Understanding the Motion of the Sky

To locate, understand, and appreciate the astronomical objects you look at, you need a basic understanding of how the sky moves. This is especially true if you have a tripod with an equatorial mount, since these are specifically designed to match the motion of the sky.

Note: this article is written from the perspective of an observer in the Northern hemisphere. The same concepts apply in the Southern hemisphere, except for the absence of a stationary pole star.

What’s the Problem?

The beginner in our fictional article was disturbed by the fact that objects he was looking at kept drifting out of his field of view, always in the same direction. He assumed there was something loose on his telescope. There probably was something loose, but that was not why things were moving out of his field of view; it was because the rotation of the Earth makes objects in the sky appear to move.

Beginners will also notice that objects aren’t in the same place each night. The stars move slowly, causing certain constellations to move around in the North, while others are visible only during certain seasons. Other objects, like the Moon, appear to have yet another schedule, moving around the sky at their own pace.

What You’ve Probably Noticed

Even if you haven’t been studying astronomy, you have probably noticed certain things through your life:

• The Sun always rises in the East and always sets in the West, in roughly the same spot (moving North and South a bit as the seasons change).
• The Moon always rises in the East and sets in the West, in about the same locations as the Sun.
• You may not have noticed that stars rise and set, but you have probably noticed:
  • Different constellations are visible at different times of year.
  • Certain constellations, like the Big Dipper, are almost always visible, but show up at different places in the sky throughout the year — sometimes upside-down or standing on one end or the other.

What’s Going On?

It’s fairly simple geometry. Which we’re not going into in detail here — there are many excellent books on planetary mechanics.

All the motions and changes you see are a result of four simple facts:

1. The Earth is spinning on its axis, one turn every 24 hours.
2. The Moon is orbiting around the Earth, one orbit every 27.3 days.
3. The Earth and all the other planets are orbiting the Sun, all in the same direction, and all in roughly the same plane (i.e. it’s like they are all laid out on a large dinner plate with the Sun at the centre). The outer planets orbit more slowly than the inner planets.
4. The stars are stationary. (They do, in fact, move very quickly. But they are so far away that the motion appears to us to be too slow to perceive without special instruments.)

What You See When You Look Up

The above facts are sufficient to explain all the motions you see when you look at the sky. Standing on the ground, we do not perceive the motion of the Earth, either its rotation or its orbit around the Sun — instead, it seems to us as though we are stationary and the sky is moving around us.

Since the Earth is rotating around its axis, the stars directly above the axis don’t seem to move much. The North Star is almost directly above the axis and seems completely stationary. As we move away from due North, the stars appear to move, tracing circular paths around the North Star, with one time around the circle taking 24 hours. The North Star itself would appear directly overhead if you were standing on the North Pole. If you are South of the North Pole, the North Star will appear somewhere between the horizon and directly overhead. The angle above the horizon is equal to your latitude so, in Ottawa, I see it as about 45 degrees above the horizon.

The North Star doesn’t move, so it is always visible. Other stars, if they are close to the North Star, will always be visible even though they will move around it. Such stars are called circumpolar. Stars sufficiently far from the North Star will be visible only part of the night, since they will rotate below the horizon. Which stars are visible during the night hours varies during the year as the Earth orbits the Sun.

Because the Earth is rotating toward the East (i.e. it is spinning counter-clockwise as seen from above the North Pole) everything appears to rise in the East and set in the West: the Sun, the stars, the Moon, and the planets.

Because the planets all lie in roughly the same plane, the Sun and Planets all follow approximately the same path through the sky. This path, called the Ecliptic, is the projection onto the sky of the plane of the solar system. The easily visible planets like Mars, Saturn, and Jupiter are always on or very close to this line.

What You See In Your Telescope

When you look through your telescope, you are looking at a very small section of the sky, so the apparent movement of the stars is greatly amplified. Through a typical telescope and eyepiece, stars will move completely out of your field of view in a minute or two.

Modern telescopes include motors to rotate the telescope at the same rate at which the Earth rotates. When everything is correctly aligned, this will result in the stars appearing to be stationary in the telescope, permitting long observation without constant aiming adjustments.

Timing and Movement

It’s interesting (or so I think anyway) to do some simple math and think about the effects of some of the movements we see.

Movement in One Night

Since the Earth rotates every 24 hours, any given star must move completely around the sky in 24 hours. A complete circle around the sky is 360 degrees. 360 degrees in 24 hours is 360/24 = 15 degrees per hour, or 15/60 = 0.25 degrees per minute.

You can do a lot with those figures. Some examples:

1. The angular diameter of the Moon is about 0.5 degrees. This means that a star will travel a distance in the sky equivalent to the apparent width of the moon in about 2 minutes. (Stars don’t “overtake and pass” the moon, since the moon is moving too. You need to compare to a stationary object like a chimney to see this motion.)
2. Suppose Jupiter has just risen, but it’s so close to the horizon that you can’t easily observe it yet. When will it be higher? Suppose we’d like to wait till it travels about 45 degrees across the sky. That will take about 45 / 15 = 3 hours.
3. A typical amateur telescope with a typical eyepiece (say, a 200 mm8-inch Dobsonian reflector with a 20mm Plossl eyepiece) shows you a piece of sky about 1 degree wide. So, stars will drift completely through this field of view in about 4 minutes. Or, if you centre a star, it will drift out of your field of view in about 2 minutes.
4. Observing planets is worse. We like to use high power, with a narrower field of view. That same telescope, set up for 200x magnification, only shows about 1/2 degree of sky, so Saturn or Jupiter will drift out of your field of view in about a minute. This is why owners of non-motorized telescopes appreciate the wider-field eyepieces like Naglers or Radians, to keep objects in their field of view longer.

Movement Between Nights

The Earth orbits the Sun once every 365.25 days. So, at some fixed time of night (say, midnight) any given star will be in a given position one day, slightly moved from that position the next day, and so on, returning to the same position 365.25 days later.

So, at the same time of night, a star moves its apparent position 360 / 365.25 = 0.99 degrees each day. Let’s call it 1 degree.

So if a star — say, Sirius — is just at the horizon at 9:00 PM on a given day, it will be about 30 degrees higher at 9:00 PM about 30 days later. If the Big Dipper is sitting flat in the sky at midnight on a given day (i.e. horizontal and able to hold water), at midnight 180 days later it will be upside down, on the other side of the North Star.

The Planets

The planets appear to move across the sky, following the Ecliptic, at almost the same rate at which the stars move. However, since the planets are also orbiting the Sun at their own rates, they do not appear completely stationary against the background stars. Instead, they will move slowly between the stars and constellations. The planets closest to the Sun move quickly, so Mercury and Venus will appear to change their position in the sky, relative to the stars, quite quickly — noticeably moving in only a few days. The outer planets move slowly, so Jupiter and Saturn will appear to very slowly drift between the stars, leaving one constellation and entering the next every year or two.

It was this motion across the background of stars that first drew the attention of early observers to the planets, making it obvious that something different was going on with those points of light.

The planets can even appear to move backward against the stars for brief periods, because of the line of sight effects of the Earth and the other planet’s position in their orbits. Explaining this occasional backward motion was one of the biggest challenges for early astronomers trying to work out an accurate model of the sky.

The Moon

The Moon orbits the Earth every 27.3 days. 360 degrees / 27.3 days = approximately 13 degrees per day. So at any given time of night, the moon will appear to have moved 13 degrees in the sky from one day to the next.

The phases of the moon are caused by the angle between the Sun, the Moon, and the Earth (since the moon “shines” only by reflecting the light of the Sun toward our eyes; it does not emit any light of its own).

A full moon is when the Sun and Moon are on opposite sides of the Earth. We are directly between them, so the light of the Sun is reflected straight back at us. This is why a full moon always rises exactly at sunset, and sets exactly at sunrise. That’s in theory — in practice, it vary depending on your longitude within your time zone and with the exact time the moon is 100% full during the night of full moon; so don’t set your watch by it. You’ll sometimes read stories or see movies involving a full moon rising late at night. That’s an error, it can’t happen that way; if the full moon is on the horizon, it’s sunset or sunrise, give or take an hour.

After the full moon, the shrinking crescent (called waning) rises later and later in the evening, until it actually rises during daylight and is visible in the early morning. Eventually the moon is completely invisible when it is between the Earth and the Sun, reflecting no light toward us. Then the crescent starts to grow (waxing), visible early in the evening.

We always see almost exactly the same “face” of the moon. This does not mean the moon is not rotating — if it was not rotating, we would see all sides of it as it orbited around the earth. We see only one face because the moon rotates on its axis every 27.3 days — exactly the same speed at which it orbits the earth. So, it rotates just fast enough to always keep the same face towards us as it orbits. This is not a coincidence — it is a result of tidal forces between the Earth and the Moon “adjusting” the moon’s rotational speed over many years until the present stable state was reached. This is a natural effect for any large moon orbiting any large body, and all of the large moons in our solar system (e.g. those of Jupiter and Saturn) are locked to face their planet in the same way.

Conclusion

The sky is an active place, with stars whirling around the North pole, and the Sun and planets tracing an invisible path through the sky at varying speeds. While everything appears stationary to a casual glance upward, your telescope will magnify the motion enough to actually see it.

Understanding the motion of the sky is important to help you plan your observing sessions, know where to find interesting objects, and understand the changes you’ll encounter throughout the year.