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Astronomy with an online telescope

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Picture of Pauline Woolley

Pauline Woolley Post 1

15 Jan 2021, 12:27

star brightness diffennce


I am still trying to get my head around working out the difference in brightness between magnitudes.

The difference between a +2 star and a +3 is 2.5 times.  But how do we get to that answer?  The course content says that from a +1 to a +6 is 100 times.

Is each step between magnitudes always 2.5.

My maths isn't great but I will not let it put me off!

Thanks.  Really enjoying the course!

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Jonathan Berry Post 2 (unread) in reply to 1

16 Jan 2021, 17:22
Still grappling the topic myself, I shan't try to explain. However, this wiki link may shed some light (sorry) on the topic. 

Essentially it looks like the scale is r logarithmic so a step in either direction I THINK is 2.5 brighter / dimmer. +2.0 in either direction would be 6.31 times brighter or dimmer.

The first of the two links is the general wiki link, the second is a chart which may help the grasping of magnitude / relative brightness.

I'm new to this too so please take what I write with a Saturn sized pinch of salt :D

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Pauline Woolley Post 3 (unread) in reply to 2

16 Jan 2021, 18:19
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Alan Cayless Post 4 (unread) in reply to 1

17 Jan 2021, 12:25 Edited by the author on 17 Jan 2021, 12:25

Hi Pauline;

Thanks for asking about this.  The magnitude scale is devised so that a change of five magnitudes equates to a factor of 100 in brightess.   So as you have mentioned,  a magnitude +1 star is 100 times brighter than a magnitude +6 star.

The important thing is that this is a multiplication scale, rather than an addition scale (this is also referred to as a logarithmic scale).   Each step in magnitudes multiplies the brightness by a certain amount.

It turns out that a single step in magnitude (e.g. from +3 to +2) mutliplies the brightness by 2.5 (2.511 to be exact).   If you try multiplying by 2.511 five times you'll find you've multiplied by 100.


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Pauline Woolley Post 7 (unread) in reply to 4

18 Jan 2021, 17:28

Hi Alan,

Thanks for this.  That has helped! Loving the course!


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Venessa Alexander Post 12 (unread) in reply to 4

26 Jan 2021, 15:37

Hi Alan

I put down 2.51 in my quiz answer and is was marked as incorrect!  This is a great course, am really enjoying it, thanks for all the time everyone has put in to it

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Alan Cayless Post 13 (unread) in reply to 12

27 Jan 2021, 16:14 Edited by the author on 27 Jan 2021, 16:17

Hi Venessa;

Thanks for reporting this - it should have accepted your answer.  It seems the quiz is a bit picky and has been programmed only to recognise the rounded value 2.5. 

I've changed it to accept the more accurate value.


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Paul Mckay Post 5 (unread) in reply to 1

17 Jan 2021, 15:43 Edited by the author on 17 Jan 2021, 16:12

Magnitude/brightness relationship


I really struggled with the magnitude to brightness (luminosity) relationship. The definition to use is that a change of brightness (dL) of 100 times is a magnitude difference (dm) of 5. Note the use of the words 'times' for brightness and 'difference' for magnitude. These are important mathematically.

Stars with brigtness ratio of 100 have a mag. difference of 5. For a unit change in mag. the change in dL is the fifth root of 100, that is 1001/5 = 2.51 approx. For a mag. change of 2, brightness change is 1002/5 = 6.31. On your calculator, use the xn button. Try it for various values of dm of 3, 4, 5 etc.

The general expression for a brightness change dL for a mag. change of dm is therefore:

dL = 100dm/5

The general expression for a magnitude difference, dm, for a change of brightness, dL, is found by taking logs of both sides.

logdL = (dm/5) x log100, rearrange for dm

dm = 2.5 x logdL

These expressions allow you calculate changes in one parameter given the other, even if they are not whole numbers. They are what astronomers use! This is of course beyond what is needed for the Open Learn course or GCSE Astronomy but it explains the maths behind the statements.

Hope this has not confused you too much but it does take a bit of thinking about.


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Pauline Woolley Post 8 (unread) in reply to 5

18 Jan 2021, 17:31


Yes well beyond my 30 year old GCSE but thanks for your reply.

Note the use of the words 'times' for brightness and 'difference' for magnitude. These are important mathematically.

However, your sentence here really helps to clear up these points so big thanks for that.


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James Fleeman Post 6 (unread) in reply to 1

17 Jan 2021, 17:33

I couldn't do this either, and neither could most of my family.

I also couldn't understand the answer given!

My brother eventually cracked it for me:

Mag 2.5 = 10 to power of 1

Mag 5 = 10 to power of 2

Its the only bit of 'advanced' maths so don't let it put you off. Its a wonderful course!

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Pauline Woolley Post 9 (unread) in reply to 6

18 Jan 2021, 17:32

Hi James,

I love the fact you have got your family involved!  Thanks for the 'advanced' warning.  I am loving the course!


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Dennis Ramirez Post 10 (unread) in reply to 1

19 Jan 2021, 08:48

Hi I hope I will be able to help with this problem, I am going to give you a simple way of geting what you are looking for, the mathematics here are simple but is a result of more complex math, without seen them.

Step 1. take the difference of the brigthness of the two starsas an example say that star A is mag 6 and star B is mag 2.5 then the diffrence is 6-2.5=3.5

Step 2 multiply this number by 0.2 in our case 3.5x0.2 = 0.7

step 3 Now rise 100 to the power of the last result ie 100^0.7=25.12 ie stars B is aproximately 25 times brigther.

in your example the diference is 2.5 so we multiply by 0.2, 2.5x0.2=0.5, we rise 100 to this power ie 100^0.5=10 as in the notes of activity 2chapter 3

last example let say we have a satr of magnitude 6 and another magnitude 1

so we take the difference 6-1=5 the we multiplu by 0.2 ie 5X0.2=1

then we raise 100 to the power of 1 ie 100^1=100 as in the notes 

it is very simple you only need a decent calculator and do not let the math 

diminish your enthusiasm math is only another language that need  practice

that is all. I hope this will help you.


Picture of Pauline Woolley

Pauline Woolley Post 11 (unread) in reply to 10

22 Jan 2021, 14:31

Hi Dennis,

Many thanks for for your reply.  I find maths difficult but I am not letting it diminish my enthusiasm like you say.  It's a language I have not spoken for many decades but even though I don't grasp it entirely I see it's necessity and it's beauty!



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