, just shy of 6 trillion) miles long.
Needless to say, even 'nearby' stars aren't really close in the conventional sense and even the 180 million mile 'step to the left' we make in our orbit around the Sun isn't really significant compared to the huge distances between stars. Still, we have been able to see some nearby stars move relative to the background stars. Proxima Centauri, as our closest neighbore, moves the most of any star.
We now get to the reason why I did the background explanation of arc and what an arcsecond is. Relative to the background stars around it (which are much to far for the movement of the Earth to make any effect at all), Proxima Centauri moves about .77 arcseconds. That means that its position shifts less than 1/3600 the width of your pinky at arm's length!
With precision instruments and a clear night sky though, astronomers can measure that shift. We call the shift parallax. Proxima Centauri has a parallax of .77 arcseconds.
And now we can answer the original question about parsecs. A persec is the distance an object would have to be in order for it to have a parallax of 1 arcsececond. That means that it is close enough that as we move around the Sun, it appears to move 1 arcsecond relative to the background stars. This distance is about 3.26 lightyears. Why don't we just use lightyears then?
Although physicists have a good reputation for being very intelligent people, the truth is they are also human and like to avoid complicating things when they can. Converting a parallax to parsecs is very easy:
Distance (In parsecs) = 1 / Parallax.
Simple and easy to remember. So for Proxima Centauri, 1/.77 = 1.29 parsecs. Multiply by 3.26 to convert the parsecs to lightyears and you get about 4.2 lightyears.
Now in defense of Han Solo, it was later 'clarified' (rationalized after the fact) by one of the later Star Wars novels that he was in fact meaning distance. He was referring to his ship's ability to skim close to black holes along the 'Kessel Run' without getting sucked in, cutting distance off the trip. Not what was originally intended, but it doesn't change the fact that the use of the parsec is wrong even when used in this context.
So a contest for you. I've already explained why the original use of parsec, as a measure of time, is incorrect. If you leave a comment telling me the other reason that using a parsec in this case is incorrect, you get to ask a question and I will give it top priority.
A hint, as it may not be obvious. There is a problem with using parsecs -at all- in Star Wars.
Now that we have an understanding of how arc is measured, we can talk about parallax. Parallax is the phenomenon that astronomers use to determine how far away an object is. Although parallax sounds impressive, it is actually something that people deal with every day without thinking about it.
If you've ever looked out the window while riding in a car, you probably noticed that close things appear to be going by faster than things that are further away. The reason why is obvious, if something is 10 feet away and you move 5 feet, you've made a major change in the distance between you. Conversely, if something is a mile away, that same 5 feet doesn't change much at all.
This same principle works for stars as well. Most stars are so far away that it doesn't matter what we do, they don't seem to move at all relative to one another. This is like looking at 2 objects, one which is 10 miles away and 1 which is 11 miles away. Moving ten feet doesn't change the relative position of the two objects at all. They look just as close to one another as they did originally.
However, some stars are close enough that we can see them move ever so slightly. Astronomers take an observation of a star's position in the sky, then wait six months. In six months, the Earth will have moved to the other side of the Sun along its orbit, giving us the greatest change in perspective possible. This turns out to be just enough for us to see nearby stars move relative to the 'background stars'. The picture below is exaggerated, but it illustrates the point.
First, an Astronomical Unit is defined as the distance from the Earth to the Sun. Although not useful for interstellar distances, AUs are convenient for expressing distances within the solar system, such as the distance between planets. In a form that might be more familiar to you, 1 AU is 92, 955, 886.6 miles.So the 'baseline', or the distance between the two observations is over 180 million miles. This is quite a step up from moving 5 feet to get a different perspective! However, the distances we are comparing this shift to also increased many times over. Proxima Centauri, the closest star to us after the Sun, is about 4.2 lightyears away. A quick refresher, a lightyear is the distance that light will travel in a year. Since light travels at 186 thousand miles a second, the distance it covers over the course of a year is hard to visualize. Without going into scientific notation, a single lightyear is around 5,880,000,000,000 (or rather, just shy of 6 trillion) miles long.
Needless to say, even 'nearby' stars aren't really close in the conventional sense and even the 180 million mile 'step to the left' we make in our orbit around the Sun isn't really significant compared to the huge distances between stars. Still, we have been able to see some nearby stars move relative to the background stars. Proxima Centauri, as our closest neighbore, moves the most of any star.
We now get to the reason why I did the background explanation of arc and what an arcsecond is. Relative to the background stars around it (which are much to far for the movement of the Earth to make any effect at all), Proxima Centauri moves about .77 arcseconds. That means that its position shifts less than 1/3600 the width of your pinky at arm's length!
With precision instruments and a clear night sky though, astronomers can measure that shift. We call the shift parallax. Proxima Centauri has a parallax of .77 arcseconds.
And now we can answer the original question about parsecs. A persec is the distance an object would have to be in order for it to have a parallax of 1 arcsececond. That means that it is close enough that as we move around the Sun, it appears to move 1 arcsecond relative to the background stars. This distance is about 3.26 lightyears. Why don't we just use lightyears then?
Although physicists have a good reputation for being very intelligent people, the truth is they are also human and like to avoid complicating things when they can. Converting a parallax to parsecs is very easy:
Distance (In parsecs) = 1 / Parallax.
Simple and easy to remember. So for Proxima Centauri, 1/.77 = 1.29 parsecs. Multiply by 3.26 to convert the parsecs to lightyears and you get about 4.2 lightyears.
Now in defense of Han Solo, it was later 'clarified' (rationalized after the fact) by one of the later Star Wars novels that he was in fact meaning distance. He was referring to his ship's ability to skim close to black holes along the 'Kessel Run' without getting sucked in, cutting distance off the trip. Not what was originally intended, but it doesn't change the fact that the use of the parsec is wrong even when used in this context.
So a contest for you. I've already explained why the original use of parsec, as a measure of time, is incorrect. If you leave a comment telling me the other reason that using a parsec in this case is incorrect, you get to ask a question and I will give it top priority.
A hint, as it may not be obvious. There is a problem with using parsecs -at all- in Star Wars.
Tuesday, February 9, 2010
Parsecs Part One: Background
If you've ever seen the original Star Wars, you'll no doubt remember Han Solo's famous boast about the Millennium Falcon, "It's the ship that made the Kessel Run in less than twelve parsecs." This usage turns out to be incorrect for two reasons.
But before we get into that, some background information is needed. The name "parsec" is unfortunate, as it sounds like a fancy science-fiction term for "part of a second". As it turns out, parsecs do relate to seconds, but not seconds of time. It refers to seconds of arc.
Now lets talk about what a 'second of arc' is. Hold your hand out as far as you can and look at your pinky finger. At arm's length, your pinky is appears to be about 1 degree in width. There are 360 degrees in a circle, so if you copied your pinky 360 times you could make a loop around yourself at arm's length.
Each degree is divided into "minutes of arc", or arc-minutes. There are 60 arc-minutes in1 degree of arc. So looking back at your pinky, an arcminute is 1/60 of that width.
Finally, each arcminute is further divided into "seconds of arc", or arc-seconds. There are 60 arcseconds in an arcminute. At arm's length, that means an arcsecond is a mind-boggling 1/3600 the width of your pinky.
Now that we have our background information, we can discuss what a parsec actualy is here.
But before we get into that, some background information is needed. The name "parsec" is unfortunate, as it sounds like a fancy science-fiction term for "part of a second". As it turns out, parsecs do relate to seconds, but not seconds of time. It refers to seconds of arc.
Now lets talk about what a 'second of arc' is. Hold your hand out as far as you can and look at your pinky finger. At arm's length, your pinky is appears to be about 1 degree in width. There are 360 degrees in a circle, so if you copied your pinky 360 times you could make a loop around yourself at arm's length.
Each degree is divided into "minutes of arc", or arc-minutes. There are 60 arc-minutes in1 degree of arc. So looking back at your pinky, an arcminute is 1/60 of that width.
Finally, each arcminute is further divided into "seconds of arc", or arc-seconds. There are 60 arcseconds in an arcminute. At arm's length, that means an arcsecond is a mind-boggling 1/3600 the width of your pinky.
Now that we have our background information, we can discuss what a parsec actualy is here.