Updated 30 September 2010

Amateur Astronomer's Notebook

How Far Away is that Star?


People are often told that "that star is "x" light years away"... but what does that really mean? Can the vast distances of astronomy really be comprehended by the human brain? This page will attempt to put some of the vast quantities of astronomy into terms more compatible with human thinking...

How far is Vega, really?

The bright summer star Vega is about 27 light years away. That means that the light that left that star in 1983 is just getting to Earth in 2010. Light travels at 186,000 miles per second, and it took 27 years for it to get here... but can anyone really comprehend just how far this distance is? Lets take a look:

27 light years is equal to about 1.5837x10^14 miles, or, one hundred fifty eight million, three hundred seventy thousand million miles! But this too is more or less meaningless. Let's try to put this into perspective by scaling down the distance; let's say that the distance between Earth and Vega is the same as the distance between New York and Los Angeles (about 2700 miles). Now, on this same scale, how far would the distance to the Moon (about 250,000 "real" miles) be?

Answer: about 7 millimeters!!!

So, if you are standing in Los Angeles and you move less than a centimeter closer to New York, you have moved (at the scale of our model) as far as the distance between the Earth and Moon, a distance that few cars can go in their lifetimes. And, keep this in mind also: Vega is in our backyard. Galaxies are yet millions of times farther out!

Another way of looking at it...

People often say "if only I could win the lottery...", so I presume that people can "relate" to this prospect. Well, let's say you did win the million dollar lottery. Let's also say that you had a "miracle" car which could get 1000 miles per gallon of gasoline, and that the cost of gasoline was one cent per gallon. With this car and your winnings, could you buy enough gasoline to make it to Vega (assuming there was a road to drive on)? Pick from the following multiple choice possibilities:

  1. Yes, with gasoline to spare
  2. Just barely
  3. Enough to get about half way there
  4. Not nearly enough

If you picked number 4, NOT NEARLY ENOUGH, you are correct! Even if you bought one million dollars worth of gasoline at the cost of one cent per gallon (a total of 100 million gallons), you could only drive 100 billion miles with this "miracle" car. Vega is 1584 times further out!!! On our "New York to Los Angeles" scale, you would "run out of gas" only 1.7 miles from your house! If you were to drive so that you were one hundred billion miles closer to Vega, it would appear to the eye just as it does from Earth; no brighter and no bigger. Only an extremely sensitive detector could measure the minuscule increase in brightness that would result from moving ten billion miles closer to Vega. Vega is indeed extremely far away...


The "Great Galaxy in Andromeda"

The "Great Galaxy in Andromeda" (often just called the "Andromeda Galaxy") is perhaps the most famous galaxy outside of our own Milky Way. It is one of about a dozen galaxies that together with the Milky Way make up the "Local Group". Basically, the Andromeda Galaxy is the closest "real" galaxy to our own Milky Way (we'll not count the Large and Small Magellenic Clouds in this example, which technically are the closest galaxies to the Milky Way). Andromeda is a "close by" or "neighborhood" galaxy; it is generally believed to be about 2.2 million light years away. In terms of the universe, this truly is "very close by". How far is 2.2 million light years? For starters, the light that you see from Andromeda tonight has been on its journey for 2.2 million years. Had you been around 2.2 million years ago, the sky as we know it today would be largely unrecognizable (due to stellar motion). None of the familiar constellations would look as they do today. But, how far is the Andromeda Galaxy, really?

One example...

Most people today drive on the freeway (in the US anyway) at about 70 mph despite a posted speed limit of 55 mph. Let's say you had a really fast car, a car similar to one used in NASCAR racing. Such a car can manage a speed of nearly 200 mph. If you were to take this car, and drive it at full speed continuously (we'll assume no refueling or maintenance stops are necessary), how long would it take to reach the Andromeda Galaxy? Answer: about 7.36 trillion years, which is about 1600 times older than our solar system! So, the speed at which some of the fastest cars can travel is absurdly inadequate for intergalactic travel...

Let's use the "lottery and gasoline" example...

To further illustrate the distance to the Andromeda Galaxy, we'll modify one of the examples used earlier for the star Vega. This time, let's assume that everyone in the USA (about 300 million people in 2007) won the million dollar lottery every day of the year for one full year. This would mean we would have 365 times 300 million million dollars (that's 109,500 trillion dollars!). This time we'll use a "real" car, say a Honda Civic which can get about 38 miles per gallon of gasoline. We'll also use a gasoline price of $3.00 per gallon (the price of a gallon of gas in 2007). Can we buy enough gasoline to make to Andromeda without running out of gas? Actually, we would only make it about 10.7% of the way even with the purchase of this staggering amount of fuel. To make it to Andromeda in a Honda Civic we would need about 36,500 trillion gallons of gasoline! A standard Honda Civic would have to be modified to carry this amount of gasoline. The gas tank would need to have the capacity of about 730 million ocean going supertankers (with capacity of 50 million gallons each)! And, we'll be waiting a long time to "fill up" at the gas station. Even if the pump had the flow capacity of Niagara Falls, it would take over two thousand three hundred years to fill the tank! Despite this attempt to bring to reality the distance to the Andromeda Galaxy, the true distance remains "mind boggling". And, as mentioned before, the Andromeda Galaxy is one of the very closest galaxies! Some of the farthest galaxies known are yet thousands of times farther out...


Notes

300,000,000 people x $1,000,000 x 365 = 109,500 trillion dollars (109 500 000 000 000 000).

2.2million light years = 186,000 miles per second x 60 seconds/minute x 60 minutes/hour x 24 hours/day x 365 days/year = 12904531200000000000 miles.

Can buy 36500 000 000 000 000 gallons of gas with 109,500 trillion dollars.

Can go 38 x 36500000000000000 miles or 1387000000000000000 miles with 36500000000000000 gallons of gas.

Thatís only 10.7% of the way! (1387000000000000000 / 12904531200000000000).

Large supertanker holds 50,000,000 gallons. Would need 730 000 000 of them to hold the gas (36500000000000000 / 50,000,000).

Average flow of Niagara Falls is 500,000 gallons/sec. This is the same as 15768000000000 gallons per year. This would take 2314 years to fill the 730 000 000 supertankers!


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