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THE NUMBERS: THE MATHEMATICS OF BRIGHTNESS

      The 1st magnitude stars are about 100 times brighter than the 6th magnitude stars. In particular, the 1st magnitude stars are about 2.512 times brighter than the 2nd magnitude stars, which are about 2.512 times brighter than the 3rd magnitude stars, and so on. (At the 6th magnitude, you get up into some big numbers: 1st magnitude stars are about 100 times brighter.) You mathematicians out there recognize this as a geometric progression. Each magnitude is the 5th root of 100 (meaning that when you multiply a number by itself four times – for example,

– the result is 100). If you doubt my word and do this calculation on your own, you get a slightly different answer because I left off some decimal places.

      Thus, you can calculate how faint a star is – compared to some other star – from its magnitude. If two stars are 5 magnitudes apart (such as the 1st magnitude star and the 6th magnitude star), they differ by a factor of 2.512⁵ (2.512 to the fifth power), and a good pocket calculator shows you that one star is 100 times brighter. If two stars are 6 magnitudes apart, one is about 250 times brighter than the other. And if you want to compare, say, a 1st magnitude star with an 11th magnitude star, you compute a 2.512¹⁰ difference in brightness, meaning a factor of 100², or 10,000.

      The faintest object visible with the Hubble Space Telescope is about 25 magnitudes fainter than the faintest star you can see with the naked eye (assuming normal vision and viewing skills – some experts and a certain number of liars and braggarts say that they can see 7th magnitude stars). Speaking of dim stars, 25 magnitudes are five times 5 magnitudes, which corresponds to a brightness difference of a factor of 100⁵. So the Hubble can see

, or 10 billion times fainter than the human eye. Astronomers expect nothing less from a billion-dollar telescope. At least it didn’t cost $10 billion.

      You can get a good telescope for well under $1,000, and you can view the billion-dollar Hubble’s best photos on the Internet for free at hubblesite.org.

Looking back on light-years

      The distances to the stars and other objects beyond the planets of our solar system are measured in light-years. As a measurement of actual length, a light-year is about 5.9 trillion miles long.

      People confuse a light-year with a length of time because the term contains the word year. But a light-year is really a distance measurement – the length that light travels, zipping through space at 186,000 miles per second, over the course of a year.

      When you view an object in space, you see it as it appeared when the light left the object. Consider these examples:

      ❯❯ When astronomers spot an explosion on the Sun, we don’t see it in real time; the light from the explosion takes about 8 minutes to get to Earth.

      ❯❯ The nearest star beyond the Sun, Proxima Centauri, is about 4 light-years away. Astronomers can’t see Proxima as it is now – only as it was four years ago.

      ❯❯ Look up at the Andromeda Galaxy, the most distant object that you can readily see with the unaided eye, on a clear, dark night in the fall. The light your eye receives left that galaxy about 2.5 million years ago. If there was a big change in Andromeda tomorrow, we wouldn’t know that it happened for more than 2 million years. (See Chapter 12 for hints on viewing the Andromeda Galaxy and other prominent galaxies.)

      Here’s the bottom line:

      ❯❯ When you look out into space, you’re looking back in time.

      ❯❯ Astronomers don’t have a way to know exactly what an object out in space looks like right now.

      When you look at some big, bright stars in a faraway galaxy, you must entertain the possibility that those particular stars don’t even exist anymore. As I explain in Chapter 11, some massive stars live for only 10 million or 20 million years. If you see them in a galaxy that is 50 million light-years away, you’re looking at lame duck stars. They aren’t shining in that galaxy anymore; they’re dead.

      If astronomers send a flash of light toward one of the most distant galaxies found with Hubble and other major telescopes, the light would take billions of years to arrive. Astronomers, however, calculate that the Sun will swell up and destroy all life on Earth a mere 5 billion or 6 billion years from now, so the light would be a futile advertisement of our civilization’s existence, a flash in the celestial pan.

      HEY, YOU! NO, NO, I MEAN AU

      Earth is about 93 million miles from the Sun, or 1 astronomical unit (AU). The distances between objects in the solar system are usually given in AU. Its plural is also AU. (Don’t confuse AU with “Hey, you!”)

      In public announcements, press releases, and popular books, astronomers state how far the stars and galaxies that they study are “from Earth.” But among themselves and in technical journals, they always give the distances from the Sun, the center of our solar system. This discrepancy rarely matters because astronomers can’t measure the distances of the stars precisely enough for 1 AU more or less to make a difference, but they do it this way for consistency.

Keep on moving: Figuring the positions of the stars

      Astronomers used to call stars “fixed stars,” to distinguish them from the wandering planets. But in fact, stars are in constant motion as well, both real and apparent. The whole sky rotates overhead because Earth is turning. The stars rise and set, like the Sun and the Moon, but they stay in formation. The stars that make up the Great Bear don’t swing over to the Little Dog or Aquarius, the Water Bearer. Different constellations rise at different times and on different dates, as seen from different places around the globe.

      Actually, the stars in Ursa Major (and every other constellation) do move with respect to one another – and at breathtaking speeds, measured in hundreds of miles per second. But those stars are so far away that scientists need precise measurements over considerable intervals of time to detect their motions across the sky. So 20,000 years from now, the stars in Ursa Major will form a different pattern in the sky. (Maybe they will even look like a Great Bear.)

      In the meantime, astronomers have measured the positions of millions of stars, and many of them are tabulated in catalogs and marked on star maps. The positions are listed in a system called right ascension and declination – known to all astronomers, amateur and pro, as RA and Dec:

      ❯❯ The RA is the position of a star measured in the east–west direction on the sky (like longitude, the position of a place on Earth measured east or west of the prime meridian at Greenwich, England).

      ❯❯ The Dec is the position of the star measured in the north–south direction, like the latitude of a city, which is measured north or south of the equator.

      Astronomers usually list RA in units of hours, minutes, and seconds, like time. We list Dec in degrees, minutes, and seconds of arc. Ninety degrees make up a right angle, 60 minutes of arc make up a degree, and 60 seconds of arc equal a minute of arc. A minute or second of arc is also often called an “arc minute” or an “arc second,” respectively.

      DIGGING DEEPER INTO RA AND DEC

      A star at RA 2h00m00s is 2 hours east of a star at RA 0h00m00s, regardless of their declinations. RA increases from west to east, starting from RA 0h00m00s, which corresponds to a line in the sky (actually half a circle, centered on the center of Earth) from the North Celestial Pole to the South Celestial Pole. The first star may be at Dec 30° North, and the second star may be at Dec 15° 25’12” South, but they’re still 2 hours apart in the east–west direction (and 45° 25’12” apart in the north–south direction). The North and South Celestial Poles are the points in the sky – due north and due south – around which the whole sky seems to turn, with the stars all rising and setting.

      Note the following details about the units of RA and Dec:

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