Why is Mars so easily visible to the naked eye?

[Solon]

I have been trying to figure out why I can see Mars, by eye, even when it is very close to a bright, almost full Moon. Firstly, Mars at its closest to Earth only has an angular diameter of less than 1/2 an arc minute, while the accepted limit of resolution of the eye is 1 minute. That equates, by my recconing, to seeing a basketball at about 2,000 meters.
With a self luminous body such as a star, I am told it is due to luminosity, but Mars is only reflecting the Suns light. The apparent diameter of Mars, using Celestia, is over 4 minutes, which explains why it is so easily visible, but why is it so apparently large?
Mars has an albedo not much greater than the Moon, averaging about .15, and I have used a Lambertian model of reflection. Total solar irradiance at Mars averages less than half of Earth (and the Moon) value.
Where I have run into difficulties, and can find nobody so far to calculate, is how many photons per second would reach an observer on Earth, and how many per second are required for them to consciously register. I have read that the eye may have single photon sensitivity, but between 150 and 500,000 photon/sec are needed for us to become aware of.
Just wondering if I am missing something obvious here, or if we really don't understand light, vision and perception well enough to be able to fully explain the process?

 

[russ_watters]

Welcome to PF!

I have been trying to figure out why I can see Mars, by eye, even when it is very close to a bright, almost full Moon. Firstly, Mars at its closest to Earth only has an angular diameter of less than 1/2 an arc minute, while the accepted limit of resolution of the eye is 1 minute.

"Resolution" is being able to tell two objects apart or being able to see the size of one object. It isn't required for viewing a point object, such as a planet or start. Only brightness matters in visibility.

but why is it so apparently large?

Point objects that are bright can appear large due to blooming or saturation. Basically, you're seeing extra glare and atmospheric refraction that isn't exactly along the line of sight of the planet, making for a larger apparent diameter.

 

[Solon]

Only brightness matters in visibility.

Well that's where I can't understand this model, as the tiny looking Sun seen from the surface of Mars surely is not lighting Mars to such a brightness that it can be seen so easily from Earth? I'd really like to see some figures, my results fall far short, in fact Mars would only be visible by eye out to about 300,000 miles. Or less.

Point objects that are bright can appear large due to blooming or saturation.

Fair enough, but Mars is by no means bright by my understanding, that's why I am here, cap in hand, wondering if anyone can provide an end-to-end explanation of the mechanisms, formulas and calculations required to quell the doubts I'm having. I've asked around, no satisfactory responses so far, maybe all the really smart folk hang out on PF?

 

[Drakkith]

Well that's where I can't understand this model, as the tiny looking Sun seen from the surface of Mars surely is not lighting Mars to such a brightness that it can be seen so easily from Earth? I'd really like to see some figures, my results fall far short, in fact Mars would only be visible by eye out to about 300,000 miles. Or less.

It would help if we knew how you were calculating this figure so we can correct where you've gone wrong.

 

[davenn]

Well that's where I can't understand this model, as the tiny looking Sun seen from the surface of Mars surely is not lighting Mars to such a brightness that it can be seen so easily from Earth? I'd really like to see some figures, my results fall far short, in fact Mars would only be visible by eye out to about 300,000 miles. Or less.

how on Earth did you come up with that figure ??

do you realize how big Mars is, say compared to the Moon ?
Do you realize the Moon is ~ 240,000 miles distant from the Earth ?
then consider how huge and bright Mars would be in our sky if it was in the same position as the moon

Dave

 

[davenn]

it would help if we knew how you were calculating this figure so we can correct where you've gone wrong.

snap :)

d

 

[russ_watters]

To do the calc, I'd start with the moon's magnitude, then ratio the square of the earth-sun to mars-sun distances and earth-moon and earth-mars distances.

Edit: using that method with the numbers pulled out of the air, I get a mag of -1.5, which sounds pretty reasonable. So let's see how your calc compares.

 

[Solon]

To do the calc, I'd start with the moon's magnitude,

The magnitude as seen from Earth I assume. Than got me to wondering about the magnitude from the ISS say, where there is much less atmosphere to affect the Moonlight. All the images I can find however show the Moon from the ISS in a Moonrise or Moonset position, so looking through a dense column of atmosphere, with a line of sight to the Moon that dips down pretty deep into the atmosphere. I'd like to know how the Moon appears in a mid-day position, looking perpendicular to Earth surface, but can not find such an image. Or an image of Mars at all from the ISS, too bad they don't do any astro-photography from the ISS when it is such a good platform.
The Solar-Solspec experiment has been up and running on the ISS for quite some time now, but it does not seem capable of doing analysis of the Moon, which I think would be interesting seeing as it has a 1 nm resolution. What sunlight wavelengths are absorbed, or created through solar UV emissions? Also, I was hoping there might be a video of the Moon from the ISS from one of the colour cameras on the Canadarm2, but again don't see anything. Would the Moon look the same from there as on a video taken from Earth?
I did find an interesting page about the sky at night being blue, not black, which seems to indicate a Moonlight spectrum the same as Sunlight. So I learned something today, if not the answers I'm looking for.
The Digital Blue Sky at Night(PDF)
http://www.osa-opn.org/opn/media/Images/PDFs/9357_19075_97281.pdf?ext=.pdf
This is the best image of the Moon from the ISS that I can find, but it seems to be a crop of one of the larger images that are taken close to Moonrise or Moonset, with the Earth just out of shot.
http://i.space.com/images/i/000/005/980/i02/moon-watching-night-100916-02.jpg?1294154541
from:
http://www.space.com/55-Earth's-moon-formation-composition-and-orbit.html

 

[Drakkith]

Except for being a tiny bit brighter and not having to deal with blurring from the atmosphere, it doesn't look any different from the ISS than it does from the surface of the Earth. Of course if you get really really in depth you could measure the intensity of each part of the spectrum and you'd see a very small difference thanks to atmospheric absorption and scattering, but this is far too little to "see" normally.