Magicis Stellarum et Plantae
written by Katherine Lutz
Astronomy textbook. - Second edition
Last Updated
05/31/21
Chapters
15
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1,357
Astronomical Measurements
Chapter 14
12a. Days
Most of our measurements of time on Earth are relative to astronomical movements. For example, the length of a day is based on the amount of time it takes for Earth to rotate once on its axis. It actually only takes 23 hours, 56 minutes for the Earth to rotate one time, not 24 hours like the days on our calendars. The 23 hour, 56 minute day is measured by picking a star at its highest point in the night sky, and measuring how long it takes until it is next at its highest point. This is called a sidereal day. The 24-hour day is based on the length of time from when the Sun is at its highest point one day to the next. This is called a solar day. A solar day is slightly longer than a sidereal day because not only is the Earth rotating, it also is revolving around the Sun at the same time. This extra motion accounts for the 4-minute difference.
12b. Months
Our measurement of months is based on based on the Moon – this is where the word ‘month’ comes from. Just like days, there are two slightly different measurements possible. It takes 27⅓ days for the Moon to make full orbit around the Earth, relative to the stars. This is a sidereal month. However, our measurement of the month comes from the apparent orbit of one cycle through each phase of the Moon. This takes 29⅓ days and is called a synodic month. Synodic months are what we measure on our calendars, and are more relevant to magic than sidereal months, as the phases of the Moon are more important than the Moon’s location in relation to other stars.
12c. Years
As you may know, a year is the length of time it takes for the Earth to travel around the Sun, relative to the stars. This is called a sidereal year. You also may run across the term ‘tropical year’ – this refers to the length of time between one spring equinox and the next. A tropical year is 20 minutes shorter than a sidereal year. Although that does not seem very long, a calendar based on the sidereal year would get out of sync with the seasons by one day every 72 years. The difference between these two measurements arises from equatorial precession, which is discussed in another chapter.
12d. Time of Day
One way to measure the time of day is by the Sun’s actual position in the local sky. This is apparent solar time, which is what a sundial measures. In apparent solar time, noon is the exact moment the Sun is highest in the sky. However, apparent solar time is a local time, which means it will be different wherever you are on Earth. In the 19th century, Muggles devised a standard time system, which involved dividing land into time zones. Within each time zone, there is a standard time, such that all clocks within the zone read the same time, which may be different from the apparent solar time by half an hour or more. Some areas of the world also use daylight savings time, which requires setting clocks an hour ahead in the spring to maximise sunlight in the evening, and setting clocks back an hour in the fall.
However, many wizards, especially those who are less in touch with the Muggle world, still use apparent time. These wizards claim it is more important for magical folk to be in sync with solar regularities than it is for them to be in sync with other people, leading to the stereotypical belief that wizards often are late to social appointments.
12e. Astronomical Units
One unit used to measure distances is an astronomical unit, commonly abbreviated as AU. An astronomical unit is the average distance Earth is away from the Sun. An AU is equivalent to about 150 million kilometres (93 million miles.) However, an AU is too small to measure interstellar distances, for which light-years or parsecs more commonly are used.
12f. Light-years
An astronomical measurement unit you will encounter frequently is the light-year. A light-year is simply the distance light can travel in one year. Light travels about 300,000 kilometres (186,000 miles) per second, so it can travel about 10 trillion kilometres (6 trillion miles) in one year. Be aware that although ‘year’ is in the name, a light-year is a measure of distance, not time. When your friend complains to you that his Charms homework will take ‘light-years’ to complete, correct him and tell him that although it will take a long amount of time, light-years do not measure time. Perhaps the parchment on which he writes the essay will be light-years long.
One thing to keep in mind when working with stars and galaxies many light-years away is that the further away you look in distance, the farther back you look in time. This is due to the fact that it takes time for light to reach us. If we are looking at the light from a star that is ten light-years away, it has taken ten years for the light to travel to us, so we are seeing the star as it was ten years ago. Thus, as we look further and further away from Earth, we can find out about the history of the universe.
Tied to this idea is the fact that it is only possible for us to observe a portion of the universe. Since the universe is about 14 billion years old, there has only been time for the light from objects within 14 billion light-years of us to reach Earth. This sphere of a 14 billion light-year radius is called our observable universe.
12g. Parsec and Parallax
No definition of parsecs would be complete without, first, an explanation of parallax. Parallax is the apparent movement of a star in the sky due to the movement of the Earth around the Sun. You can do a simple demonstration of parallax by holding your wand up at arm’s length in front of your face. First, close your left eye, focusing on your wand with only your right. Then open your right eye and close your left. As you rapidly switch between your observing eyes, you will notice that the wand appears to move in comparison to the rest of the room around you. This is because of the small distance between your eyes, which changes the angle at which you are viewing your wand.
The same phenomenon occurs with our view of stars as Earth moves around the Sun throughout the year. If you observe a nearby star, it will appear to move compared to a background of more distant stars between your observations in January and July, or any two points six months apart from each other. In our analogy with your wand, the wand is the nearby star, and your two measurement points in January and July, which take place on opposite sides of the Sun, are the viewpoints from your left and right eyes.
A star’s parallax angle is equal to half of its yearly back-and-forth shift. A star farther away would have a smaller parallax angle, which you can demonstrate by moving your outstretched wand closer to your face and seeing that it appears to move more.
A parsec is defined as the distance to an object with a parallax angle of 1 arcsecond (a unit of angular measurement comprising 1/60 of an arcminute). The word parsec is a combination of the words ‘parallax’ and ‘arcsecond.’ Stellar distances often are stated in kiloparsecs (1,000 parsecs) or megaparsecs (1 million parsecs.) A parsec is equal to 3.26 light-years, or about 31 trillion kilometres (19 trillion miles).
Most of our measurements of time on Earth are relative to astronomical movements. For example, the length of a day is based on the amount of time it takes for Earth to rotate once on its axis. It actually only takes 23 hours, 56 minutes for the Earth to rotate one time, not 24 hours like the days on our calendars. The 23 hour, 56 minute day is measured by picking a star at its highest point in the night sky, and measuring how long it takes until it is next at its highest point. This is called a sidereal day. The 24-hour day is based on the length of time from when the Sun is at its highest point one day to the next. This is called a solar day. A solar day is slightly longer than a sidereal day because not only is the Earth rotating, it also is revolving around the Sun at the same time. This extra motion accounts for the 4-minute difference.
12b. Months
Our measurement of months is based on based on the Moon – this is where the word ‘month’ comes from. Just like days, there are two slightly different measurements possible. It takes 27⅓ days for the Moon to make full orbit around the Earth, relative to the stars. This is a sidereal month. However, our measurement of the month comes from the apparent orbit of one cycle through each phase of the Moon. This takes 29⅓ days and is called a synodic month. Synodic months are what we measure on our calendars, and are more relevant to magic than sidereal months, as the phases of the Moon are more important than the Moon’s location in relation to other stars.
12c. Years
As you may know, a year is the length of time it takes for the Earth to travel around the Sun, relative to the stars. This is called a sidereal year. You also may run across the term ‘tropical year’ – this refers to the length of time between one spring equinox and the next. A tropical year is 20 minutes shorter than a sidereal year. Although that does not seem very long, a calendar based on the sidereal year would get out of sync with the seasons by one day every 72 years. The difference between these two measurements arises from equatorial precession, which is discussed in another chapter.
12d. Time of Day
One way to measure the time of day is by the Sun’s actual position in the local sky. This is apparent solar time, which is what a sundial measures. In apparent solar time, noon is the exact moment the Sun is highest in the sky. However, apparent solar time is a local time, which means it will be different wherever you are on Earth. In the 19th century, Muggles devised a standard time system, which involved dividing land into time zones. Within each time zone, there is a standard time, such that all clocks within the zone read the same time, which may be different from the apparent solar time by half an hour or more. Some areas of the world also use daylight savings time, which requires setting clocks an hour ahead in the spring to maximise sunlight in the evening, and setting clocks back an hour in the fall.
However, many wizards, especially those who are less in touch with the Muggle world, still use apparent time. These wizards claim it is more important for magical folk to be in sync with solar regularities than it is for them to be in sync with other people, leading to the stereotypical belief that wizards often are late to social appointments.
12e. Astronomical Units
One unit used to measure distances is an astronomical unit, commonly abbreviated as AU. An astronomical unit is the average distance Earth is away from the Sun. An AU is equivalent to about 150 million kilometres (93 million miles.) However, an AU is too small to measure interstellar distances, for which light-years or parsecs more commonly are used.
12f. Light-years
An astronomical measurement unit you will encounter frequently is the light-year. A light-year is simply the distance light can travel in one year. Light travels about 300,000 kilometres (186,000 miles) per second, so it can travel about 10 trillion kilometres (6 trillion miles) in one year. Be aware that although ‘year’ is in the name, a light-year is a measure of distance, not time. When your friend complains to you that his Charms homework will take ‘light-years’ to complete, correct him and tell him that although it will take a long amount of time, light-years do not measure time. Perhaps the parchment on which he writes the essay will be light-years long.
One thing to keep in mind when working with stars and galaxies many light-years away is that the further away you look in distance, the farther back you look in time. This is due to the fact that it takes time for light to reach us. If we are looking at the light from a star that is ten light-years away, it has taken ten years for the light to travel to us, so we are seeing the star as it was ten years ago. Thus, as we look further and further away from Earth, we can find out about the history of the universe.
Tied to this idea is the fact that it is only possible for us to observe a portion of the universe. Since the universe is about 14 billion years old, there has only been time for the light from objects within 14 billion light-years of us to reach Earth. This sphere of a 14 billion light-year radius is called our observable universe.
12g. Parsec and Parallax
No definition of parsecs would be complete without, first, an explanation of parallax. Parallax is the apparent movement of a star in the sky due to the movement of the Earth around the Sun. You can do a simple demonstration of parallax by holding your wand up at arm’s length in front of your face. First, close your left eye, focusing on your wand with only your right. Then open your right eye and close your left. As you rapidly switch between your observing eyes, you will notice that the wand appears to move in comparison to the rest of the room around you. This is because of the small distance between your eyes, which changes the angle at which you are viewing your wand.
The same phenomenon occurs with our view of stars as Earth moves around the Sun throughout the year. If you observe a nearby star, it will appear to move compared to a background of more distant stars between your observations in January and July, or any two points six months apart from each other. In our analogy with your wand, the wand is the nearby star, and your two measurement points in January and July, which take place on opposite sides of the Sun, are the viewpoints from your left and right eyes.
A star’s parallax angle is equal to half of its yearly back-and-forth shift. A star farther away would have a smaller parallax angle, which you can demonstrate by moving your outstretched wand closer to your face and seeing that it appears to move more.
A parsec is defined as the distance to an object with a parallax angle of 1 arcsecond (a unit of angular measurement comprising 1/60 of an arcminute). The word parsec is a combination of the words ‘parallax’ and ‘arcsecond.’ Stellar distances often are stated in kiloparsecs (1,000 parsecs) or megaparsecs (1 million parsecs.) A parsec is equal to 3.26 light-years, or about 31 trillion kilometres (19 trillion miles).
