Closest to the moon by walking

According to a BBC report this morning, the explorer Fynes, having just
climbed Everest to become the first person to do this and cross both
Arctic and Antarctic, spoke of his ascent as being the closest you can
get to the Moon by walking. This got me thinking.

Taken literally, you don't have to think long to realise it's at least
not always true, because the Moon isn't always overhead. Know about the
moon's orbit, think a little longer, and you realise your timing has to
be just right. Consider the shape of the Earth, and you will wonder if
Everest is even the right mountain to climb.

So how do you get closest to the Moon by walking? Who might the current
record holder be? And when and where could a record attempt be made?

Firstly, the Earth-Moon distance varies each month by several times the
diameter of the whole planet, never mind the height of a mountain, so
you have to choose exactly the right time of month.

Secondly, the Earth as a whole is almost like a smooth ball, so it
matters greatly whether the moon is very nearly directly above you
rather than somewhere else. If the moon is just 1 degree away from
zenith, you effectively lose 972m of height, and it doesn't frequently
get that close to being overhead at Everest [1].

Thirdly, the right combination might easily occur at night, not exactly
a traditional time of day for being atop such a large mountain.

But is Everest even the right mountain for a record attempt at any time?
Mountain peaks are quoted in height above sea level, but the Moon's
orbit is determined by the centre of the Earth, not sea level; and at
the equator, sea level is over 21,000m further from the centre of the
Earth than it is at the poles. So, we need to consider the heights of
mountains relative to the centre of the Earth.

According to the equation I have to hand[2], the peak of Everest is
about 6,382,305m from the centre of the Earth, equivalent to a mountain
of only 4165m on the equator. So, it seems to be easily beaten by Mt
Kenya's 5199m on the equator, or three degrees further South by
Kilimanjaro's 5895m, worth about 5830m. But all of these appear to be
beaten by Chimborazo in Ecuador, which I get to be worth about 6260m
were it exactly on the equator; and Huascaran in Peru, worth about
6250m.

Consequently, I suspect record attempts should be made from Ecuador or
Peru, not Nepal; though given the frequency with which Kilimanjaro is
climbed, the current record holders may be fairly ordinary tourists who
just happened to be atop that peak when the moon passed very close to
overhead at exactly the right time of month.

Finally, the Moon isn't flat either, so if you want to become the
nearest to the surface of the Moon, rather than its centre, you have to
consider the presence of lunar mountains and crater rims, too. (As seen
from the Earth, the moon rocks significantly back and forward and up and
down, so the point on the Moon that is nearest to us - and its height -
varies considerably.)

So I wonder if it's possible to be sure who has got closest to the Moon
by walking. More tractable, perhaps, if you want to claim a new record
for getting closest to the Moon by walking, when and where should you
climb?

Peter Munn 21/05/2009


[1] The sea-level point on Earth that is nearest to the Moon, the
sublunar point, traces a path as our planet revolves. On average the
path oscillates between the tropic of Capricorn and the tropic of Cancer
each day, but some months it oscillates less, travelling between about
18 degrees North and South, some months more, moving between about 29
degrees North and South, and most months somewhere between these
extremes. Everest is 28 degrees North, so the sublunar point will pass
near enough to Everest sometimes, but not every month, and even less
often at the right time of month and a convenient time of day. I
suspect good opportunities arise only every few years.

[2] Derived from the 1997 British Astronomical Association handbook:
distance of sea level from centre of Earth =
(0.99832707 + 0.00167644*cos(2*phi) - 0.00000352*cos(4*phi) +
0.00000001*cos(6*phi)) * 6378.140 km, where phi is the latitude angle
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