Classification by luminosity (A-level only): The Hipparcos scale.

The idea

The Hipparcos scale is the historical magnitude system used to classify how bright stars appear from Earth. Hipparchus ranked naked-eye stars into six classes, with first magnitude being the brightest and sixth the faintest. The scale is inverted: a smaller magnitude number means a brighter object. It is logarithmic, so a difference of five magnitudes corresponds to a brightness ratio of exactly 100, meaning each step is about 2.512 times in brightness. Apparent magnitude m describes observed brightness, while absolute magnitude M describes intrinsic luminosity at a standard distance of 10 parsecs. The distance modulus m − M = 5 log₁₀(d/10) links them. Astronomers still use this scale, extending it to negative magnitudes for very bright objects such as Sirius and to values above 6 for objects seen with telescopes.

What earns the marks

• State that the Hipparcos scale is an inverted scale: smaller magnitude values correspond to brighter objects, so magnitude 1 is brighter than magnitude 6.
• Explain that the scale is logarithmic, with a difference of 5 magnitudes corresponding to a brightness ratio of 100, so one magnitude corresponds to a brightness ratio of 100^(1/5) ≈ 2.512.
• Distinguish between apparent magnitude, which measures observed brightness from Earth, and absolute magnitude, which measures intrinsic luminosity at a standard distance of 10 parsecs.
• Use the distance modulus relationship m − M = 5 log₁₀(d/10) to connect apparent magnitude, absolute magnitude and distance in parsecs.
• Recognise that the scale extends beyond the original six classes, including negative magnitudes for very bright objects and values greater than 6 for faint objects observed with telescopes.

Common mistakes and how to put them right

• Treating a larger magnitude number as brighter.

  Put it right by remembering the scale is inverted, so a smaller number means a brighter object.

• Assuming the scale is linear, so that a difference of 2 magnitudes means twice the brightness.

  Put it right by applying the logarithmic relationship where 5 magnitudes correspond to a factor of 100 in brightness.

• Confusing apparent magnitude with absolute magnitude.

  Put it right by defining apparent magnitude as observed brightness and absolute magnitude as brightness at a standard distance of 10 parsecs.

Exam tips

• When comparing brightness, convert magnitude differences into brightness ratios using the factor 100 for every 5 magnitudes, or 2.512 per single magnitude.
• Always state whether a magnitude value is apparent or absolute, and give the standard distance of 10 parsecs when defining absolute magnitude.
• Show the distance modulus calculation clearly, substituting values into m − M = 5 log₁₀(d/10) and solving for the required quantity.