Guide to year 1 Astronomy
written by Annie Lovegood
having trouble with your Astronomy homework read this book
Last Updated
05/31/21
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Guide to year 1 Astronomy lesson 7
Chapter 7
In this introductory lesson about the solar system, you will learn some facts about the Sun and the planets, which will be discussed in more detail in Year Four. After briefly describing each of the planets, I will show you how various astronomers interpreted their apparent motion in the sky, how they actually move in space, and what makes them move the way they do.
The Sun
The Sun, a hot ball of hydrogen and helium, is the source of all the energy and magic in the solar system, aside from the miniscule amount we get from the other stars. As we have learned in previous lessons, the amount of magic we receive from a celestial body depends on the amount of light it sends us, as well as its size, and the Sun’s average diameter is 1,391,980 kilometers, about ten times as great as the largest planet! It also sends us the most light - about 400 thousand times as much as the full Moon and 12.5 billion times more than the next brightest star, Sirius. Its surface temperature is about 10,000 degrees Fahrenheit. It actually has a name – Sol, the Latin word for sun – which is where the word “solar” comes from. While the Sun is undoubtedly important, more details will be provided about this blazing behemoth in your Fifth Year, so now we turn to the planets.
The Sizes of the Planets
As mentioned in Lesson Four, each planet reflects a significant amount of magic to us. The strength of this magic depends upon its size, among other things, so we begin our discussion about the planets by touching on their diameters. The planets, in increasing order of distance from the Sun, are Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, and Neptune. To give you an idea of just how much variation there is between these bodies, here is a diagram of the planets and Pluto to scale, with the size of each planet shown. As you can see, Jupiter, the largest planet, is more than 28 times as big in diameter as Mercury, the smallest one. The diameter of Saturn given here doesn’t include its rings, whose diameter is about 280,000 kilometers, even bigger than Jupiter.
Source: here
The planets are divided into two groups: the inner planets and the outer planets. Since we are going to describe the planets in increasing order of distance from the Sun, we will discuss the inner ones first.
The Inner Planets
Source: here
The inner planets are Mercury, Venus, Earth, and Mars, and they are separated from the outer ones by the asteroid belt. They all have rocky surfaces and are much smaller than the outer ones, but they reflect just as much magic to us because they are closer to both the Sun and Earth, making their angular sizes comparable to those of the outer planets. As you will learn later, at the best of times, Venus reflects more magic to us than any of the outer planets, and Mars and Mercury reflect more than two of them. As budding magical astronomers, you will certainly want to learn about these fascinating celestial objects. Here, as promised, is a brief description of each of them.
Mercury, the innermost planet, has no moons, but its surface looks like that of Earth’s Moon, with mountains, plains, and craters. It has a very thin atmosphere, which exerts about 200 trillion times less pressure than Earth’s atmosphere. It’s made up mostly of oxygen, sodium, and helium, but there’s so little of it that its composition doesn’t affect the magic reflected from the surface. The sunlit side of Mercury can reach temperatures as high as 427°C, whereas the temperature can fall as low as -220°C once the Sun goes down.
Mercury.
Source: here
Venus, which, like Mercury, has no moons, is covered entirely by a thick layer of clouds made mostly of sulphuric acid. The planet’s surface can’t be seen from above the clouds, but it has been spotted and photographed by spacecraft that landed there, showing mountains, plains, and depressions, but not many small craters. Venus’s atmosphere exerts 92 times as much pressure as the Earth’s atmosphere and is made up of mostly carbon dioxide with a bit of nitrogen. The temperature is extremely hot, night and day and all over the planet’s surface, reaching about 462°C, even hotter than Mercury. It’s a bit cooler on the top of the tallest mountain, Maxwell Montes, where the temperatures are a nippy 380°C. Because Venus is almost the same size as the Earth, they are often called sister planets. You wouldn’t want to have such a toxic sister, though!
Venus.
Source: here
Earth will be studied in great detail in Year Three, so I won’t get into too much detail here. Suffice it to say that our home planet has one moon, called Luna or Selena. It is tidally locked to Earth, meaning that tidal forces exerted by Earth make the same side of the Moon face us at all times.
Mars’s surface, like Mercury’s, also has mountains, plains, and craters. It looks reddish because of the iron oxide that covers most of the planet and is blanketed with dust. Some parts of the surface look darker than others because they’re made of different types of rocks. Additionally, while there is no liquid water on the surface of Mars, some was discovered underneath the surface, leading to speculation that life may once have existed there and possibly still does. Wouldn’t it be exciting if future voyages to the planet discover life outside our world, either past or present? The poles are also covered with frozen water and, in the winter, frozen carbon dioxide as well. Its atmosphere, which is made up of mostly carbon dioxide, exerts about 100 times less pressure than the Earth’s. Nevertheless, it occasionally creates dust storms all around the planet, obscuring our view of Mars and preventing the Sun’s heat from powering our rovers on the surface. The temperature ranges from -143°C at the poles to as high as 35°C at the equator at Martian noon, when the Sun is highest in the sky. Mars has two moons, Phobos and Deimos, both of which are tidally locked.
Mars.
Source: here
The Outer Planets
Continuing our journey away from the Sun, we turn to the outer planets: Jupiter, Saturn, Uranus, and Neptune. They are all made out of gas, so, unlike their inner brethren, they don’t have a surface, but they have either a solid or liquid core (we don’t yet know which), and they’re huge, explaining their designation as “the gas giants.” All of the outer planets have rings, although only Saturn’s are bright enough to be seen through a small telescope.
Jupiter.
Source: here
When you look at Jupiter, what you see are clouds of ammonia crystals alternating between darker and lighter colours, as shown in the image above. If you look carefully at the lower left side of that image, you’ll see a reddish spot, called the Great Red Spot, which is shown in greater detail below. It’s the largest of many vortexes, caused by interaction between the varying circulation patterns of the gases carrying the clouds of different colours. Source: here
The planet is made up of mostly hydrogen with a smaller amount of helium and some trace gases. The temperature outside of the planet is about -160°C, but it increases as one descends through the gases, becoming hotter than the surface of the Sun near the core. The planet emits a lot of radiation, which makes it incredibly dangerous to get anywhere near it. Jupiter has 79 known moons, 12 of which were discovered as recently as 2018. The four largest moons, Io, Europa, Ganymede, and Callisto, are called the Galilean moons, as they were discovered by Galileo.
Saturn, too, is made up of mostly hydrogen and helium. Its claim to fame isn’t what its body looks like, although there is a vortex at each of its poles, but rather its prominent rings. These are not solid but made up of chunks of frozen water ranging from about ten meters to the size of a speck of dust. The rings are only about 20 meters thick, so when they are viewed from the Earth edge-on, it takes a powerful telescope to see them. They extend from 6,630 to 120,700 kilometers outwards from the planet’s equator. Galileo was the first one to see the rings, although his telescope wasn’t powerful enough for him to see that they were actually separated from the body of the planet, so he called them ears. The temperature just above the atmosphere is about -185°C. Saturn has 82 known moons (three more than Jupiter!), the largest of which is Titan, whose atmosphere, which you can’t see through, exerts almost 1.5 times as much pressure as the Earth’s. Until very recently, only 62 of those moons had been known, but on October 7, 2019, the International Astronomical Union announced that 20 more of Saturn’s moons have been discovered by a team led by Scott Sheppard using the Subaru telescope on Hawaii’s Mauna Kea.
Saturn.
Source: here
Uranus and Neptune cannot be seen with the naked eye; you need at least a pair of binoculars, but more likely a telescope, to see them. Even with a telescope, they don’t show much in the way of surface features, although Neptune does have a dark spot. As you can imagine, it’s even colder out by Uranus and Neptune than it is near Saturn. Uranus has 27 known moons, whereas Neptune has 14; its largest, Triton, is about 100 times as massive as all its other moons put together. Like Jupiter and Saturn, these two planets are both primarily made up of hydrogen and helium, but they also have a fair amount of ice, namely water, ammonia, and methane ice. Because of this, they’re sometimes called the “ice giants.” You may wonder why I just referred to frozen water as water ice. Well, we astronomers have our own jargon. For example, we call any solid substance that is typically liquid or gaseous here on Earth an ice. There will be more astro-babble in the rest of this lesson, which deals with the motion of the planets. You’ll come across it in everything written by Muggles about astronomy, so you might as well get used to it now.
Uranus (left) and Neptune (right).
Source: here
The Motion of the Planets
Revolution of the planets around the Sun
As seen from Earth, it appears as if the Moon, the Sun, the planets, and the stars all revolve around Earth once per day. Back in the days of ancient Greece, this observation led to the geocentric model of the solar system (geocentric meaning “Earth centred,” from the Greek word ‘geos,’ which means Earth), created by Ptolemy, a Greek mathematician, astronomer, and geographer. In this model, the Moon is the closest body to the Earth, followed by Mercury, Venus, the Sun, Mars, Jupiter, Saturn, and finally the fixed stars. Ptolemy studied the movements of the bodies in the sky and noted that the planets moved with respect to the stars. To account for this motion, he assumed that the planets revolved in perfect circles, called epicycles, around a point that, in turn, revolved around Earth in a circle.
Another ancient Greek mathematician and astronomer, Aristarchus of Samos, believed that the Sun, not Earth, was the centre of the solar system. His model is termed “heliocentric,” after the Greek word ‘helios,’ meaning sun. It was deemed impious by the Stoic philosopher Cleanthes, so Aristarchus never published his model. We know about it today only because Archimedes published it, even though he didn’t believe in it. The Polish astronomer Nicolaus Copernicus wrote a book expounding the same model, which was published in 1543, some 18 centuries after Aristarchus did. The heliocentric model wasn’t accepted right away, although it received support from Galileo, who became convinced of its correctness when he observed the phases of Venus, partly because both the Protestant and Catholic Church condemned heliocentrism as being impious and forced him to recant under threat of torture.
The fact that Venus exhibits the full range of phases proves that Ptolemy’s geocentric model was incorrect, because if Venus were always closer than the Sun to Earth than the Sun, it would only ever be in the crescent phase. That said, the phases of Venus do not prove that every geocentric model is wrong. There is a geocentric model, proposed by the pagan Martianus Capella in the fifth century C.E., that is compatible: the Sun, Mars, Jupiter, Saturn, and the stars all revolve around the Earth, but Mercury and Venus revolve around the Sun. Fortunately, Galileo chose to align this observation with the Copernican model, which was later proven to be essentially correct.
But it took some time for it to be accepted by the scientific community for a reason quite apart from religious opposition: there was, in fact, a flaw in his model. Like Ptolemy, Copernicus believed that the planets could only move in circles, so he too introduced epicycles. Later, Tycho Brahe made some extremely accurate observations of the positions of the planets in the sky, which Copernicus’s model couldn’t account for. Then Johannes Kepler studied Brahe’s published observations and proposed an alternative heliocentric model taking them into account. This model was governed by a series of three laws.
Kepler’s First Law states that a planet revolves around the Sun not in a circle but in an ellipse, which is like a flattened (or stretched out) circle, and that the Sun isn’t in the middle of the ellipse but off to one side, as shown in the picture below. Actually, his First Law says exactly where in the ellipse the Sun is: it’s at one of two points in the interior of the ellipse called foci. You don’t need to know the technical specifics of foci in your First Year, but it’s something to look forward to at the N.E.W.T. level.
Kepler’s Second Law states that an imaginary line between the Sun and any planet sweeps out equal areas in equal amounts of time, as shown in the image below. The important thing to note is the implication of this law: a planet will speed up as it approaches the Sun and slow down as it recedes.
Kepler’s Second Law.
Source: here
To introduce Kepler’s Third Law, I need to teach you a bit of mathem … don’t panic; it’s no more difficult than anything I’ve already mentioned, and I’m not going to test you on it - yet. Do you recall what the square of a number is? Multiply a number by itself and you get its square. For example, to get the square of 3, you multiply 3 by 3, and you get 9. Now, multiply the square by the original number and you get its cube. Continuing with the same example, multiply 9 by 3 and you (should) get 27, which is the cube of 3.
Kepler’s Third Law says that if you divide the square of the time it takes for any planet to revolve around the Sun by the cube of the average distance from the planet to the Sun, you get the same answer no matter which planet you choose. Qualitatively speaking, this means that planets that are closer to the Sun move faster than planets that are farther away.
The two images below depict the locations of the inner planets 44 days apart and let you see the implications of all of Kepler’s Laws directly. By examining them, you’ll see that Mars and Mercury don’t travel in circles and that the Sun isn’t in the centre of the paths they take, illustrating Kepler’s First Law. The Second Law is seen from the fact that 44 days is half the time it takes Mercury to revolve around the Sun, and yet the planet has moved just under half way around its orbit, as it is farther away from the Sun during this half. You’ll also note that while Mercury moves almost a full half-revolution around the Sun in this time period, Venus only moves about a quarter, and Mars even less, illustrating the Third Law.
The inner planets.
Source: here
The inner planets 44 days later.
Source: here
Now that I’ve shown you how the planets move, please bear with me while I tell you the names of the various features of the paths they take.
Length of a planet’s orbit = aphelion + perihelion.
Eccentricity of a planet’s orbit (amount by which the Sun is off centre) = (aphelion - perihelion)/length.
Kepler’s Laws describe how the planets move, but not what makes them move in just that way. That problem was solved by the English mathematician, physicist, and astronomer Isaac Newton, arguably the greatest scientist of all time. Among his many discoveries are his three laws of motion, which are as follows:
An object remains at rest or continues to move in a straight line at a constant speed unless acted upon by an outside force.
The force required to make an object change its speed and/or direction of motion is equal to the mass of the object multiplied by the rate of change.
If one object exerts a force on a second object, then the second object will exert the same amount of force on the first one, but in the opposite direction.
Newton reasoned that an unsupported object falls to the ground instead of floating in the air because a force acts on it. If you drop a stone, it will fall straight down. If you throw it horizontally, it will keep moving horizontally but will also fall down until it hits the ground. If you could throw it hard enough, your stone would never hit the ground, but would continue to fall around the curvature of our spherical planet. This same force that causes our stone to fall keeps the Moon from travelling in a straight line away from the Earth. The Moon is moving fast enough that instead of hitting the Earth, it falls continuously around it - its revolution. After careful research and contemplation, Newton concluded that the force that both pulls an unsupported object near the Earth to the ground and holds the Moon in its revolution is exerted by the Earth itself, and he called that force gravity. By similar logic, the Sun must exert a force on the planets to keep them from drifting away, and it is this force that makes a planet speed up as it approaches the Sun and slow down as it recedes. He concluded that every body attracts every other body, and he called that principle the Law of Universal Gravitation.
But how much force does one body exert on another one? The more mass a body has, the more force it will exert on others. However, Galileo had previously shown that a heavy object falls at the same rate as a light one, meaning that the more massive a falling object, the more force the Earth must exert on it to make it fall at the same rate, according to Newton’s Second Law. From Kepler’s laws of motion, Newton also concluded that the farther apart two objects are, the smaller the force will be by an amount equal to the square of the distance between them, and that’s why planets that are closer to the Sun move faster than planets that are farther away. By Newton’s Third Law of Motion, the falling object will exert the same amount of force on the Earth but in the opposite direction. The same holds true for any two bodies, including celestial ones. In fact, the planets, especially Jupiter, do make the Sun wobble a bit. The formula for the amount of force that two objects exert on each other is as follows:
The rotation of the planets
Aside from revolving around the Sun, each planet also rotates about an imaginary line called an axis, which passes through the centre of the planet and intersects the planet’s surface at its two poles. That’s why the Sun, the planets, and the stars all appear to revolve around Earth. There is an imaginary circle around the middle of the planet, equally distant from the poles, called the equator. The plane of the equator is usually tilted relative to the plane of the planet’s orbit. The angle between these planes is called the inclination.
To give you an idea of the variability between the planets, the table below shows the period of revolution, perihelion, aphelion, inclination, and period of rotation of each of the eight planets in addition to the corresponding values for the Moon. The distance between the Sun and a planet is too big to be expressed in kilometers – for Neptune it is several billion kilometers – so another unit is used, called the Astronomical Unit (A.U.), which is the average distance between the Sun and the Earth: 149,597,870.7 kilometers (92,955,807.3 miles).
Does it seem strange that the rotation periods of Venus and Uranus are negative? Their equators are actually inclined more than 90 degrees from their orbits, so they rotate backwards! Does it also seem a bit strange that the period of rotation of the Earth isn’t exactly one day? While Earth makes one full rotation, it also moves a bit around the Sun; consequently, it has to rotate a little more before the Sun gets to the same place in the sky and a full day has passed!
Since this lesson is so long, there will not be an essay today, just the usual ten-question quiz. Additionally, you will not be tested on the most difficult concepts of the day - yet.
The Sun
The Sun, a hot ball of hydrogen and helium, is the source of all the energy and magic in the solar system, aside from the miniscule amount we get from the other stars. As we have learned in previous lessons, the amount of magic we receive from a celestial body depends on the amount of light it sends us, as well as its size, and the Sun’s average diameter is 1,391,980 kilometers, about ten times as great as the largest planet! It also sends us the most light - about 400 thousand times as much as the full Moon and 12.5 billion times more than the next brightest star, Sirius. Its surface temperature is about 10,000 degrees Fahrenheit. It actually has a name – Sol, the Latin word for sun – which is where the word “solar” comes from. While the Sun is undoubtedly important, more details will be provided about this blazing behemoth in your Fifth Year, so now we turn to the planets.
The Sizes of the Planets
As mentioned in Lesson Four, each planet reflects a significant amount of magic to us. The strength of this magic depends upon its size, among other things, so we begin our discussion about the planets by touching on their diameters. The planets, in increasing order of distance from the Sun, are Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, and Neptune. To give you an idea of just how much variation there is between these bodies, here is a diagram of the planets and Pluto to scale, with the size of each planet shown. As you can see, Jupiter, the largest planet, is more than 28 times as big in diameter as Mercury, the smallest one. The diameter of Saturn given here doesn’t include its rings, whose diameter is about 280,000 kilometers, even bigger than Jupiter.
Source: here
The planets are divided into two groups: the inner planets and the outer planets. Since we are going to describe the planets in increasing order of distance from the Sun, we will discuss the inner ones first.
The Inner Planets
Source: here
The inner planets are Mercury, Venus, Earth, and Mars, and they are separated from the outer ones by the asteroid belt. They all have rocky surfaces and are much smaller than the outer ones, but they reflect just as much magic to us because they are closer to both the Sun and Earth, making their angular sizes comparable to those of the outer planets. As you will learn later, at the best of times, Venus reflects more magic to us than any of the outer planets, and Mars and Mercury reflect more than two of them. As budding magical astronomers, you will certainly want to learn about these fascinating celestial objects. Here, as promised, is a brief description of each of them.
Mercury, the innermost planet, has no moons, but its surface looks like that of Earth’s Moon, with mountains, plains, and craters. It has a very thin atmosphere, which exerts about 200 trillion times less pressure than Earth’s atmosphere. It’s made up mostly of oxygen, sodium, and helium, but there’s so little of it that its composition doesn’t affect the magic reflected from the surface. The sunlit side of Mercury can reach temperatures as high as 427°C, whereas the temperature can fall as low as -220°C once the Sun goes down.
Mercury.
Source: here
Venus, which, like Mercury, has no moons, is covered entirely by a thick layer of clouds made mostly of sulphuric acid. The planet’s surface can’t be seen from above the clouds, but it has been spotted and photographed by spacecraft that landed there, showing mountains, plains, and depressions, but not many small craters. Venus’s atmosphere exerts 92 times as much pressure as the Earth’s atmosphere and is made up of mostly carbon dioxide with a bit of nitrogen. The temperature is extremely hot, night and day and all over the planet’s surface, reaching about 462°C, even hotter than Mercury. It’s a bit cooler on the top of the tallest mountain, Maxwell Montes, where the temperatures are a nippy 380°C. Because Venus is almost the same size as the Earth, they are often called sister planets. You wouldn’t want to have such a toxic sister, though!
Venus.
Source: here
Earth will be studied in great detail in Year Three, so I won’t get into too much detail here. Suffice it to say that our home planet has one moon, called Luna or Selena. It is tidally locked to Earth, meaning that tidal forces exerted by Earth make the same side of the Moon face us at all times.
Mars’s surface, like Mercury’s, also has mountains, plains, and craters. It looks reddish because of the iron oxide that covers most of the planet and is blanketed with dust. Some parts of the surface look darker than others because they’re made of different types of rocks. Additionally, while there is no liquid water on the surface of Mars, some was discovered underneath the surface, leading to speculation that life may once have existed there and possibly still does. Wouldn’t it be exciting if future voyages to the planet discover life outside our world, either past or present? The poles are also covered with frozen water and, in the winter, frozen carbon dioxide as well. Its atmosphere, which is made up of mostly carbon dioxide, exerts about 100 times less pressure than the Earth’s. Nevertheless, it occasionally creates dust storms all around the planet, obscuring our view of Mars and preventing the Sun’s heat from powering our rovers on the surface. The temperature ranges from -143°C at the poles to as high as 35°C at the equator at Martian noon, when the Sun is highest in the sky. Mars has two moons, Phobos and Deimos, both of which are tidally locked.
Mars.
Source: here
The Outer Planets
Continuing our journey away from the Sun, we turn to the outer planets: Jupiter, Saturn, Uranus, and Neptune. They are all made out of gas, so, unlike their inner brethren, they don’t have a surface, but they have either a solid or liquid core (we don’t yet know which), and they’re huge, explaining their designation as “the gas giants.” All of the outer planets have rings, although only Saturn’s are bright enough to be seen through a small telescope.
Jupiter.
Source: here
When you look at Jupiter, what you see are clouds of ammonia crystals alternating between darker and lighter colours, as shown in the image above. If you look carefully at the lower left side of that image, you’ll see a reddish spot, called the Great Red Spot, which is shown in greater detail below. It’s the largest of many vortexes, caused by interaction between the varying circulation patterns of the gases carrying the clouds of different colours. Source: here
The planet is made up of mostly hydrogen with a smaller amount of helium and some trace gases. The temperature outside of the planet is about -160°C, but it increases as one descends through the gases, becoming hotter than the surface of the Sun near the core. The planet emits a lot of radiation, which makes it incredibly dangerous to get anywhere near it. Jupiter has 79 known moons, 12 of which were discovered as recently as 2018. The four largest moons, Io, Europa, Ganymede, and Callisto, are called the Galilean moons, as they were discovered by Galileo.
Saturn, too, is made up of mostly hydrogen and helium. Its claim to fame isn’t what its body looks like, although there is a vortex at each of its poles, but rather its prominent rings. These are not solid but made up of chunks of frozen water ranging from about ten meters to the size of a speck of dust. The rings are only about 20 meters thick, so when they are viewed from the Earth edge-on, it takes a powerful telescope to see them. They extend from 6,630 to 120,700 kilometers outwards from the planet’s equator. Galileo was the first one to see the rings, although his telescope wasn’t powerful enough for him to see that they were actually separated from the body of the planet, so he called them ears. The temperature just above the atmosphere is about -185°C. Saturn has 82 known moons (three more than Jupiter!), the largest of which is Titan, whose atmosphere, which you can’t see through, exerts almost 1.5 times as much pressure as the Earth’s. Until very recently, only 62 of those moons had been known, but on October 7, 2019, the International Astronomical Union announced that 20 more of Saturn’s moons have been discovered by a team led by Scott Sheppard using the Subaru telescope on Hawaii’s Mauna Kea.
Saturn.
Source: here
Uranus and Neptune cannot be seen with the naked eye; you need at least a pair of binoculars, but more likely a telescope, to see them. Even with a telescope, they don’t show much in the way of surface features, although Neptune does have a dark spot. As you can imagine, it’s even colder out by Uranus and Neptune than it is near Saturn. Uranus has 27 known moons, whereas Neptune has 14; its largest, Triton, is about 100 times as massive as all its other moons put together. Like Jupiter and Saturn, these two planets are both primarily made up of hydrogen and helium, but they also have a fair amount of ice, namely water, ammonia, and methane ice. Because of this, they’re sometimes called the “ice giants.” You may wonder why I just referred to frozen water as water ice. Well, we astronomers have our own jargon. For example, we call any solid substance that is typically liquid or gaseous here on Earth an ice. There will be more astro-babble in the rest of this lesson, which deals with the motion of the planets. You’ll come across it in everything written by Muggles about astronomy, so you might as well get used to it now.
Uranus (left) and Neptune (right).
Source: here
The Motion of the Planets
Revolution of the planets around the Sun
As seen from Earth, it appears as if the Moon, the Sun, the planets, and the stars all revolve around Earth once per day. Back in the days of ancient Greece, this observation led to the geocentric model of the solar system (geocentric meaning “Earth centred,” from the Greek word ‘geos,’ which means Earth), created by Ptolemy, a Greek mathematician, astronomer, and geographer. In this model, the Moon is the closest body to the Earth, followed by Mercury, Venus, the Sun, Mars, Jupiter, Saturn, and finally the fixed stars. Ptolemy studied the movements of the bodies in the sky and noted that the planets moved with respect to the stars. To account for this motion, he assumed that the planets revolved in perfect circles, called epicycles, around a point that, in turn, revolved around Earth in a circle.
Another ancient Greek mathematician and astronomer, Aristarchus of Samos, believed that the Sun, not Earth, was the centre of the solar system. His model is termed “heliocentric,” after the Greek word ‘helios,’ meaning sun. It was deemed impious by the Stoic philosopher Cleanthes, so Aristarchus never published his model. We know about it today only because Archimedes published it, even though he didn’t believe in it. The Polish astronomer Nicolaus Copernicus wrote a book expounding the same model, which was published in 1543, some 18 centuries after Aristarchus did. The heliocentric model wasn’t accepted right away, although it received support from Galileo, who became convinced of its correctness when he observed the phases of Venus, partly because both the Protestant and Catholic Church condemned heliocentrism as being impious and forced him to recant under threat of torture.
The fact that Venus exhibits the full range of phases proves that Ptolemy’s geocentric model was incorrect, because if Venus were always closer than the Sun to Earth than the Sun, it would only ever be in the crescent phase. That said, the phases of Venus do not prove that every geocentric model is wrong. There is a geocentric model, proposed by the pagan Martianus Capella in the fifth century C.E., that is compatible: the Sun, Mars, Jupiter, Saturn, and the stars all revolve around the Earth, but Mercury and Venus revolve around the Sun. Fortunately, Galileo chose to align this observation with the Copernican model, which was later proven to be essentially correct.
But it took some time for it to be accepted by the scientific community for a reason quite apart from religious opposition: there was, in fact, a flaw in his model. Like Ptolemy, Copernicus believed that the planets could only move in circles, so he too introduced epicycles. Later, Tycho Brahe made some extremely accurate observations of the positions of the planets in the sky, which Copernicus’s model couldn’t account for. Then Johannes Kepler studied Brahe’s published observations and proposed an alternative heliocentric model taking them into account. This model was governed by a series of three laws.
Kepler’s First Law states that a planet revolves around the Sun not in a circle but in an ellipse, which is like a flattened (or stretched out) circle, and that the Sun isn’t in the middle of the ellipse but off to one side, as shown in the picture below. Actually, his First Law says exactly where in the ellipse the Sun is: it’s at one of two points in the interior of the ellipse called foci. You don’t need to know the technical specifics of foci in your First Year, but it’s something to look forward to at the N.E.W.T. level.
Kepler’s Second Law states that an imaginary line between the Sun and any planet sweeps out equal areas in equal amounts of time, as shown in the image below. The important thing to note is the implication of this law: a planet will speed up as it approaches the Sun and slow down as it recedes.
Kepler’s Second Law.
Source: here
To introduce Kepler’s Third Law, I need to teach you a bit of mathem … don’t panic; it’s no more difficult than anything I’ve already mentioned, and I’m not going to test you on it - yet. Do you recall what the square of a number is? Multiply a number by itself and you get its square. For example, to get the square of 3, you multiply 3 by 3, and you get 9. Now, multiply the square by the original number and you get its cube. Continuing with the same example, multiply 9 by 3 and you (should) get 27, which is the cube of 3.
Kepler’s Third Law says that if you divide the square of the time it takes for any planet to revolve around the Sun by the cube of the average distance from the planet to the Sun, you get the same answer no matter which planet you choose. Qualitatively speaking, this means that planets that are closer to the Sun move faster than planets that are farther away.
The two images below depict the locations of the inner planets 44 days apart and let you see the implications of all of Kepler’s Laws directly. By examining them, you’ll see that Mars and Mercury don’t travel in circles and that the Sun isn’t in the centre of the paths they take, illustrating Kepler’s First Law. The Second Law is seen from the fact that 44 days is half the time it takes Mercury to revolve around the Sun, and yet the planet has moved just under half way around its orbit, as it is farther away from the Sun during this half. You’ll also note that while Mercury moves almost a full half-revolution around the Sun in this time period, Venus only moves about a quarter, and Mars even less, illustrating the Third Law.
The inner planets.
Source: here
The inner planets 44 days later.
Source: here
Now that I’ve shown you how the planets move, please bear with me while I tell you the names of the various features of the paths they take.
Length of a planet’s orbit = aphelion + perihelion.
Eccentricity of a planet’s orbit (amount by which the Sun is off centre) = (aphelion - perihelion)/length.
Kepler’s Laws describe how the planets move, but not what makes them move in just that way. That problem was solved by the English mathematician, physicist, and astronomer Isaac Newton, arguably the greatest scientist of all time. Among his many discoveries are his three laws of motion, which are as follows:
An object remains at rest or continues to move in a straight line at a constant speed unless acted upon by an outside force.
The force required to make an object change its speed and/or direction of motion is equal to the mass of the object multiplied by the rate of change.
If one object exerts a force on a second object, then the second object will exert the same amount of force on the first one, but in the opposite direction.
Newton reasoned that an unsupported object falls to the ground instead of floating in the air because a force acts on it. If you drop a stone, it will fall straight down. If you throw it horizontally, it will keep moving horizontally but will also fall down until it hits the ground. If you could throw it hard enough, your stone would never hit the ground, but would continue to fall around the curvature of our spherical planet. This same force that causes our stone to fall keeps the Moon from travelling in a straight line away from the Earth. The Moon is moving fast enough that instead of hitting the Earth, it falls continuously around it - its revolution. After careful research and contemplation, Newton concluded that the force that both pulls an unsupported object near the Earth to the ground and holds the Moon in its revolution is exerted by the Earth itself, and he called that force gravity. By similar logic, the Sun must exert a force on the planets to keep them from drifting away, and it is this force that makes a planet speed up as it approaches the Sun and slow down as it recedes. He concluded that every body attracts every other body, and he called that principle the Law of Universal Gravitation.
But how much force does one body exert on another one? The more mass a body has, the more force it will exert on others. However, Galileo had previously shown that a heavy object falls at the same rate as a light one, meaning that the more massive a falling object, the more force the Earth must exert on it to make it fall at the same rate, according to Newton’s Second Law. From Kepler’s laws of motion, Newton also concluded that the farther apart two objects are, the smaller the force will be by an amount equal to the square of the distance between them, and that’s why planets that are closer to the Sun move faster than planets that are farther away. By Newton’s Third Law of Motion, the falling object will exert the same amount of force on the Earth but in the opposite direction. The same holds true for any two bodies, including celestial ones. In fact, the planets, especially Jupiter, do make the Sun wobble a bit. The formula for the amount of force that two objects exert on each other is as follows:
The rotation of the planets
Aside from revolving around the Sun, each planet also rotates about an imaginary line called an axis, which passes through the centre of the planet and intersects the planet’s surface at its two poles. That’s why the Sun, the planets, and the stars all appear to revolve around Earth. There is an imaginary circle around the middle of the planet, equally distant from the poles, called the equator. The plane of the equator is usually tilted relative to the plane of the planet’s orbit. The angle between these planes is called the inclination.
To give you an idea of the variability between the planets, the table below shows the period of revolution, perihelion, aphelion, inclination, and period of rotation of each of the eight planets in addition to the corresponding values for the Moon. The distance between the Sun and a planet is too big to be expressed in kilometers – for Neptune it is several billion kilometers – so another unit is used, called the Astronomical Unit (A.U.), which is the average distance between the Sun and the Earth: 149,597,870.7 kilometers (92,955,807.3 miles).
Does it seem strange that the rotation periods of Venus and Uranus are negative? Their equators are actually inclined more than 90 degrees from their orbits, so they rotate backwards! Does it also seem a bit strange that the period of rotation of the Earth isn’t exactly one day? While Earth makes one full rotation, it also moves a bit around the Sun; consequently, it has to rotate a little more before the Sun gets to the same place in the sky and a full day has passed!
Since this lesson is so long, there will not be an essay today, just the usual ten-question quiz. Additionally, you will not be tested on the most difficult concepts of the day - yet.
