I come up with 4757 km

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Rock is dead. Long live Paper and Scissors.

That's seems to assume that the 384,400 km is the distance from the center of the Moon to the barycenter. Usually, isn't the distance from center of Earth?

Regardless, it shouldn't affect the answer too much.
But when the moon is on the horizon, the barycenter is under the moon, not the observer.
Weird I got a third answer.

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I got 4728.1672816728167281672816728167 km. Welcome to the board (and the game), SLC!

I assumed that the centre of the Earth is the origin of reference, so the 384,400 km is the fixed distance between the centres.

At zenith the centre of the Moon is 384,400 - 6378 = 378,022 km

When on the horizon, Pythagoras' Theorem gives:

r² + d² = m²

r= Earth's radius = 6378 km
d= Moon's distance from observer
m= Moon's distance from Earth (centre to centre) = 384,400 km

=> d = 384,347 (to the nearest km).

So the Moon is 6325 km further away when on the horizon, or about 1.67%

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- Learn a lot teaching others.

That's exactly the answer I got.

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Assuming that the worst-case scenario is to be found at the North (or South) Pole, and assuming that the Moon is never greater than 28.58 degrees north (or south) of the equator, then applying the Law of Cosines, I get:

m² + r² -2mr*cos61.42 = d²

=> d = 381,390 km (to nearest km)

That's 2,957 km closer than when it's on the horizon, a difference of about 0.78%.

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- Learn a lot teaching others.

You're up, I think, Eroica

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http://cleardarksky.com/c/DrhmNCcs0.gif

I am a British astronomer.

I had hoped to make history by becoming the first to achieve something significant in astronomy. But I was beaten to it by just two months. My rival, a German, made history in Europe while I laboured in South Africa.

I did, however, set a record, which still stands to this day.

Who am I?

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You are (or rather, were) Thomas Henderson. You aimed to be the first to measure the distance to a star using the parallax method, and you were beaten narrowly by Friedrich Bessel, who took all the credit.

You were beaten not for the first measurment - only for the publication. You measured more than 10 000 stallar positions "by hand", and I would doubt that any single person has ever measured more.

True? 8-[

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Non sunt multiplicanda entia praeter necessitatem.

=D> =D> =D> Correct!

Not quite the record I was referring to. Henderson's publication concerned the distance of Alpha Centauri, which still holds the record as the closest system to the Sun.

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- Learn a lot teaching others.

I, on the other hand, am not a person. I am an object. I stand for a cosy and friendly situation long gone.

Nobody, probably, will ever meet me again, except the lights that slowly wheel above me, sometimes putting me in the shadow of a nearby decrepit metal scaffold. One of the lights is eating at me, slowly destroying what was my original purpose.

It's a humble existence, but not without grace.

What am I?

*sniff*

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Non sunt multiplicanda entia praeter necessitatem.

You just might be an Apollo lunar rover. Cozy and friendly enough to carry two astronauts for an open-air, err I mean vacuum, rock hunt in the countryside. Alternating bi-weekly between freezing and scorching temperatures from the brightest of the lights above. Occasionally shadowed by the decrepit LM descent module. Bombarded by solar radiation and ultraviolet light.

It's either that or I got to dig out my Masonic Renaissance Painter/Vampire theory again.

Are you the second Apollo Soyuz project Saturn V, or perhaps its command module that's in a museum (the Smithsonian?)...

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HOUSTON: Roger, Tranquility. Be advised there's lots of smiling faces in this room, and all over the world.
TRANQUILITY: There are two of them up here.
COLUMBIA: And don't forget one in the command module.

--From the Apollo 11 transcripts

No. Nice scenery, though. And, ssshhhht , don't tell them about our hidden vampires, will you? We're supposed do go secretly about that one!

No, and no - I hope, though, that occasionally somebody does enter the Smithsonisn ans has a look at all the stuff there

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Non sunt multiplicanda entia praeter necessitatem.

Ok, so you're not a rover, but I suspect you are on the moon, at tranquility base (which evokes images of a cozy and friendly situation). The light that is eating at you is undoubtedly the Sun. The nearby metal scaffolding is what is left of the lunar module. The sun is slowly destroying your original purpose, so that kind of implies you are still functioning. I conclude that you are laser ranging retroreflector left by Apollo 11.

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Rock is dead. Long live Paper and Scissors.

I'll guess the american flag.

Edit: At tranquility base...

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Hanlon's Razor - "Never attribute to malice that which can be adequately explained by stupidity."
Asimov's addition - "Or ignorance."

"On two occasions, I have been asked [by members of Parliament], 'Pray, Mr. Babbage, if you put into the machine wrong figures, will the right answers come out?' I am not able to rightly apprehend the kind of confusion of ideas that could provoke such a question."
-- Charles Babbage

No - But I find your answer extremely interesting. I wouldn't ever associate a national flag with "friendly and cosy". Maybe that's my German neurosis - and I hope you don't think I wanted to make an underhand remark with the "long gone"...

The race is still open! \/ :-k

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Non sunt multiplicanda entia praeter necessitatem.

My thought about it was the flag was planted not for America but all mankind (cozy and friendly), and we haven't sent someone to another world in a long time (long gone).

If you didn't notice, jfribrg also posited an answer.

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Hanlon's Razor - "Never attribute to malice that which can be adequately explained by stupidity."
Asimov's addition - "Or ignorance."

"On two occasions, I have been asked [by members of Parliament], 'Pray, Mr. Babbage, if you put into the machine wrong figures, will the right answers come out?' I am not able to rightly apprehend the kind of confusion of ideas that could provoke such a question."
-- Charles Babbage

Ah. Well, I do not entirely agree when you say that the flag was planted for all mankind - I think national flags are about who someone belongs to and someone else doesn't. As a poster remarked caustically in a different thread (I quote from memory): "all mankind was represented on the Moon - by American taxpayers's money". But let's not get too philosophical here. "Cozy and friendly" is just that, no mental gymnastics involved.

Uuhuh, thanx

No.
I wasn't aware that the reflectors are actually decaying. But of course they have to, if you think about it.
A lot of good (and also correct) reasoning here, but still off target.

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Non sunt multiplicanda entia praeter necessitatem.