Earthrise on the moon ... commonplace
Almost all of us know that the Moon is always turned to the Earth on the same side. From school physics courses, we also know that the reason for this is Earth tides, which forever hid from us the opposite, “dark” side of the Moon. The principle of tidal capture postulates that the host planet is almost always located at one point in the sky of its satellite. However, I said this too clearly, because in reality this is possible only under ideal conditions. Fortunately, the world is far from ideal, which allows us to observe the full sunrises and sunsets of the Earth on the Moon ...
Astronomers have long noticed that the Moon kind of "sways" during the lunar month, substituting us up to 10% of the area of the "dark" side. As a result, even before the flight of the Luna 3 station, astronomers had maps of 60% of the lunar surface.
This phenomenon was called libration. At the moment, there are 4 types of librations, we will focus on two main librations in latitude and longitude.
1. Latitude librations are caused by the inclination of the axis of the diurnal rotation of the Moon to the plane of its orbit (amplitude of 6 ° 50 min), as a result of which the Moon "substitutes" for us the north or south pole.
2. Longitude librations are caused by non-zero eccentricity of the lunar orbit.
The eccentricity of the orbit in a simplified version displays the degree of deviation of the satellite or planet’s orbit from the ideal circle. 0 means perfectly round orbit. Greater than 0, but less than 1, to one degree or another an elongated orbit (elliptical), with e = 1 parabolic, and with e> 1 - hyperbolic. As you noticed, the orbit gradually extends with an increase in eccentricity from 0 to 1, breaking at e = 1 (reaching the second space in a given orbit).
Librations of the moon, view from the Earth.
The eccentricity of the moon is on average 0.05, which is quite enough for small deviations to appear between the speed of the moon's rotation around the Earth and the moon's own rotation around its axis. This provokes longitude libration with an amplitude of 7 ° and 54 min.
Obviously, both types of libration also cause the Earth to move in the sky of the Moon - where the blue planet for a month describes a huge ellipse with a largest diameter of 18 °. Considering that the angular dimensions of the Earth from the Moon are “only” about 2 ° (four times larger than the sizes of the Moon visible from the Earth), this will allow future lunar colonists to observe though slow but spectacular sunrises and sunsets of their native planet in certain areas of the Moon.
Earthrise in the "zones of libration", the lunar pole, mid-latitudes and the equator (Stellarium program).
However, the least patient colonists may well observe this “in fast rewind” from the orbit of the moon (Kaguya / JAXA probe).
And a little bonus. Although Iapetus, Saturn’s satellite, most likely doesn’t have any stargate where the hero of Arthur Clark’s book “Space Odyssey 2001” managed to please, but thanks to the irregularities in the orbit of this satellite, one can observe quite epic sunrises of “The Lord of the Rings”.