The magnitude of Earth from Moon

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Discussion Overview

The discussion revolves around determining the magnitude of Earth as viewed from the Moon, particularly during a full Earth phase. Participants explore the relationship between the magnitudes of Earth, Moon, and Sun, and the application of Pogson's equation in this context. The conversation includes considerations of albedo and ashen light, as well as the mathematical relationships involved in these calculations.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested, Mathematical reasoning

Main Points Raised

  • One participant questions how to determine the magnitude of Earth from the Moon using known values for the Moon and Sun.
  • Another participant states that the full Earth is 43 times brighter than the full Moon, but this cannot be derived solely from the magnitudes of the Moon and Sun.
  • Several participants discuss the use of Pogson's equation and the need to calculate the area and reflectivity differences between Earth and Moon to determine the magnitude.
  • There is a mention of measuring the magnitude of ashen light from both the Moon and Earth, with some suggesting that knowing these values could aid in determining the magnitude of Earth from the Moon.
  • Participants propose mathematical relationships involving ratios of radii and albedo to derive the magnitude of Earth.
  • One participant seeks clarification on how to determine the ashen light of Earth, similar to the ashen light observed on the Moon.
  • Another participant asserts that the magnitude of ashen light from Earth is equal to that of the Moon.

Areas of Agreement / Disagreement

The discussion contains multiple competing views and remains unresolved regarding the exact methods and calculations for determining the magnitude of Earth from the Moon. Participants express uncertainty about the implications of ashen light and the necessary measurements.

Contextual Notes

Participants reference various assumptions, such as the reflectivity (albedo) of Earth and Moon, and the need for specific measurements to apply Pogson's equation effectively. There are also unresolved mathematical steps related to the calculations discussed.

Numeriprimi
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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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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.
 
Hmm, however, how do you know that the full Earth is 43 times brigter than full Moon?
 
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?
 
Numeriprimi said:
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.
 
Numeriprimi said:
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.
 
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.
 
Numeriprimi said:
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.
 
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?
 
Last edited:
  • #10
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.
 
  • #11
Numeriprimi said:
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?
 
  • #12
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)
 
Last edited:
  • #13
Numeriprimi said:
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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  • #14
Yeah, I calculated it :-) Thank you very much, it is everything.
 

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