9

Draw a picture of Sun, moon, observer, as viewed from the side: SSSSSSSSSSSS \ / \ / \ / \ / MMMM \/ Since the triangles formed by the diameter of the sun and the observer, and the diameter of the moon and the observer are similar, you can write down the connection between the given distances using length ratios, or ...


7

The widely cited figure of 384400 km is the Moon's mean inverse sine parallax value. This is not the same as the semi-major axis length, which is closer to 385000 km. An even better value is 384748 km, which is the value specified in The lunar ephemeris ELP2000. I generally use 385000 km unless I need a more precise figure. A nice easily memorizable value ...


6

You are asking about tidal locking. Some moons are tidally locked, others are not. There are several factors that lead to or militate against tidal locking: The distance at the planet about which the moon orbits. The time needed to tidally lock a moon is proportional to the distance at which the moon orbits the planet, raised to the sixth power. Close-in ...


3

Most of the irregular moons do not quite have synchronous rotation: Regular satellites are usually tidally locked (that is, their orbit is synchronous with their rotation so that they only show one face toward their parent planet). In contrast, tidal forces on the irregular satellites are negligible given their distance from the planet, and rotation periods ...


3

You are asking about the Moon's diurnal libration. While it is small (about 1°), it is easily measurable. It is also overwhelmed by the much larger librations due to the Moon's non-circular orbit and due to the Moon's orbit being inclined with respect to the Earth's equatorial plane.


1

If images taken at same time (UTC), the Moon would be at different altitudes in sky, for some locations it would be below horizon. Next there would be a small shift of Moon with respect to stars in background. This is a parallax effect. There are observing projects that measure this during total lunar eclipses. Smallest is a bit of extra east-west libration ...


1

From @JamesK's answer, I used similar triangles (△EMH ∼ △ESJ) to solve for the diameter of the moon. $${EM \over ES}={MH \over SJ}$$ $$\Rightarrow {MH}= {{EM \times SJ} \over ES}$$ $$\Rightarrow {MH}= {{(3.84×10^8)×(1.39×10^9)} \over {2×(1.496×10^{11})}}$$ $$\Rightarrow {MH}= 1784 \ km.$$


1

It looks like your question will be closed since you haven't responded to the comments asking for additional information yet, so I'll leave a partial answer. I can update this once you respond to the comments asking for details. Parallax The Moon will appear at different RA/Dec at the same time but from different places on the Earth's surface. It's possible ...


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