October 2017 Discover

OUT THERE

66 DISCOVERMAGAZINE.COM

CLOCKWISE FROM TOP LEFT: NASA/ESA/J. HESTER AND A.LOLL (ASU); NASA/JHUAPL/SWRI; ERNIE MASTROIANNI/DISCOVER; NASA/ESA/J. HESTER

AND A.LOLL (ASU)

optical density that he moved across

the field of view of his eyepiece. He

noted the point where a star would

disappear and could then determine

its brightness.

Around the same time, other

astronomers were developing the

concept of using magnitudes less than

1, but they did leave certain aspects

of the original system intact. For

example, Hipparchus had quantified

the general limiting magnitude of the

human eye as 6th magnitude, and that

rough estimate has endured.

DOING THE MATH

In 1856, another English astronomer,

Norman R. Pogson, realized

that astronomers considered a

1st-magnitude star about 100 times

brighter than a 6th-magnitude one.

He therefore suggested standardizing

that relationship. The ratio between

magnitudes thus became the fifth root

of 100, or 2.5118865, a number now

known as Pogson’s ratio.

Ever since, astronomers recognize

that a star of a certain magnitude is

2.5118865 times brighter than a star

one magnitude fainter. The rest of

us round off to 2.5, which is plenty

accurate. Pogson had defined a

logarithmic scale.

The scale was also convenient

because 19th-century researchers

studying vision thought the eye

sensed differences in brightness on a

logarithmic basis: Our eyes perceive

equal ratios of intensity as equal

intervals of brightness.

Today, we know the eye is not quite

a logarithmic detector. So a 5th-

magnitude star doesn’t appear to the

eye to be exactly halfway in brightness

between 4th- and 6th-magnitude stars.

Close, but not exactly.

Because a one-magnitude differ-

ence equals the fifth root of 100, a

difference of five magnitudes equals a

hundredfold difference in brightness.

To see a real-life example, step outside

one night this winter and find the

brightest nighttime star, Sirius, the

Dog Star, in the constellation Canis

THE CRAB SUPERNOVA OF 1054 –6.0

VENUS AT MAXIMUM BRIGHTNESS –4.9

THE ANDROMEDA GALAXY (M31) 3.4

PLUTO AT ITS BRIGHTEST 13.7