# The magnitude of Earth from Moon

#### Numeriprimi

Hello,
I was wondering that I'm a astronaut on Moon and I thought about a one question...
If I look at the Earth (in "full moon") from the Moon, what magnitude will have the Earth? Ok, I know some typical values that the magnitude of Moon from Earth is -13 mag and the magnitude of Sun from Earth is -25 mag. However, the magnitude of Earth from Moon I don't know. Can I determine it from this values? The Pogson's equation is best for it, but how...?

Thank you very much and sorry for my bad English.

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#### snorkack

Full Earth, or full Moon and therefore new Earth?
Full Earth is 43 times brighter than full Moon. No, you cannot derive that from the magnitudes of Moon and Sun. But now you can apply Pogson´s equation.

#### Numeriprimi

Hmm, however, how do you know that the full Earth is 43 times brigter than full Moon?

#### Numeriprimi

No. One more question. Can I determine the magnitude of Earth on Moon, if I will be know magnitude of ashen lights by Moon and Earth?

#### Bandersnatch

Hmm, however, how do you know that the full Earth is 43 times brigter than full Moon?
Using the difference in radii, you need to calculate how much larger the area of the Earth is than that of the Moon as seen from the same distance, and multiply the result by the difference in reflectivity(albedo). All values can be found on wikipedia.

#### snorkack

No. One more question. Can I determine the magnitude of Earth on Moon, if I will be know magnitude of ashen lights by Moon and Earth?
Yes.

#### Numeriprimi

Yes, the first soulution I know. I can say that: (r_2/r_1)^2 * A_1/A_2 = I_1/I_2 ... And than I can numericated the magnitude of Earth from Moon by Pogson's equation.
However, what with the ashen lights? How can I numericate the magnitude of Earth on Moon by this? I really don't know.

#### snorkack

Yes, the first soulution I know. I can say that: (r_2/r_1)^2 * A_1/A_2 = I_1/I_2 ... And than I can numericated the magnitude of Earth from Moon by Pogson's equation.
However, what with the ashen lights? How can I numericate the magnitude of Earth on Moon by this? I really don't know.
Say that you measure the magnitude of full Moon as -12,74, and also measure the magnitude of ashen light as -2,74. Either way, you are observing from the same distance light reflected by Moon straight back towards the source of light. If ashen light, lit by full Earth, is 10,0 magnitudes dimmer than full Moon, lit by Sun, you can conclude that full Earth also is 10,0 magnitudes dimmer than Sun. So measuring magnitude of Sun as -26,8, you can deduce the magnitude of full Earth is -16,8.

As for the solution with albedo: you need to measure that albedo.

#### Numeriprimi

Ok, I understand. Thank you very much! Hmm...

And if I will know the magnitude of full Earth and full Moon and the ratio between radius of Earth and radius of Moon, I can determine the radius betwenn albedo of Earth and albedo of Moon, yeah?

2,5 log ((r_E/r_M)^2 * A_E/A_M) = 2,5 log I_E/I_M = m_M - m_E
... so, the albedo ratio is 3, right?

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#### Numeriprimi

one more question... is also any way, how to determine the ashen light of Earth? no light of buildings etc., only the ashen light like on Moon.

#### snorkack

one more question... is also any way, how to determine the ashen light of Earth? no light of buildings etc., only the ashen light like on Moon.
What do you mean as ashen light?
Moonlit ground?

#### Numeriprimi

I'm standing on Earth and watching on the Moon (-13 mag) - I'm seeing the ashen light of Moon (-3 mag).

opposite situation:
I'm standing on Moon and watching on the Earth (-16 mag, no lighting by people) - I'm seeing the ashen light of Earth. How can I determine the magnitude of ashen light by Earth? (for example, in the situation just before when the Earth comes to ,,new moon" and the Moon is on full moon)

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#### snorkack

I'm standing on Earth and watching on the Moon (-13 mag) - I'm seeing the ashen light of Moon (-3 mag).

opposite situation:
I'm standing on Moon and watching on the Earth (-16 mag, no lighting by people) - I'm seeing the ashen light of Earth. How can I determine the magnitude of ashen light by Earth?
It is equal to the magnitude of ashen light of Moon.

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#### Numeriprimi

Yeah, I calculated it :-) Thank you very much, it is everything.