PHYS1160 Lesson Plan

Lesson 2 - What physics is important to astronomy? The basic physics required for understanding astronomy.

Lesson learning outcomes:

By the end of this lesson, you should be able to:

1.   Explain key physics concepts, such as speed, velocity, acceleration,  mass, weight, and motion (such as travelling in a circle).

2.   Compare and contrast Newton’s laws of motions and Kepler’s laws, and their effects on astronomical objects.

3.   Describe how tides on Earth work.

4.   Explain key concepts of matter, including changes in phases and energy levels.

5.   Explain spectra, thermal radiation, and the Doppler effect, and relate them to astronomy .

2.1 Introduction – describing motion – gravity, force, mass

Acceleration and gravity

When we think of terms that we use to describe motion, we can think of a car travelling along a road. The speed of the car tells us how far it will travel in a certain time period. The velocity of the car tells us its speed and direction. The acceleration of the car tells us whether the car is changing velocity because acceleration is defined as a change in velocity. Acceleration is either positive (velocity is increasing) or negative (decelerating, velocity is decreasing).

The acceleration due to gravity is something that we observe in daily life. When you drop objects and they hit the ground, the object is accelerating at a rate that is equal to the acceleration due to gravity, or 9.8 m/s^2. If you drop two objects of the same mass, they will have the same acceleration, e .g., 100 kg bag of feathers and a 100 kg rock. The reason that we usually don’t observe this in real life is due to air resistance, but for objects either in a vacuum (the air particles have been removed) or that have similar air resistance, we do observe this phenomenon.

Momentum and force

An object’s momentum is related to its velocity and mass (specifically, it is the product of its velocity and mass), and the momentum of an object changes when either its velocity or mass change. A classic example showing a change in an object’s momentum is a car collision. A car has a particular momentum as it approaches an obstacle (since it has both mass and a non-zero velocity). Once the car collides with the obstacle, there is a significant force that the car imparts onto the obstacle, and due to the conservation on momentum, momentum is imparted as well. Force is related to an object’s mass and acceleration (it is defined as the product of mass and acceleration).

Forces are present all of the time, even if there is no change in velocity or momentum. In fact, when opposite forces cancel, such as the force due to your body weight on a chair and the force of the chair pushing back at you (we will talk about this more later on), then we say that the net force is zero.

We apply similar ideas to objects in orbit. An orbiting object is constantly changing its direction, which means that there must be a force acting on the object (remember, changing direction counts as changing velocity).

Mass and weight

Mass is the amount of matter in your body, whereas weight is the force that you impart on the ground due to your mass and is given by your mass multiplied by the acceleration due to gravity. Weight is measured in Newtons and mass is measured in kg, therefore, when you stand on a set of bathroom scales, you are measuring your mass, not your weight.

Weightlessness

Imagine you are skydiving. If you were to stand on a set of bathroom scales (very difficult to achieve!) while falling, you would notice that the scales read 0. It is clear that this is not because there is no gravity (otherwise you wouldn’t be falling!) or that your mass is zero; it is because you are accelerating towards the Earth.

This is the same as what happens in space. There is a misconception that there is no gravity in space, especially if we think about astronauts floating around on the Space Station, but in this scenario, it is not true. The astronauts are free- falling, which is why they float. Additionally, they don’t crash into the Earth because they are travelling so fast .

There are a couple of cool TED-Ed Animations related to this:

Gravity and the human bodyTED-EdAnimation!

Free falling in outer spaceTED-EdAnimation!

2.2 Newton’s Laws of Motion

Newton published three laws of motion. These are:

1)   Objects move at a constant velocity if there is no net force acting on them.

Recall our discussion earlier regarding the concept of net force. This law doesn’t mean that there are no forces acting on the object, it just means that all of the forces are balanced. And if they are, then the object that is at rest will remain at rest, or an object that is travelling at a constant speed will continue to do so. Objects at rest remaining at rest makes sense, but what about travelling objects? This law suggests that a car travelling along a highway at a constant speed will continue to do so even if you take your foot off the accelerator, but we know this isn’t the case. Why? It’s because the car also has air resistance and friction acting upon it . This law explains why spacecraft do not need fuel to travel long distances (once they are significantly far away from Earth’s gravitational effect).

2)   Force is the product of mass and acceleration and is also the rate of change of momentum.

This law not only explains the force of gravity (and the difference between mass and weight), but also why two objects that have the same force exerted on them will accelerate by difference amounts if their masses are different. Think about throwing a tennis ball and throwing a bowling ball. The bowling ball is a lot heavier, therefore exerting the same force to move it will mean that it has a lower acceleration than the tennis ball.

This law also explains why objects that are travelling in a circle experience a force (or an acceleration towards the centre of the circle).

Figure 4.7 from The Cosmic Perspective.

3)   For any force, there is an equal and opposite reaction force.

We touched on this law earlier (recall the chair example, where the chair exerted a force back onto you when you sat on it). This law is also very important for the study of astronomy, because it tells us that objects always attract each other via the gravitational force. For example, since we have mass, we exert a gravitational force onto the Earth, just like the Earth does to us. Since our mass is much smaller than the Earth’s, the gravitational force we exert is much, much smaller. This law also explains how rocket launches work; rockets do not push off the ground, they expel hot gas backwards, which in turn produces an equal and opposite force in the opposite direction.

2.3 Energy

Conservation of momentum

How does the Earth continually orbit the Sun? We touched on the conservation of momentum previously. Here, we are considering the conversation of angular momentum. This sounds complicated, but it is not particularly difficult. Objects that are in orbit have angular momentum because they are moving in circles.

It means that bodies in orbit will remain in the stable orbit that they are in, and bodies with larger orbital distances (higher radius of arc) will move slower in their orbits than those bodies with smaller orbital distances (we will talk about this later on!).

This concept also why the Earth continues to rotate on its axis. Provided that the Earth isn’t transferring its momentum to another object, it will keep rotating at the same rate. In reality, the Earth’s rotation rate is decreasing because it is gradually transferring its angular momentum to the Moon.

Conservation of energy and basic types of energy

Just like momentum and angular momentum, energy cannot be created nor destroyed. So where do objects get energy from? There are three basic types of energy. The unit of energy is the Joule.

1)   Kinetic energy .

This is the energy of motion. Falling objects, orbiting objects, and molecules moving in the air are examples of objects with kinetic energy.

Thermal energy is also a form of kinetic energy . Thermal energy is the collective kinetic energy of many particles moving around randomly within a substance. In astronomy, we use the Kelvin scale to measure temperature.

The density of particles also plays a part in thermal energy. Take, for example, an oven at 200 C and water at 100 C. The density of water molecules is much higher than the air particles inside the oven, which means that if you place your hand in both the oven and water, you get burned much more significantly in the water than if you put your arm in the oven. Another example is water at 100 C and steam at 100 C. Steam will burn you much more significantly than water at the same temperature, because the particles have more space to traverse and can travel faster but with the combined effect that on contact with the skin, the gaseous water particles will become water and in the process, release a lot of energy. Even though the density is lower, it is not so low such that the effect is negligible, like the oven.

It is useful to remember that temperature is measure of the kinetic energy of particles, whereas heat is the transfer of energy.

2)   Radiative energy.

Radiation is often used synonymously with “light” . Light, or electromagnetic radiation, carries energy.

3)   Potential energy.

This is stored energy and can be converted to either kinetic energy or radiation. For example, a rock balancing on a ledge has potential energy, because it will be converted to kinetic energy when it falls.

2.4 The Universal Law of Gravitation

Newton expressed the force of gravity mathematically with the universal law of gravitation. The law is neatly described by a formula, however, it can also be described conceptually. The law shows that every mass attracts every other mass and the way we describe the attraction is the force of gravity. The strength of the gravitational force between two objects is directly proportional to the product of their masses, and it also decreases with the square of the distance between their centres of mass.

You might remember Kepler’s laws from earlier. Well Newton’s law of gravitation just extends upon those laws. How? Well, here are Kepler’s laws:

Kepler's 1st law:  The planets move in elliptical paths with the Sun at one focus.

Kepler's 2nd law:  (The law of areas) The line between the planet and the Sun sweeps out equal areas in equal times. Kepler's 3rd law: The square of the orbital period of the planet is proportional to the cube of the semi-major axis of the orbit.

Figure 4.19 from The Cosmic Perspective.

Kepler’s first law can be explained by the fact that one object does not orbit the other (e.g., we don’t orbit the Sun), but rather, both objects orbit the centre of mass, which is at one of the foci of the elliptical orbit . The conversation of angular momentum shows that planets orbiting further out will travel slower in their orbital path compared to planets orbiting closer.

In fact, the universal gravitation law shows that planets are not the only objects with elliptical orbits. Any object orbiting another will orbit the centre of mass and therefore have an elliptical orbit.

2.5 Orbital energy

A planet’s orbital energy still satisfies the law of conservation of energy, because it is the combination of several different types of energies. What types? Well, there is kinetic energy because the planet is moving, but also potential energy because if the planet stopped moving it would fall towards the central mass.

Do these energies stay constant throughout the orbit? No! We know this because the orbit is elliptical and the velocity of the planet changes with distance from the central mass. If it is isolated (as in, no other object causes the orbit to change), then the planet will not lose energy during its orbit and its orbital energy will be conserved.

Figure 4.21 from The Cosmic Perspective.

What happens when objects encounter each other in space?

In this case, objects can exchange orbital energy via a gravitational interaction/encounter. It’s useful to remember that the energy exchange is the same, but its effect will be much more noticeable for a low mass object compared to a high mass object. Take as an example the New Horizons spacecraft en route to Pluto. New Horizons was deliberately sent past Jupiter to change its trajectory and gain energy. Jupiter lost the same amount of energy during the encounter, but due to its very large mass, the effect was negligible.

Atmospheric  drag  can also alter the  orbit  of an object.  For example,  satellites  in  low-Earth  orbit,  including  the International Space Station, experience drag and friction from the Earth’s upper atmosphere, causing it to lose energy and enter lower orbits. Some of this energy can be converted to thermal energy also, which contributes to the increase in temperature of objects falling through the atmosphere. TheISS needs regular booststo ensure that atmospheric drag does not cause it to come back to the Earth’s surface.

If we want to escape Earth’s gravity and leave orbit (making the orbit “unbound”, as opposed to “bound”, i.e., elliptical), then we need to reach what is called the escape velocity. Recall earlier how we said that to get into orbit in the first place, you needed to increase your horizontal velocity. The concept is similar here, however, we need to increase it even further. To send rockets to the Moon or Mars, we need to convert the chemical energy of the fuel into the orbital energy of the rocket such that its velocity exceeds 11 km/s, which is the escape velocity of the Earth. Note that this doesn’t depend on the mass of the object trying to reach escape velocity (a rocket in this case), but it does depend on where the object is trying to exit from (upper atmosphere vs. the surface).

2.6 Tides and tidal forces

We learnt earlier that the strength of gravity decreases as the inverse of the distance squared, meaning, in the most basic of terms, that gravity becomes weaker with increasing distance. You might think that this works just for planets at different distances, but it also works on a single planet or moon. Think about the Moon around the Earth. They both feel a gravitational force between them due to the other. For example, the side of the Earth and Moon that are closest to each other will feel a stronger gravitational force between them given that their distance is shorter than, say, if we were to consider the opposite sides. This difference in gravitational force across a body creates a stretching or tidal force, which essentially “flattens” the Earth and Moon just a little bit! Tidal forces can be strong enough to cause changes in the shape of a small moon, and we will learn about this later on.

True or false: tides are created by the Moon pulling the Earth’s oceans towards it. Well, it’s partly true. We would only have one high tide per day if that were the case. However, we actually have two high tides per day. What is causing it? Earth must be stretching from its centre in both directions (toward and away from the Moon). This tidal force arises from the difference in the force of gravity attracting different parts of Earth to the Moon.

The Sun also exerts a gravitational force on the Earth that results in a tidal force, but you might be surprised to learn that although the Sun is more than a million times the mass of the Moon, it is so much farther away from the Earth than the Moon that its gravitational force on the Earth is about half that of the Moon.

You might have heard the terms “spring” and “neap” tides. Spring tides occur when the Sun and Moon work together along the same axis (full and new moons), whereas neap tides occur at first- and third-quarter moons.

Optional extra – Tidal friction

We spoke about tidal forces before. The story is a bit more complicated than how it was described. The effect that tidal forces have on an object is tidal friction. In the Earth-Moon system, the Earth bulges (due to tidal forces from the Sun and Moon) but it also continues to rotate. As it rotates, the Moon’s gravity tries to pull the “bulges” back to be along the Earth-Moon line, creating a competition between the two phenomena. This has two important effects: first, it actually tends to slow the Earth’s rotation, and second, it simultaneously pulls the Moon ahead in its orbit a little bit. As the Earth loses rotational energy, the Moon gains orbital energy and slowly moves further away from the Earth.

Figure 4.27 from The Cosmic Perspective.

The same effect described above works the other way too; the Moon has tidal bulges due to the gravitational attraction with the Earth. In fact, this is what causes the synchronous rotation of the Moon (i.e., the phenomenon where only one side of the Moon faces the Earth at all times). Challenge yourself to describe how this works.

2.7 Matter

Atoms are made of particles called protons (positively charged particles in the nucleus), neutrons (neutrally charged particles in the nucleus), and electrons (negatively charged particles surrounding the nucleus). The nucleus is incredibly small in size; however, it contains most of an atom’s mass given that protons and neutrons, which are roughly equal in mass, are around 2000 times more massive than an electron.

Electrical charge is a physical property that will dictate how strongly an object is going to interact with electromagnetic fields, and total electrical charge is always conserved. The charge of a proton is the basic unit of positive charge (+1), whereas the electron is the basic unit of negative charge (- 1). The strong force holds positively charged protons together in the nucleus. Electrons exist around the nucleus as a “cloud” (in that we can’t pinpoint their positions), and this cloud would be several kilometres in diameter if your fist was the size of a nucleus.

Elements are determined by the number of protons in their nucleus, and we call this number the atomic number. The combined number of protons and neutrons is called the atomic mass number. You might already know that there can be different versions of the same element. Although the number of protons in the nucleus remains constant, the number of neutrons can change (and this won’t change the charge of the atom either). The same chemical element but with different numbers of neutrons are called isotopes.

Molecules are formed when atoms combine, and this can either be atoms that are the same chemical element or different. Molecules with two or more types of chemical elements are called compounds.

2.8 Phases

We are all familiar with the main phases of matter: solid, liquid, and gas. Atoms and molecules change their behaviour in each of these phases due to the chemical bonds changing. There is more than one way to cause an element or molecules to change phase, but we will start with the most common, which is temperature changes causing phase changes.

Temperature

Let’s consider phase changes due to temperature changes by considering water. First, we will consider water in the form of ice (a solid).

At very low temperatures, the water molecules have a low average kinetic energy that allows them to bind to their neighbours in a solid structure. The molecules are still vibrating despite being in a solid structure. As temperatures rise, the vibrations become stronger. Eventually, the temperature will rise to the melting point of the substance (water, in this case).

At the melting point, the solid ice bonds are broken, and the molecules can freely move around one another. At this point, the substance has become a liquid. We know though that the molecules in a liquid still aren’t completely free; there is still a bond that connects them. You can visualise this bond by thinking of the surface tension of liquid. Some liquids, water especially, have very strong liquid bonds (in water’s case, thanks to hydrogen bonding) that creates high surface tension.

As temperatures rise, the kinetic energy of the molecules will be enough to break all bonds, and the molecules will be able to move freely. It is at this point that the substance has reached its boiling point and has become a gas .

Something that might be contradictory to think about though is the presence of clouds; Earth’s atmosphere must contain water vapour so that it can condense to form clouds and rain. But Earth’s atmosphere is not above the boiling point of water, so what is happening? Well, a few things, but a major contributor is the fact that temperature is a measure of the average kinetic energy of particles. This means that there will be particles that have kinetic energies significantly below the average and some particles with energies significantly above. In fact, water vapour is always present alongside solid ice and liquid water. The process of changing a liquid to a gas is called evaporation. From solid to gas (with no liquid phase) is called sublimation. With higher temperatures come higher rates of sublimation and evaporation.

Let’s not stop at the gas phase though. What happens if we keep increasing the temperature far beyond the boiling point? As we said earlier, as the temperature of a substance rises (the kinetic energy of particles increases), the particles move faster. They  are also  colliding with each other  and the  collisions  become  more energetic with  increasing temperature. Eventually, collisions are so energetic that molecules can break apart into their constituent components (for water, this is H+ and OH- initially. The OH- eventually breaks into individual O and H atoms). This is called molecular dissociation.

Raising temperatures even further results in a process called ionisation, where collisions can “strip” electrons off atoms. Ionisation produces charged atoms due to the removal of negative electrons, and the resulting charged atom (either positive or negative) is called an ion. Atoms can be singly ionised (one electron has been removed), doubly ionised (two electrons), etc., until all of the outer electrons have been removed and the atom is fully ionised.

Pressure

We will now talk about the effect that pressure has on the change of phases of substances. Pressure, which is a force per unit area, is around us in our everyday lives. It is also vital in the processes that occur on Earth. Consider Earth’s iron core; the  pressure  is  incredibly  high due to the  mass of all  of the  material surrounding  it, so even though temperatures are high enough to melt the core, it remains solid due to the pressure. Also consider diving into the ocean. The deeper you dive, the more pressure is exerted on your body due to the weight of the water above you. In fact, even on the Earth’s surface, there is a pressure on you due to the weight of the atmosphere, and this is actually given the unit 1 atm (atmosphere) at sea level.

The amount of water vapour that condenses into liquid water is directly related to the amount of water vapour that exists in the atmosphere, or rather, the pressure due to the water vapour in the air is related to the amount that condenses, and this is the law of partial pressures. You might have heard that the boiling point decreases when you’re on the top of a mountain, and this makes sense. The pressure due to the atmosphere is significantly less at high altitudes, the pressure due to water vapour is low, and the water evaporates at lower temperatures. This also explains why liquid water does not exist on bodies like the Moon or Mars, which have essentially no atmosphere.

2.9 Light

Perhaps it has not crossed your mind before, but have you ever considered how we know what we do about the universe? How do we actually do the science of astronomy? Until modern day telescopes and techniques allowed us to observe objects across a large range of the electromagnetic spectrum, all ancient astronomy (and a large portion of modern astronomy!) is done by observing light. We will talk more about telescopes, but let’s have a closer look at light.

Light is an electromagnetic wave that carries energy (recall that we touched on this earlier). The unit of measurement for energy is the Joule . If you think about the light bulbs in your house though, you’ll notice another unit called the Watt. It is a measurement of power of a light source, and this is the rate of energy transfer per second. E.g., a 100 W light bulb requires 100 J of energy per second it is turned on.

Visible light, the colours we see, are just one small portion of what we call the electromagnetic spectrum. A prism will split white light into the colours of the rainbow. Black is the absence of light.

Interaction of light

The way that light interacts with objects is really important for our understanding of astronomy. Light interacts with matter in multiple ways, being:

1)   Emission. Objects emit light, such as a light bulb.

2)   Absorption. Objects absorb light, such as when your hand is warmed when placed near a light bulb.

3)   Transmission. Light is transmitted through objects, namely transparent objects such as glass.

4)   Reflection and scattering. Light is reflected off objects rather uniformly, such as a mirror, or scattered in random directions, such as everyday objects.

Basics of light

You might have heard that light is both a particle and a wave, and indeed, it does exhibit characteristics of both particles and waves. The basic properties of light are the wavelength, frequency, speed, and amplitude. The wavelength is the distance from one peak to the next (or one trough to the next). The wavelength of red light is around 700 nanometres (nm), and for violet light 400 nm. The frequency of the wave is the number of peaks/troughs passing a point each second. The speed of the wave is the distance a particular point on the wave travels in a given time period. The amplitude of the wave is the half height from trough to peak and tells us the brightness of the light .

We have said that light is an electromagnetic wave, but what does this actually mean? It means that light is a combination of two fields: electric fields and magnetic fields. You might have heard of one, both, or none of these terms before. For this unit, it is not important that you know what they are in great detail, but to understand what we mean when we use these terms, recall before that we were talking about gravity. You can think of the Earth creating a gravitational field, which describes the strength of Earth’s gravity at varying distances. Similarly, electric fields and magnetic fields describe the strengths of electric and magnetic forces. Earth has a magnetic field produces by the iron core, which we utilise when we use compasses (they point to geographic north, or magnetic south).

Light travels through space at the speed of light, (around 300,000 km/s) and light, unlike some waves, do not need a medium to travel along.  Interesting relationships between all of the properties of light include that the longer the wavelength, the lower the frequency, and vice versa. We say that light comes in the form of individual pieces called photons.

Electromagnetic spectrum

As we said earlier, there is more radiation that spans beyond the visible part of the electromagnetic spectrum.

Figure 5.7 from The Cosmic Perspective.

In the figure above, we can see the common cosmic sources for electromagnetic radiation of different wavelengths. Note that there is also another energy unit listed above, called the electron volt, which is related to Joules.

2.10 Energy in atoms

We know that when light interacts with matter, things happen. We also know that we can learn about distant objects by observing the light that is coming from those objects. But there are a few missing pieces of the puzzle. When discussing light previously, we mentioned that there are a few ways that light interacts with matter. Specifically, these are: emission, absorption, transmission, and reflection/scattering. But what do these mean physically?

Atoms need to transform the energy contained within them to electric and magnetic fields (electromagnetic waves, or light). The answer is in the electrons: the electrons interact with photons of light. This begins to stray into the realm of quantum physics, but we won’t be getting too detailed.

Atoms contain energy through their mass-energy (Einstein’s famous E = mc^2 equation describes this!), kinetic energy through their movement, and electrical potential energy through their arrangement of the electrons around the nucleus.

You might have heard the term “quantised” when looking at energy levels of electrons around atoms. If you haven’t, that’s okay, we are going to talk about it now. As we said before, there is an energy stored in the way that electrons are arranged around the nucleus of an atom, and interestingly, the energy that electrons have can only have discrete (or quantised) amounts. The way to think about this is when you climb a ladder; you can only stand on the steps, not in between. The possible (or allowed) energies are called the energy levels of the atom. The lowest possible energy is the ground state, with higher states being those with higher energy (NOT physically more distant from the nucleus!).

Electrons can transition between energy levels by gaining or losing the exact difference in energy between two levels (they do not need to be adjacent levels). The gain or loss in energy comes in the form of a photon that has the exact energy required by the electron.

2.11 Light and astronomy: Spectra

You’ve heard the word “spectrum” before when we were discussing the electromagnetic spectrum. We are going to be looking  at  something  similar  here,  but when we  refer  to “spectrum”  or “spectra”  (plural), we  are  referring  to  a representation of the intensity of electromagnetic radiation at different wavelengths.

Visible spectrum of the Sun,NASA.

The process of obtaining spectra is called spectroscopy . You can obtain spectra for many objects; however, we are going to focus on astronomical objects . There are different types of spectra that are based upon the ways that light interacts with matter. We will consider the below spectrum in our discussion.

The first type of spectrum is the continuous spectrum (blue to infrared in the image above). If there are no interruptions in the spectrum (and it is continuous), it suggests that the light has been emitted from the object and has arrived to us uninterrupted.

Emission spectra (ultraviolet in the image above) typically arise from low-density gas clouds. The atoms are continuously colliding with each other and sometimes these collisions transfer enough (and the right amount of!) energy to atoms such that an electron will undergo a transition to a higher energy level. The electron does not stay in the higher energy level state for long and will release a photon when it transitions to a lower energy level (this happens in a fraction of a second, so essentially immediately). The wavelengths that these occur at will be observed in the emission spectrum.

Interesting fact: the transitions between particular levels of hydrogen atoms have specific names. E.g., the transition between level 1 and other levels is called the Lyman series, with Lyman alpha being between levels 1 and 2, Lyman beta for levels 1 and 3, etc. Transitions between level 2 and other levels is the Balmer series.

Absorption line spectra (infrared in the image above) are typically observed when our view of a light source is obstructed by a cool gas cloud. Depending on the composition and temperature of the gas cloud, photons with specific energies (i.e., specific wavelengths) will be absorbed by the atoms in the cloud, resulting in a dark line in the spectrum. Even though the photons are then re-emitted, they are done so in random directions, meaning that the dark lines are still present .

Chemical “fingerprints”

Above we described the transitions between energy levels in hydrogen atoms and even earlier than that, we said that “there is an energy stored in the way that&