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Guru
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Bright Earth Challenge

10/24/2006 1:30 PM

Roger's interesting post on the inverse square law made me remember this 'paradox'.

Venus and Earth are about the same size, with Earth about 40% farther from the Sun than Venus. Earth therefore catches about half as much of the Sun's energy than Venus, due to the inverse square law effect. Further, the reflectivity of Earth is much less than that of Venus, with her bright eight-eight's cloud cover.

Despite these facts, an astronaut in low Earth orbit will see Venus at her best visual brightness as much less bright than what an astronaut in low Venus orbit would see Mother Earth at her best visual brightness. How is this possible?

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Guru
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#1

Re: Bright Earth Challenge

10/24/2006 3:22 PM

I will take a wild stab at it (I always do, anyway). Okay, Jorrie. Might it have something to do with the viewing angle relative to the source of light? In other words, when an observer views Earth from Venus the brightest transition would place the observer near Venus in between the Sun and Earth. So, the phase of the Earth is full.

When the observer is near Earth the brightest transition for Venus is still less than full, so only a portion of the planet's surface is illuminated and reflecting light back at the observer.

Other than that I have to throw up a white flag, which is highly reflective and readily seen. ;-)

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Guru
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#2
In reply to #1

Re: Bright Earth Challenge

10/24/2006 3:38 PM

Quote: "Okay, Jorrie. Might it have something to do with the viewing angle relative to the source of light?"

Maybe, maybe not - it depends a lot on the actual values, which, unfortunately, were not given...

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#5
In reply to #2

Re: Bright Earth Challenge

10/24/2006 7:23 PM

I know! ;-)

On further reflection I also wonder about the light scattering of Venus versus Earth. What I mean is that albedo is the ratio of the % of light reflected back to the observer. I assume that quanta is measured in a uniform way and I would suppose that the observer or "instrument" is inline between the planet or object and the point source of illumination. The albedo for Earth is about .35, whereas the albedo is about .7 for Venus.

That tells me that more photons are reflected back to the measuring instrument for Venus and less for Earth. Only two things could happen for the case of Earth. One, more photons are absorbed by the planet. This is more like bond albedo. Two, more photons are scattered at an angle that does not return to the observing instrument. Or a combination of those two effects.

As all three of us have mentioned, the viewing angle for Earth and Venus are not equal relative to the light source. Venus can only be observed obliquely to the Sun (at best), whereas the Earth can be in a position much closer to the way albedo is measured for an observer in orbit about Venus.

Now the kicker. If less light is scattered from Venus (more is reflected back to the light source), then Venus will not appear as bright when the light source is oblique to the observer as it would where you measure its albedo. In this configuration Venus would not be its brightest and since Earth appears to either scatter and/or absorb more photons it may be possible that oblique viewing of Earth would have a smaller dimming effect than it would for Venus.

That's my theory. ;-)

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#3

Re: Bright Earth Challenge

10/24/2006 3:57 PM

If I'm in earth's orbit looking at Venus, and Venus is on the same side of the sun as the earth, then I'm looking at the dark side of Venus. If I'm seeing Venus with a maximum surface illuminated, then Venus must be on the opposite side of the sun, and so the distance between us is sun-to-earth plus sun-to-venus.

If I'm in orbit around Venus and Venus is on the same side of the sun as the earth, then the earth is at maximum illumination, and the distance bewteen us is sun-to-earth minus sun-to-Venus.

The difference being that Venus is between earth and the sun.

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The Engineer
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#4

Re: Bright Earth Challenge

10/24/2006 4:18 PM

When viewed from Earth, Venus has phases, with "full venus" occuring when Earth and Venus are farthest from each other. We never actully see "full venus", since it's "full" phase occurs when it's behind the sun out of view. When the Earth and Venus are closest to each other, this corresponds with "new venus", when we see little or no light from venus. From Venus, the Earth is always "full Earth" because it's orbit is inside of the Earths.

Is that why? It doesn't really mention anything about "low orbit" in my answer so I'm not sure this is what you are looking for.

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Guru

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#6

Re: Bright Earth Challenge

10/24/2006 9:36 PM

Venus first:

So when is Venus at her best visual brightness? Without actually having run the numbers myself, I can only speak of the conditions under which Venus would appear brightest.

From our vantage point in low Earth orbit (or more simply, from Earth) Venus' best visual brightness occurs somewhere between the most distant point in her orbit where we can still see her just before she disappears behind ol' Sol, but where we also see, consequently, nearly her entire illuminated face - to some other point in her orbit where she is closer to Earth, but where we also see less of her illuminated face. We see a nearly-fully-illuminated-and-more-distant Venus on the one hand, and a closer-but-less-illuminated Venus on the other. When she is at her closest approach, of course, we don't see her at all (except in eclipse), neither do we see her at her very fullest illumination at the (most distant) point in her orbit which takes her directly behind the Sun.

Of the mathematical relations at our disposal we have, on the one hand the Inverse Square Law whose independent variable here is a function of Venus' relative orbital position, and some spherical-triggish-like function giving us the illuminated fraction of her face as a function of her relative orbital position on the other. From these relations (or perhaps better yet, from where the second derivative of the algebraic combination of these functions equals zero (indicating a maximum in the first derivative (ignoring closest and farthest approaches) which we pray is not a local maximum), we'd know roughly where in her orbit Venus appears to be brightest from our astronaut's point of view, and we'd have a mathematical relationship describing the apparent magnitude from any point in Venus' orbit relative to us.

Now, Earth:

From the perspective of our cosmonaut orbiting Venus, she sees Gaia at her brightest when the two planets are at their closest approach. Not only that, but our orbiting adventuress Miss Gredenko sees all of the illuminated portion of Earth's face - a perspective we simply couldn't enjoy from Earth simply because no one seems willing to get up off his dead ass long enough to figure out an easy way to see through 800,000 miles of thermonuclear fury. In Miss Gredenko's case I'd also run the numbers. At least in her case the math is a bit simpler. For one thing we can dispense with that business with the spherical trig.

That's how I might approach this problem, not knowing the actual numbers myself.

--Europium

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Guru

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#7
In reply to #6

Re: Bright Earth Challenge

10/24/2006 10:07 PM

Some hidden assumptions:

1) There is no sleight-of-hand going on here such as, "Well the glare of the Sun makes Venus appear so much dimmer." My guys both have highly-directional photometers, just so you know.

2) Mention of that low-Earth/Venus-orbit business makes me suspicious, too. Perhaps a pair of red herrings? Perhaps (more) sleight of hand?

3) I have root privileges and I know where you're parked.

--Euromuip

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Guru
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#8
In reply to #7

Re: Bright Earth Challenge

10/25/2006 2:58 AM

Quote from "Euromuip": "Some hidden assumptions:....

2) Mention of that low-Earth/Venus-orbit business makes me suspicious, too. Perhaps a pair of red herrings? Perhaps (more) sleight of hand?"

If it were Mars/Earth it would have been 'red herrings'. With Venus, orbit is required due to the filthy weather! Granted, on many places on Earth it is not required, but I kind'a like the symmetry. No "sleight of hand" - promise!

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Guru

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#9
In reply to #8

Re: Bright Earth Challenge

10/25/2006 3:23 AM

Now, Jorrie, this is definitely not a nice thing to do to other people, and you know that.

Now, as 'low' happens to be a rather subjective term for an orbit, I submit that my Miss Gredenko would definitely not have made such an obvious and silly mistake and orbit under that nasty nine-hundred-degree, sulfuric-acid cloud deck just to meet your quite obviously arbitrary and as-yet-undefined criterion for low orbit. Now, Miss Gredenko is clearly much smarter than that - and so are we. After all, we spent a whole shitload of rubles just to send her to Venus on this friggin' wild goose chase. Not to mention the costs of all that training and a whole shitload of vodka to boot. (Jorrie, have you any friggin' idea how much a tanker of Stolichnoya costs these days?) BTW, care for some? On second thought, no.

You've been bad.

Now, please put your nose in that corner over there - yes, that one - for ten minutes. One peep out of you and I'm taking your spaceships away.

muiporuE--

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Guru

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#10
In reply to #8

Re: Bright Earth Challenge

10/25/2006 4:25 AM

And just so you know exactly why you're standing in the corner, Mr. Jorrie, I feel that your thinly veiled suggestion that my little orbital apparatchik might have even considered trying to orbit under that horrid cloud deck, or, even worse, had actually thought to land her craft on that hellish surface and from there had tried to observe the apparent magnitude of the Earth at its closest approach through all that nasty mess was, well, inexcusable. And might I also point out that even if she hadn't known the atmospheric details beforehand (and she did, in fact, because our training is very thorough), she still would have known of the local inclement weather from your original post. And now you know why you've been bad.

But as you are still standing in the corner (you have three minutes left, by the way), please allow me to take advantage of the situation and to express my own personal opinion that the book, "Men are from Mars, Women are from Venus," is very appropriately titled indeed.

You did mention Mars in your last post, didn't you? Well, that got me thinking (not always the wisest course of action, as you can clearly see). I believe the title is very appropriate because, after all, don't men tend to reflect the highly-esteemed-yet-cold-but-rarefield attributes of the Martian atmosphere, whilst women tend to similarly reflect those of their own home planet? Attributes such as unbearable heat (hot enough to melt Russian spacecraft), highly acidic, poisonous, toxic and, most certainly, very windy? Plus, the conditions are permanent.

Thought I'd mention it anyway - just to help you pass the time.

(you have one minute left)

muiporuE--

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Guru
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#11
In reply to #10

Re: Bright Earth Challenge

10/25/2006 6:44 AM

Since "muiporuE" let me out of the corner, I re-read some of the posts and I must say it is hotchpotch of solid stuff and waffling! Europium, you must take the engineering cake here: you started off waffling, then made a solid engineering input before going off target again - anyway, it was humorous and CR4 can always do with a bit of that!

It is clear that not too many respondents have watched Venus at her best; otherwise they would have roughly known where it happens. Some came close though! Before spilling the beans, let's give a few more a chance to state their view...

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Guru

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#14
In reply to #11

Re: Bright Earth Challenge

10/25/2006 10:10 AM

I appreciate the honor Your Honor, but I'm somewhat unclear from your post where, in which post, exactly, I did the engineerin' and where I did the waffling. Usually I leave that up to my cat, Heisenberg.

You sure you're not just tryin' to placate me after me stickin' you in that corner?

And speakin' of which, you gonna behave now? You don't wanna lose them spaceships!

muiporuE--

PS: I have this odd habit of signing my name backward when my post is meant to be taken as being somewhat tongue-in-cheek. So when you see my sig like that, please tend not to take the foregoing nonsense too literally. It'll get you in trouble and, Lord knows, you been enough of that already...

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Guru
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#12

Re: Bright Earth Challenge

10/25/2006 7:59 AM

OK Jorie here goes at trying to put some numbers to it. I have cheated somewhat and used a drafting package to work out how much of the planet is illuminated by the Sun, please fee free to insert the trigonometric equations.

For simplicity lets say Venus is 10 Blogs for the Sun and the intensity of the from the sun at a distance of 1 Blog is 100*

So using the inverse square law the amount of light being reflected from

Venus would be 100* x 10-2 = 1000m*

Earth would be 100* x 14-2 = 510m*

So lets look at the situation when Earth a Venus are in various relative positions. From the diagram you can see that we need to introduce the amount of the planet that is illuminated. So lets look at the various relative positions.

a./ When the planets align as in a then the intensity of

Venus from Earth is 0% x 1000m* x 4-2 = 0.000m*

Earth from Venus = 100% x 510m* x 4-2 = 31.875m*

b/. For situation b we get

Venus from Earth = 50% x 1000m* x 10-2 = 5.000m*

Earth from Venus = 85% x 510m* x 10-2 = 4.355m*

c/. For situation c we get

Venus from Earth = 78% x 1000m* x 17-2 = 2.700m*

Earth from Venus = 90% x 510m* x 17-2 = 1.588m*

d/. For situation d we get

Venus from Earth = 90% x 1000m* x 22-2 = 1.860m*

Earth from Venus = 97% x 510 x 22-2 = 1.824m*

e/. For situation e we get

Venus from Earth = 100% x 1000m* x 24-2 = 1.736m*

Earth from Venus = 100% x 510m* x 24-2 = 0.885m*

So you can see that at no time is Venus brighter than Earth.

I havn't taken into account the fact that Venus has 100% cloud cover while earth has something like 45% cloud cover but I think you can get the idea from the examples. Somebody else might like to prove it in a more mathematical way but I think an example is worth a thousand equations.

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Guru
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#13
In reply to #12

Re: Bright Earth Challenge

10/25/2006 8:28 AM

Bingo Masu!

Amazingly, although your assumptions and best positions are not all perfect, you got the apparent visual brightness ratio near perfect. Earth at her best from Venus is about 6 times brighter than Venus at her best from Earth. You got 31.9 to 5 = 6.4, which is a brilliant result, close enough for most engineering purposes!

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#15
In reply to #13

Re: Bright Earth Challenge

10/25/2006 10:33 AM

I didn't try to get the point of maximum brightness for Venus I just use divided the orbit into 8 segments and it was a fluke that it cam out so close to correct. I have been thinking about the mathematical proof and if I have a sleepless night I will have a go at it and solve it for maximum brightness.

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Guru
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#18
In reply to #15

Re: Bright Earth Challenge

10/26/2006 12:22 AM

Masu wrote: "I didn't try to get the point of maximum brightness for Venus I just use divided the orbit into 8 segments and it was a fluke that it cam out so close to correct."

According to the "Collins Guide to Stars and Planets", Venus is at its brightest from Earth when only 28% of the visible surface is illuminated, so it's at an angle around 30 degrees.

It also says that 76% of light hitting Venus is reflected. I do not have a figure for Earth, but it's probably around half of that for Venus.

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#19
In reply to #18

Re: Bright Earth Challenge

10/26/2006 10:58 AM

Albedo for Venus is about .75.

Albedo for Earth is about .35

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Guru
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#20
In reply to #19

Re: Bright Earth Challenge

10/26/2006 1:35 PM

Hero wrote:

"Albedo for Venus is about .75.

Albedo for Earth is about .35"

Thanks Hero.

Masu, use it!

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Guru

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#17
In reply to #13

Re: Bright Earth Challenge

10/25/2006 10:39 AM

Jorrie writes: "...close enough for most engineering purposes!"

An engineer and a mathematician were looking over some difficult calculations regarding the relative apparent magnitudes of Earth and Mars from various points in their orbits when Venus entered the room and began walking toward the two gentlemen. Just so that they'd get a good long look at her obvious beauty, she walked in such a way as to cover half the distance between herself and the two gentlemen that she covered in the previous interval.

The mathematician concluded, "She'll never get here!"

The engineer was a little more optimistic: "She'll get close enough!"

--Europium

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Guru
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#16
In reply to #12

Re: Bright Earth Challenge

10/25/2006 10:33 AM

Well done!

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