Ten Cool Things Seen in the First Year of LRO.
LRO stands for Lunar Reconnaissance Orbiter, an orbital satellite that is mapping the Lunar Surface.
The Moon is approximated as a two dimensional surface, a 2-Sphere, with an altitude recorded as a function of the lunar latitude (THETA) and longitude (PHI). THETA and PHI are periodic polar coordinates. In time, LRO will cover the entire lunar surface by following its trajectory, a one dimensional curve in space.
This raises an interesting problem in differential geometry. The distance along the curve is a scalar function of time, S(t), obtainable from the metric. At each instant the LRO is located at a particular point on the 2-Sphere, [THETA(S(t)), PHI(S(t))].
So here’s the tricky question: How can the two dimensional surface of the moon, a 2-Sphere, be completely covered by a one dimensional curve (the LRO orbit)?
Comments and discussion welcome. Answer to follow in this space.
Hints: “differential” "Ergodic Curves"
MORE LRO DISCUSSION
A few observations. The surface is covered with fine dust. I guess it must be micro-meteoric and ejecta from macro-meteor impacts. Micrometeors don't reach us here on Earth, they burn up. It seems to me that excavations on the moon would tell us alot about the history of the solar system. Events such as epochs of cometary bombardment would leave a stratigraphic record unlike anything we can get on Earth. In short send drill core crew to the Moon. Also, looks to me like there was an ocean on the back side.
@Mathview From memory... That ocean looking thing on the far side is actually the remnants of a molten ocean after a collision or impact from a comet or meteor. Same as on the near side. And the core drill would have to be VERY long to get anything useful as most of the surface is dust... Very fine dust. And that is rather deep in places.
Makes sense... I would suppose that you would get a chalky limestone (in texture only of course) stratification once you went down a meter or so... Yes, it would be a huge bonus to the understanding of how the solar system formed. The fact that there is no geological movement gives us an unprecedented ability to study impacts also. Makes you cry at the whole "never been back" thing.
I wonder how the coldest place in the solar system is on the moon? You would think one of those ice moons or even something closer to the edge of the solar system would be colder....