I dont understand magnitudes and intensity ratios.?

Question

If one star is 40 times brighter than another star, how magnitude brighter is it?

If two stars differ by 7 magnitudes, what is their intensity ratio?

Answer 1

Hi. Try this link: http://www.noao.edu/outreach/nop/nophigh/steve6.html

Answer 2

Each step in stellar magnitude (..either up or down) represents a magnitude change of 2.512. And remember that the smaller the magnitude number the brighter will be the star (..a magnitude 3 star is less bright than a magnitude minus 4 star) For example if one star has a magnitude of 6 and a second star is three times brighter, then the second star's magnitude would be 1.536

...2.512 x 3 = 7.536
...difference between 7.536 and 6 = 1.536

Answer 3

The magnitude of a mathematical object is its size: a property by which it can be larger or smaller than other objects of the same kind; in technical terms, an ordering of the class of objects to which it belongs.

The Greeks distinguished between several types of magnitude, including:

(positive) fractions
line segments (ordered by length)
Plane figures (ordered by area)
Solids (ordered by volume)
Angles (ordered by angular magnitude)
They had proven that the first two could not be the same, or even isomorphic systems of magnitude. They did not consider negative magnitudes to be meaningful, and magnitude is still chiefly used in contexts in which zero is either the lowest size or less than all possible sizes.

Contents [hide]
1 Real numbers
2 Complex numbers
3 Euclidean vectors
4 General vector spaces
5 Practical math



[edit]
Real numbers
The magnitude of a real number is usually called the absolute value or modulus. It is written | x |, and is defined by:

| x | = x, if x ≥ 0
| x | = -x, if x < 0
This gives the number's distance from zero on the real number line. For example, the modulus of -5 is 5.

...

[edit]
Complex numbers
Similarly, the magnitude of a complex number, called the modulus, gives the distance from zero in the Argand diagram. The formula for the modulus is the same as that for Pythagoras' theorem.


where are the Real part and Imaginary part of z. For instance, the modulus of −3 + 4i is 5.

[edit]
Euclidean vectors
The magnitude of a vector x of real numbers in a Euclidean n-space is most often the Euclidean norm, derived from Euclidean distance: the square root of the dot product of the vector with itself:


where x = [x1, x2, ..., xn]. The notation |x| is also used for the norm. For instance, the magnitude of [4, 5, 6] is √(42 + 52 + 62) = √77 or about 8.775.

[edit]
General vector spaces
A concept of magnitude can be applied to a vector space in general. This is then called a normed vector space. The function that maps objects to their magnitudes is called a norm.

[edit]
Practical math
A magnitude is never negative. When comparing magnitudes, it is often helpful to use a logarithmic scale. Real-world examples include the loudness of a sound (decibel), the brightness of a star, or the Richter scale of earthquake intensity.

To put it another way, often it is not meaningful to simply add and subtract magnitudes.

Retrieved from "http://en.wikipedia.org/wiki/Magnitude_%28mathematics%29"
Category: Elementary mathematics

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hope this helps

Answer 4

The easiest equation is:

Magnitude = log(Intensity) / .4

So if star A is 40 times brighter than star B, the magnitude difference is

log(40) / .4 = 1.602 / .4 = 4.0051 magnitudes

Answer 5

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