Let’s say a 1cm-thick cord has been strung between the exact center of the moon and the exact center of the earth.
Where, on the surface of the earth, would the cord be right now (17:23 GMT)?
If we could trace the path of the cord on a globe, would it be a perfect circle? How high above/below the equator would it go? Does it wobble?
Technically, it would be an ellipse, as most orbits are. But the eccentricity is reasonably small, so treating it as a circle is not entirely unreasonable. The distance at perigee and apogee varies from about 360,000 km to roughly 400,000 km.
There is precession (wobble) in the orbit. There’s precession to most orbits in the solar system, including Earth’s orbit about the sun. It’s not particularly important for stargazing purposes, though it’s obviously important for any orbital mechanics calculations.
And, for whatever reason, the moon’s orbit lies almost exactly on the plane of the ecliptic, so it can get up to roughly 23 degrees above/below the equator, which is the same latitude as the Tropics of Cancer and Capricorn.
You can get most of these numbers on wiki, though you might need a passing familiarity with orbital mechanics to figure out what they all mean.
You could calculate this by finding the position of the Moon on the celestial sphere, and then figuring out what point on the Earth’s surface this corrseponds to. This ephemeris table gives you the information about the right ascension & declination of the Moon. The declination of the Moon (at the bottom) will be equal to the latitude of the spot on Earth’s surface you’re looking for (positive = north, negative = south.) To find the longitude of the spot you’re looking for, you would subtract the Sun’s right ascension from the Moon’s right ascension; positive results would then be East longitude, and negative would be West longitude.
For the time & date you mentioned, I get 5.867°E, 20.64°S, which is in the South Atlantic, about 800 km off the coast of Namibia.
No, because the Earth rotates and revolves about the Sun. If the Earth wasn’t rotating or revolving, though, it would be pretty close to a great circle. Great Antibob notes that the orbit itself is an ellipse; however, this ellipse lies in a plane, and the intersection of this orbital plane with the Earth is what the “path of the cord” would be. Assuming a perfectly spherical Earth, this would be a great circle.
Because of the motion of the Earth, it takes a while to complete the cycle. The points of maximum declination of the Moon (which is what you’re asking about) are called lunar standstills, at which point the Moon is above a point about 28.5° from the Equator.
A less wordy way of saying this is GP, which I believe is geographic position. It’s used all the time in navigation.
Note also that the position of the sub-lunar point is moving across the surface of the Earth at about a thousand miles an hour, mostly due to the Earth’s rotation.
<nitpick> You might also need to be a bit more accurate about “exact center”.
Do you mean ‘center of mass’? Because the earth is not a solid rock, but toward the center is mostly different liquids (with different densities). And they are moving around, erupting through volcanoes, moving with the tectonic plates, etc.
Do you mean ‘geographic center’? Which might be hard to determine, since the earth is not a perfect sphere, but bulges out in various places. Plus the shape changes during the day, as tides go in or out.
So this question is more complicated than it seems.