If two lights light up together, why can't their "magnitudes" be added together?
The readings are first converted back to the amount of light recovered, then added together to give the total amount of light a magnitude.
Turn on one more light and the total amount of light will increase. But magnitude is not a direct count of "amounts of light": the smaller the number, the brighter it is usually, and a difference of 5 magnitude corresponds to 100 times the amount of light. First compare the two sets of stars and then combine them.
Guess first
Will two 2nd magnitude stars combined become a dimmer 4th magnitude star?
Show answer and explanation
No, the total amount of light increases — Magnitudes cannot be added directly.
Then connect experience and science
Single light intensity
The amount of light received by a 0-magnitude star is 1.
F=10^(−0.4m)
Add up the stars
Each star in the same group has the same magnitude, and the number is n.
F total=ΣnF
Return magnitude
The magnitude is undefined when the light source is zero, and 0 magnitude is not faked.
mtotal=−2.5log₁₀Ftotal
Brightness ratio and difference
Can be converted to each other.
Δm=2.5log₁₀(F bright/F dark)
Expand the calculation
Fᵢ = 10^(−0.4mᵢ) F总 = Σᵢ nᵢFᵢ m总 = −2.5 log₁₀(F总)
Convert the magnitude into the relative luminous flux at the same zero point, multiply the quantities, add them, and then convert them back to magnitude. Magnitudes cannot be added or averaged directly.
give it a try
First compare two identical stars, and then click on the three-star or star cluster example in the original book. Zero means there is no light source in this group.
No need to memorize symbols
- m
- Visual magnitude, the smaller the value, the brighter it is
- F
- Relative received light amount
- n
- Number of stars in the same group
Algorithm, accuracy and scope of application
Covers two-star/multi-star synthesis, brightness ratio and its inverse conversion used in all five examples in Chapter 56. Supports four groups of different magnitudes and quantities; does not calculate the true star radius, luminosity or distance.
my understanding check
What is the approximate difference in the amount of light received by a 0-magnitude star and a 5th-magnitude star?
100 times — Level 5 corresponds to 100 times the amount of light.
What is the amount of light when two equally bright stars come together?
Double — First add the light amount, then change it back to the magnitude.
If the star points drawn on the screen are larger, does it mean that the real star radius is larger?
No, just the brightness symbol — This diagram only represents the amount of light received and does not represent the size of the celestial body or the true response of the human eye.
What is added is light, not magnitude numbers; only by returning to the amount of light can we know how bright they are together.
Jean Meeus · Astronomical Algorithms, 2nd ed. · No. 56 chapter