A while ago in an astrophysics class we were discussing the absolute and apparent magnitude scales for categorizing the brightness of the stars in the night sky. An interesting question came up with regards to the sensitivity of the Hubble Space Telescope; would Hubble be able to detect a match on the surface of the moon if it were an Earth distance away?
The Hubble Space Telescope can detect objects as faint as 31st magnitude , and for this to seem significant we have to discuss the magnitude system.
The Stellar Magnitude System
The first trace of such a magnitude system being used is around 130 BC by the Greek astronomer Hipparchus. He ranked the stars in order of their apparent brightness by naming the brighter ones “of the first magnitude” and the dimmest he could see “of the sixth magnitude”. This system was then picked up by Ptolemy around 140 AD to use with his own catalog of data and as astronomy became more and more popular the system was more generally used.
It was Galileo and his invention of the telescope that first revolutionised this cataloging system. Using his telescope, he discovered that there are many stars that are unseen to the naked eye. He therefore added further orders of magnitude to the scale and it became apparent that there was no dimmest magnitude.
In 1856, a British astronomer Norman Robert Pogson decided that this system needed to be organised and the magnitudes given formal values. He defined a 1st magnitude star as one that is around 100 times brighter than a 6th magnitude star. This created the logarithmic scale used today, with the star Vega being a reference point.
To calculate the apparent magnitude of an object:
where f is the flux of the object. (For more about flux read: Flux ¦ Cosmos ).
Bear in mind that the apparent magnitude is the brightness that we see here on Earth. The true brightness of the star will be different depending on how far away you are. Therefore a scale called the absolute magnitude scale was created which categorised the brightness of stars from a distance of 10 parsec away (10 parsec = 3.09 x 1017metres).
Match on the Moon
The question introduced in the astrophysics class was “Could the Hubble Space Telescope detect a match on the surface of the moon provided it had a luminosity L of 7 x 10-10erg/s?”
The relationship between flux and luminosity is:
where d is the distance between the moon and Earth (384,400km).
Plugging in values you obtain a value of f of 3.78×10^(-32) erg/s⋅cm².
Using the equation mentioned previously we can use this flux to calculate the apparent magnitude:
So how does this compare to the Hubble Space Telescope?
The HST can detect up to the 31st magnitude and remembering that the larger magnitudes are fainter this means that the magnitude of the match is within the detection range.
As both are around the same magnitude, the match on the moon is an excellent way of putting into perspective the staggering capabilities of our space technology.
The James Webb Space Telescope, the successor to the HST is said to be able to see “10 to 100 times fainter than Hubble can see” .