garyd said:
Homework Statement
A telescope with aperture 10 times the human eye could see stars down to magnitude?
Homework Equations
I was not given an equation with the question but I have found the following but I do not know if it is correct.
M=Log(2.51188)*(A2/A1)^2
The Attempt at a Solution
A1= aperture of human eye-7mm
A2= 10* 7 (10>human eye)
Log(2.51188)*(70/7)= 40 (to 2 s.f.)
I am finding the concept of stellar magnitudes difficult to grasp so any help would be appreciated.
Yeah, the magnitude system is pretty stupid and annoying
. You have the right concept for this question, just the wrong equation. Since you said you found magnitudes confusing, I'll try to explain:
What you actually measure with a detector (e.g. retina, photographic plate, CCD chip, or some other kind of sensor) is what astronomers call flux, F. The flux of a source is the amount of light energy arriving from that source per second, and per square centimetre of area at the observer. In other words, it's the power per unit area, measured in watts/metre
2.
Magnitude is basically a logarithmic scale for flux, because human vision tends to work logarithmically. I.e. what appear to be "steps in brightness" by the same amount to the human eye are actually increases in flux by factors of ~10. The only tricky part is that the scale is reversed (smaller magnitudes correspond to larger fluxes). The equation for the difference in apparent magnitude in terms of the flux ratio is
m1 - m2 = -2.5log10(F1/F2)
As you can see, you don't need to know the individual fluxes in order to find the magnitude difference. All you need to know is their
ratio. So what you have to figure out is the ratio of the flux seen by the eye to the flux seen by the telescope.
As you correctly stated, the flux scales with the square of the aperture diameter. This is because the flux increases linearly with the
collecting area of the aperture, and area depends on the square of the diameter. This makes sense. Flux multiplied by area gives you the total power detected. Increase the number of square metres, and you increase the power. You can get the flux ratio from the ratio of the squares of the aperture diameters, just as you were doing. Note: it would probably be better to use the letter D for aperture diameter, since A usually means area in this context.
EDIT: Another need to know (just assumed to be common knowledge) is that humans can see down to a visual magnitude of around 6, under ideal conditions (clear, dark skies and no light pollution). If the magnitude is any larger, the star is too faint to see.