Astronomy > Just how small are we? >

• Continues from Our Solar System.

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Thinking with really big numbers: The Light Year ∞

Thinking with these small values becomes too difficult when we peer out towards very distant things. We already learned two good measurements:

• One is the mean distance from ourselves on the Earth to our Sun. This is 1 AU.

• The other is the speed of light.

Walking is too slow for astronomy, and even the AU isn’t a big enough value, so astronomers began to use the fastest thing they could measure, which is light.

A light year, abbreviated ly, is the distance light travels in one year.

Photons travel very fast. The speed of light in a vacuum is exactly 299,792,458 m/s (1,079,252,848.8 km/h).

Spoiler

More technically, a light year is defined as the distance that a photon would travel, in free space and infinitely far away from any gravitational or magnetic fields, in one Julian year (365.25 days of 86400 seconds each).

Light can slow down when passing near or through different things – think of a prism. That’s why the measurement of the speed of light is understood to be its speed in a perfect vacuum and infinitely far away from anything that might interfere.

The speed of light is so well known that the length of the “metre” is defined using its terms.

So how long is one light year?

	299,792,458 m/s	The speed of light.
x	86,400 s	The number of seconds in a day.
x	365.25	The number of days in a Julian year.
=	9,460,730,472,580,800 m	The length of one light year (m)
/	1000	The number of metres in a kilometre
=	9,460,730,472,580.8 km	The length of one light year (km)

That’s a pretty big number to work with. Using it, Proxima Centauri is only 4.365 ± 0.007 ly away.

1 ly = 9,460,528,404,879 km
1 ly = 63,239.7263 AU

Around the Earth ∞

So if we retrofitted our electric hovercar with a new science fiction-powered light-speed engine, how fast would it really go?

	299,792.458 km/s	The speed of light.
/	40,075.16 km	Circumference of the earth at the equator
=	7.48	The number of times around the earth we could go in just one second (at light speed)

That’s right. Our old hover-car can now go around the earth almost seven and a half times in just one second!

To the Sun ∞

Even at such high speeds, light will take time to get from one place to the next. How long would it take us to drive to the Sun?

	149,600,600 km	The distance from the Earth to the Sun (1 AU)
/	299,792.458 km/s	The speed of light (km/s)
=	499.01 s	The time it would take to drive from the Earth to the Sun (at light speed) – seconds
/	60	The number of seconds in a minute
=	8.31 min	The time it would take to drive from the Earth to the Sun (at light speed) – minutes

So even though we travel at over a million kilometres an hour it would take us over eight minutes to get to the Sun. This means that it takes the Sun’s light eight minutes to get to us. During daylight hours, of course. Not that the Sun turns off at night.. it still shines on our backs as we sleep.

Through our Solar System ∞

Once we begin to see the vast distance between interesting things, we begin to notice just how long it takes for light to get from one place to the next. Driving your electric hovercar that can go as fast as the speed of light, and barring traffic, it takes over five hours to commute from your house on the Earth to Pluto. I’d hate to work out there. Well, maybe if it comes with that car.

	5,909,200,000 km	The distance from the Sun to Pluto (39.5 AU)
/	1,079,252,848.8 kmph	The speed of light
=	5.475 hours	The time it takes for light to get from the Sun to Pluto

Spoiler

There is a huge asteroid belt between Mars and Jupiter, which would make it hard to drive in a straight line to Pluto. In that belt are boulders as big as a small country. Pioneer-10 passed through it completely by accident.

Our solar system isn’t the only interesting thing around. When we we look up at the sky at night we can sometimes glimpse some of our planets, but we can much more easily see other stars. We could see so many that we began to name them and group them into various constellations. Even the most ancient people studied the stars with great curiosity.

Standing on the Earth and looking up at the nighttime sky, we can see the stars appear to rotate over time thoughout the year. The pattern of stars appears almost fixed, like a black sphere overhead which has many pinpricks that let light shine through it. The number of stars which appears in our sky to the naked eye will vary from place to place and from time to time. The conditions of the atmosphere influence visibility, as do issues such as light pollution from city lights.

Spoiler

Some places have laws on light pollution and restrict light sources to certain directions (down, duh) or types. A side-note is that certain light sources only emit on a certain spectrum and can be easily filtered out for improved stargazing.

The nearest interesting thing: Proxima Centauri ∞

Ignoring our as yet unseen and disputed sister star “Nemesis“, the Sun’s nearest known stellar neighbour is the red dwarf star Proxima Centauri, of the Alpha Centauri star system. It is approximately 41,295,206,487,296.8 kilometres (km) away. That’s a long way away.

We could start saying things like 41.30 × 10¹² km, but even then the numbers are still very difficult to work with.

One we look past our own solar system, objects become so distant that measuring with things like kilometres doesn’t work very well. We could work in terms of Astronomical Units (AU), but even they are far too small.

Once we start looking at a larger picture, we need to begin to think in much faster modes of travel. This is where the light year comes in handy.

In our science fiction-powered light-speed hovercar, how long would it take us to get to Alpha Centauri from the Sun?

Alpha Centauri is 4.365 ± 0.007 ly away. Travelling at the speed of light, the fastest thing we know about, it would still take us well over four years!

Of course it’s going to take a while, it’s 41,296,088,512,815.2 km away. That’s 40 million million kilometres! You had better use the washroom before we start the trip. There isn’t much in-between our Solar system and Proxima Centauri, and there sure isn’t a truck stop.

An aside: Fuzzy math ∞

These concepts of speed and distance being used are still a bit fuzzy, scientifically speaking. Some concepts are quite a bit more hairy than others.

We do understand the speed of light pretty darn well, except that it changes for various reasons. When you put a spoon in a glass of water, you can see how it appears to be “bent” when you compare the part that’s outside of the glass to the part that’s in. This kind of stuff, and much stranger stuff still, can happen out in space.

The real problem is that we don’t fully understand distances very well. Well yes we know that the Earth’s orbit is not a circle so it’s not exactly 1 AU, but that’s not a very big deal. Sure we understand that the mass of the sun is decreasing so we’re slowly pulling away from it, but that’s not the problem. The problem is this gravity stuff. The issue can’t be easily summarized, but let’s leave it with “it’s being worked on”.

• Physical constant

  • Beginning with Paul Dirac in 1937, some scientists have speculated that physical constants may actually decrease in proportion to the age of the universe.
  • Scientific experiments have not yet pinpointed any definite evidence that this is the case, although they have placed upper bounds on the maximum possible relative change per year at very small amounts. (roughly 10^-5 per year for the fine structure constant alpha and and 10^-11 for the Gravitational constant G).