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Big Numbers
By Roy Patton
Posted on 5/12/2018 5:31 PM

Putting The Universe Into Perspective

Understanding Large Numbers used by Astronomers

By Roy Patton


(Disclaimer: None of the distances in this paper are exact figures. They are rounded off for the sake of expedience)


Typically, when an article about a deep-space object or event is written about in the news, it is invariably followed by a parenthetical “A light-year is the distance light travels in one year, about six trillion miles.” While that is an answer, it's not a good one because the reader is left to guess how far that really is. Well, to get to that answer, smaller numbers ( but still quite large) have to be dealt with, first. I will start with the distance to the Moon, then discuss millions, then billions, and, finally, trillions. Larger numbers than trillions are usually distances, which are discussed in terms of light-years.


The Distance To The Moon

The full moon is big and bright. It looks pretty close, and Astronomically speaking, it is. It's about 250,000 miles away. If I were to stop writing right now, I'd be guilty of what I just I accused news writers of doing; giving the readers a half-answer. What I have to do now is explain what 250,000 miles means. I have to give the readers some perspective as to how big that number is. The easiest way to do that is to put it in terms of everyday events. For example, if I were to get in my car and drive to the Moon at 60 miles per hour, it would take me a little more than 173.5 days to get there, or about 9 days shy of six months. Now the reader has some perspective as to how far away the moon is, and a cool fact to go along with it. Another cool fact about the distance to the Moon, although I don't know how much perspective it will give, is that all of the other planets in the solar system (not including the diameter of Saturn's rings) would fit in the space between the Earth and the Moon.



There is close to nothing a million miles from Earth, but a million and millions, are numbers used in Astronomy. A million miles is four times the distance to the Moon. It's a 23 month long drive at 60 mph. A clock would take 11.574 days to tick off a million seconds. A million is one thousand thousands, that is, if someone saved a thousand dollars a week, it would take them a thousand weeks to earn a million dollars. Remember, there are only 52 weeks in a year. 52 goes into a thousand about 19.23 times. Thus, it would take them 19.23 years to save a million dollars.

That's how big a million is. Now multiply that by 93 and that's how far away the Sun is. Double that number and you'll have the average diameter of the Earth's orbit. The planet Jupiter is about 5.2 times as far away from the Sun as Earth is, or about 483.6 million miles.



Lately, we often hear about billionaires. What is a billionaire? A billionaire is someone who has at least a billion dollars. Well, what does that mean? A billion is a thousand millions. It means that if you stacked their money in piles of $1000, there would be a million piles. It's an enormous number. It's very hard to put a billion into a perspective that the average person can easily understand. A billion seconds is about 31.7 years. It would take a person driving at 60 mph about 16,666,666.67 hours, or about 1,902.6 years to drive a billion miles. Traveling at 36,373 mph, the New Horizons spacecraft took 11.5 years to reach Pluto at a distance of about 3 billion miles. A billion square feet is equal to 22,956.8411 acres, or 35.87 square miles. Astronomically speaking, the planet Uranus is 1.784 billion miles away from the Sun. The age of the Universe is calculated to be 13.8 billion years. Thinking about how large a billion is is daunting, even for people who use it every day. Now try to imagine...



A trillion is a thousand billions, a million millions, or a billion thousands. It's a number so large that it is very difficult to comprehend, let alone try to put into perspective. “Trillions” is so large that the Earth is not big enough to contain an example large enough for us to see as individual pieces with an unaided eye, with the exception of grains of sand. It takes 31,709.79 years for a trillion seconds to pass. It would take 1,902,600 years to drive a trillion miles at 60 mph. A trillion years is 72.46 times longer than the amount of time that has passed since the Universe began.

Space scientists mostly use trillions to denote distances, but they disguise it in terms that are easier to grasp. Most notably, the light-year. A light-year is just under six trillion miles. The nearest star, Proxima Centauri, is about 25 trillion (25,000,000,000,000, or 2.5x10^13 in scientific notation), miles from Earth. To make things more comprehensible, the light-year is used. Proxima Centauri is 4.3 light-years away. It makes the math easier to use a smaller number. The Andromeda galaxy is 2.5 million light-years from us. You can see that it is easier to use the term light-year then it is to do the math, 2,500,000x6,000,000,000,000 miles. Remember, the numbers I use are approximations, and scientifically inaccurate. There aren't really that many zeros in the equation above, they are actually fours and twos and sevens and the like, and there are decimal places, too. That makes it even more reasonable to use a representation of a number, rather than the actual number when it's time to do the math.

Hopefully, this blog helps in the reader's understanding of the extremely large numbers that space scientists throw around seemingly so casually.