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We have been trying to see where the moon rises/sets on the horizon. Unfortunately, the moon is not cooperating. Even when we know the moon rise/set times (timeanddate.com), we often cannot find the moon on the horizon.
We are wondering if the moon wobbles back and forth along the horizon the same way the sun wobbles. We cannot find any website that talks about where the moon is on the horizon.
We are wondering if the moon wobbles back and forth along the horizon the same way the sun wobbles.
Yes, but over a period of 27 days compared to a full year for the Sun.
If you visualize a compass, the angle that a star rises and sets is the same angle measured from due south (for those in the northern hemisphere). This figure shows a star rising 60 degrees from due south (at an azimuth of 120 degrees). The same star sets 60 degrees from due south (at an azimuth of 240 degrees).
The rise angle and set angle can be calculated from $$cos(angle) = -\frac{sin(dec)}{cos(lat)}$$ where $dec$ is the declination of the star and $lat$ is the observer's latitude.
The same calculation applies reasonably well to the Sun and Moon. (The apparent diameters makes a small difference, as does atmospheric refraction. Let's ignore those effects for now.) Due to the motion of the Moon during the day (and to a smaller extent the Sun), the change in declination changes the rise and set angles by a small amount - a few degrees at most. For the following graphs, I have ignored this motion during the day.
For the year 2021, you can see how the rise/set angle and azimuth of the Moon changes from "north of east/west" to "south of east/west" during one month (approximately). Of course, the Sun requires an entire year to go through the same cycle.
The azimuth changes because the declination changes, and the declination changes because the Earth's axis is tilted 23.5 degrees from perpendicular to the orbital plane. The Moon's orbit is inclined another 5 to 6 degrees from that. As Uhoh has mentioned, the inclination of the Moon's orbit sometimes adds to the declination and sometimes subtracts from it. This longer cycle takes 18.6 years to complete. The rise/set angle for a full cycle looks as follows:
Here is another factor that may be affecting your observations. Between New Moon and Full, the Moon rises during the day. It may be difficult to see the Moonrise until it gets close to full. During this time span, the Moonset occurs at night. (So "measure" the Moonset and calculate the set angle from due south.) The opposite occurs from Full Moon to New: it rises during the night and sets during the day.
We are wondering if the moon wobbles back and forth along the horizon the same way the sun wobbles.
Yes, but over years even more than the Sun does!
Per answer(s) to Does the Honey moon have a precession problem? and others we can see that the Moon mostly follows the Sun, so in the summer when the Sun is high at noon it rises and sets north of east and west respectively in the northern hemisphere and in the winter it moves to south of east and west.
In the southern hemisphere exchange either north with south or summer with winter, but leave east and west as they are.
But because the Moon's orbit is inclined about 5 degrees with respect to the ecliptic, the Moon executes an additional 18 year wobble of +/-5 degrees with respect to wherever the Sun is rising and setting.
Answers to Where can I find the positions of the planets, stars, moons, artificial satellites, etc. and visualize them? will provide a number of helpful resources that may help you find where the Moon will rise and set on a given day based on your latitude and to some extent longitude.
If you have a magnetic compass (real or in your phone) don't forget to correct for magnetic declination which depending on where you are could be 10 degrees or more!
