During this week of April 12th, 2020, early risers were rewarded with the sight of a waning crescent moon and three planets, Mars, Saturn and Jupiter, all fairly close to each other just before sunrise. On the 16th, I used a different shutter speed to capture a bit of detail from the moon, one that would have not captured any light from the planets, so forgive both the cut and paste job and the enlargement of the planets to make them more visible.
Using a simulation from the excellent and free software Stellarium, we can compare sights at 4:44 AM viewed from Roxboro, Quebec to that of 4 days earlier at the same time.
We get a strong hint that, compared to the other planets, the moon is closer to the Earth. In four days, the moon has moved a lot more across the background of the stars. We also notice that Mars is closer than Saturn and Jupiter because it has traveled more than the pair relative to that triangle of stars above Mars. (Albali of Aquarius and the double stars Prima Giedi and Dabih of Capricorn).
On the 12th, the Moon and the planets seem roughly co-linear. That is clearly not the case four days later. That’s a reminder that the moon’s orbit around the earth is not in the same plane as that of the planets orbiting the sun. The moon’s plane is tilted about 5 degrees to the ecliptic, which is the circle on the celestial sphere representing the sun’s apparent path during the year. Another reminder of the tilt is the fact that we do not get a lunar or solar eclipse every full or new moon, respectively. The moon has to cross the ecliptic for that to happen.
The tilt of the plane of the moon’s orbit leads to a less familiar but equally interesting effect. When I consulted the moonrise tables at timeanddate.com , I realized that the difference in moonrise time from one day to the next can vary significantly. At our latitude of 45.5°N, the differences in moonrise varied anywhere from 21 to 81 minutes during the month of April. They have nothing to do with lunar phases and occur throughout the year. July will also have large variations: from 25 to 75 minute- differences in moonrise from one day to the next. Closer to the equator, the differences are more consistent. If you look up moonrises for Quito, Ecuador, which is only about a half degree south of the equator, the day-to day-differences this month only range from 40 to 57 minutes. Go even further from the equator than we are, for example to Oslo, Norway (~60 °N), and the differences can be as small as 6 minutes or as large as 101 minutes!
What is going on? The moon’s path around the Earth is not a circle but elliptical, leading to speeds that constantly change, peaking when it’s closest to us. Richard Talcott, senior editor of Astronomy magazine, in explaining the gap-variations in moonrise, mentions both factors, the varying speed and tilt of the plane.
It depends on how far the Moon dips below the horizon from one day to the next. Our satellite moves, on average, 13.2° per day relative to the background stars. But the angle at which the Moon’s orbit (tilted 5° to Earth’s orbit around the Sun) intercepts the eastern horizon varies considerably during any given month. When the angle is steep, the Moon will lie well below the horizon at the same time the following night and Earth must rotate more to bring it into view. When the angle is shallow, Luna dips only a few degrees below the horizon from one night to the next and rises with much less lag time.
Take November 2015 as an example. From 40° north latitude, the biggest lag in moonrise occurs with the waning gibbous Moon on the 30th, which rises 60 minutes later than it did the previous night. The smallest delay happens at the waxing gibbous phase on the 21st, which comes up 36 minutes later than it did the previous day.
A number of other variables play into the time difference. The Moon’s orbital speed is not constant, so its motion relative to the stars can be up to 12 percent faster or slower than the average during the month. Latitude also changes the numbers significantly because it alters the angle at which the lunar orbit meets the eastern horizon. In November 2015, the moonrise delay ranges from 42 to 58 minutes at 30° north and from 30 to 63 minutes at 50° north. In general, the closer you live to the equator, the less variation you will see.
Here is a great photo by Georgia Hofer. It’s a composite of images of the lunar cycle, all taken at the same time of the day and from identical spots. We see the moon at different declinations and right ascensions; all of its phases; and the varying gaps between images due to their unconstant gaps between moonrises.