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Backup: Get to know Maxwell’s Equations

This is a backup of an article on Wired,’Get to know Maxwell’s Equations – You’re Using Them Right Now,” by Rhett Allain , 8/6/19

Maxwell’s equations are sort of a big deal in physics. They’re how we can model an electromagnetic wave—also known as light. Oh, it’s also how most electric generators work and even electric motors. Essentially, you are using Maxwell’s equations right now, even if you don’t know it. Why are they called “Maxwell’s equations”? That’s after James Clark Maxwell. He was the 19th-century scientist who sort of put them together, even though many others contributed.

There are four of these equations, and I’ll go over each one and give a conceptual explanation. Don’t worry, you won’t need to refresh your calculus skills. If you do want to follow the math, let me point out that there are two different ways to write these equations, either as integrals or as spatial derivatives. I’ll give both versions—but again, if the math looks uninviting, just ignore it.

Gauss's law Maxwell


The short version is that Gauss’ law describes the electric field pattern due to electric charges. What is a field? I like this description – “It’s an energy field created by all living things. It surrounds us, penetrates us, and binds the galaxy together.”

Oh wait. That was Obi Wan’s description of the Force in Star Wars Episode IV. But it’s not a terrible description of an electric field. Here is another definition (by me):

If you take two electric charges, there is an interaction force between them. The electric field is the force per unit charge on one of those charges. So, it’s sort of like a region that describes how an electric charge would feel a force. But is it even real? Well, a field can have both energy and momentum—so it’s at least as real as those things.

Don’t worry about the actual equation. It’s sort of complicated, and I just want to get to the idea behind it. (If you have seen this physics equation before, you might think I am going to go into electric flux, but let’s see if I can do this with “no flux given.”) So let’s just say that Gauss’ law says that electric fields point away from positive charges and towards negative charges. We can call this a Coulomb field (named after Charles-Augustin de Coulomb).

coulomb field
Everyone knows that positive charges are red and negative charges are blue. Actually, I don’t know why I always make the positive red—you can’t see them anyway.

Also, you might notice that the electric field due to the negative charges looks shorter. That’s because those arrows start farther away from the charge. One of the key ideas of a Coulomb field is that the strength of the field decreases with distance from a single point charge.

But wait! Not all electric fields look like this. The electric field also follows the superposition principle. This means that the total electric field at any location is the vector sum of the electric field due to whatever point charges are nearby. This means you can make cool fields like the one below, which are the result of two equal and opposite charges (called a dipole).

And here’s the Python code I used to create it.  https://trinket.io/glowscript/18196b0cf1

dipole E field
This dipole field is going to be important for the next equation.

Gauss's law Maxwell

Yes, this looks very similar to the other Gauss’ law. But why isn’t the previous equation called “Gauss’ law for electri­cism”? First, that’s because “electricism” isn’t a real word (yet). Second, the other Gauss’ law came first, so it gets the simple name. It’s like that time in third grade when a class had a student named John. Then another John joined the class and everyone called him John 2. It’s not fair—but that’s just how things go sometimes.

OK, the first thing about this equation is the B. We use this to represent the magnetic field. But you will notice that the other side of the equation is zero. The reason for this is the lack of magnetic monopoles. Take a look at this picture of iron filings around a bar magnet (surely you have seen something like this before).

This looks very similar to the electric field due to a dipole (except for the clumps of filings because I can’t spread them out). It looks similar because it is mathematically the same. The magnetic field due to a bar magnet looks like the electric field due to a dipole. But can I get a single magnetic “charge” by itself and get something that looks like the electric field due to a point charge? Nope.

iron filings bar magnet dipole

Here’s what happens when you break a magnet in half. Yes, I cheated. The picture above shows two bar magnets. But trust me—if you break a magnet into two pieces, it will look like this.

broken iron filings bar magnet dipole

It’s still a dipole. You can’t get a magnetic field to look like the electric field due to a point charge because there are no individual magnetic charges (called a magnetic monopole). That’s basically what Gauss’ law for magnetism says—that there’s no such thing as a magnetic monopole. OK, I should be clear here. We have never seen a magnetic monopole. They might exist.

Faraday’s law

Faraday's law

The super-short version of this equation is that there is another way to make an electric field. It’s not just electric charges that make electric fields. In fact, you can also make an electric field with a changing magnetic field. This is a HUGE idea as it makes a connection between electric and magnetic fields.

Let me start with a classic demonstration. Here is a magnet, a coil of wire, and a galvanometer (it basically measures tiny electric currents). When I move the magnet in or out of the coil, I get a current.

If you just hold the magnet in the coil, there is no current. It has to be a changing magnetic field. Oh, but where is the electric field? Well, the way to make an electric current is to have an electric field in the direction of the wire. This electric field inside the wire pushes electric charges to create the current.

But there is something different about this electric field. Instead of pointing away from positive charges and pointing towards negative charges, the field pattern just makes circles. I will use the name “curly electric field” for a case like this (I adopted the term from my favorite physics text­book authors). With that, we can call the electric field made from charges a “Coulomb field” (because of Coulomb’s law).

Here is a rough diagram showing the relationship between the changing magnetic field and an induced curly electric field.

induced curly electric field magnetic field

Note that I am showing the direction of the magnetic field inside of that circle, but it’s really the direction of the change in magnetic field that matters.


Ampere-Maxwell Law

Do you see the similarity? This equation sort of looks like Faraday’s law, right? Well, it replaces E with B and it adds in an extra term. The basic idea here is that this equation tells us the two ways to make a magnetic field. The first way is with an electric current.

Here is a super-quick demo. I have a magnetic compass with a wire over it. When an electric current flows, it creates a magnetic field that moves the compass needle.

It’s difficult to see from this demo, but the shape of this magnetic field is a curly field. You can sort of see this if I put some iron filings on paper with an electric current running through it.

current thru wire creates B field

Maybe you can see the shape of this field a little better with this output from a numerical calculation. This shows a small part of a wire with electric current and the resulting magnetic field.

magnetic field created by electric current in wire

Actually, that image might seem complicated to create but it’s really not too terribly difficult. Here is a tutorial on using Python to calculate the magnetic field. There is another way to create a curly magnetic field—with a changing electric field. Yes, it’s the same way a changing magnetic field creates a curly electric field. Here’s what it would look like.

changing magnetic field creates a curly electric field

Notice that I even changed the vector colors to match the previous curly field picture—that’s because I care about the details. But let me just summarize the coolest part. Changing electric fields make curly magnetic fields. Changing magnetic fields make curly electric fields. AWESOME.

What About Light?

The most common topic linked to Maxwell’s Equations is that of an electromagnetic wave. How does that work? Suppose you have a region of space with nothing but an electric field and magnetic field. There are no electric charges and there isn’t an electric current. Let’s say it looks like this.

E field and B field in empty space

Let me explain what’s going on here. There is an electric field pointing INTO your computer screen (yes, it’s tough dealing with three dimensions with a 2D screen) and a magnetic field pointing down. This region with a field is moving to the right with some velocity v.

What about that box? That’s just an outline of some region. But here’s the deal. As the electric field moves into that box, there is a changing field that can make a magnetic field. If you draw another box perpendicular to that, you can see that there will be a changing magnetic field that can make a magnetic field. In fact, if this region of space moves at the speed of light (3 x 108 m/s), then the changing magnetic field can make a changing electric field. These fields can support each other without any charges or currents. This is an electromagnetic pulse.

An electromagnetic wave is an oscillating electric field that creates an oscillating magnetic field that creates an oscillating electric field. Most waves need some type of medium to move through. A sound wave needs air (or some other material), a wave in the ocean needs water. An EM wave does not need this. It is its own medium. It can travel through empty space—which is nice, so that we can get light from the sun here on Earth.


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Astronomical engineering: a strategy for modifying planetary orbits

How’s this for an idea for a science-fiction story?

The sun has unexpectedly started to swell into a red giant – which would engulf and destroy the Earth. So, “to save humanity, the world’s governments have banded together and constructed thousands of rocket engines across the Earth’s surface. Once installed, they propel the planet out of its solar system and onto a 2,500 year journey to resettle in Alpha Centauri.” (Grant Watson.)

The Wandering Earth (Chinese: 流浪地球) is a 2019 Chinese science fiction film directed by Frant Gwo, loosely based on the novella of the same name by author Liu Cixin. Here’s an image of one of the many “Earth Engines.”

The Wandering Earth Movie (Engine)

Our question – Could this be done in real life?

What science in the film did they get right or wrong?

Helium flash

thrusting the Earth out of orbit with rockets

How much mass would we need to do this?

Even if you could build engines large enough, mining the Earth (as these engines do in the film) causes a problem. There would barely be any Earth left by the point you mined enough dirt to thrust the planet to Proxima Centauri, 4.2 light-years away. “It would take about 95 percent of the mass of Earth to do this,” Elliott estimates.

Stopping the rotation of the Earth?

Gravitational slingshot around Jupiter

Surviving the radiation around Jupiter

Could ‘The Wandering Earth’ Actually Happen? Here’s What a NASA Engineer Says

Wandering Earth: Rocket scientist explains how we could move our planet. ARS Technia

Other options

Move human civilization to Mars, which become habitable

In principle, how could we actually move the Earth?

Astronomical engineering: a strategy for modifying planetary orbits
D. G. Korycansky, Gregory Laughlin, Fred C. Adams (7 Feb 2001)

The Sun’s gradual brightening will seriously compromise the Earth’s biosphere within ~ 1E9 years. If Earth’s orbit migrates outward, however, the biosphere could remain intact over the entire main-sequence lifetime of the Sun.

In this paper, we explore the feasibility of engineering such a migration over a long time period. The basic mechanism uses gravitational assists to (in effect) transfer orbital energy from Jupiter to the Earth, and thereby enlarges the orbital radius of Earth.

This transfer is accomplished by a suitable intermediate body, either a Kuiper Belt object or a main belt asteroid. The object first encounters Earth during an inward pass on its initial highly elliptical orbit of large (~ 300 AU) semimajor axis. The encounter transfers energy from the object to the Earth in standard gravity-assist fashion by passing close to the leading limb of the planet. The resulting outbound trajectory of the object must cross the orbit of Jupiter; with proper timing, the outbound object encounters Jupiter and picks up the energy it lost to Earth.

With small corrections to the trajectory, or additional planetary encounters (e.g., with Saturn), the object can repeat this process over many encounters. To maintain its present flux of solar energy, the Earth must experience roughly one encounter every 6000 years (for an object mass of 1E22 g). We develop the details of this scheme and discuss its ramifications.


As for the Moon, reasoning by analogy with cases of stellar binaries and third-body encounters suggests that the Moon will tend to become unbound by encounters in which O passes inside the Moon’s orbit. (As well, there is the non-zero probability of collisions between O and the Moon, which must be avoided.) Again, detailed quantitative work needs to be done, but it seems that the Moon will be lost from Earth orbit during this process. On the other hand, a subset of encounters could be targeted to “herd” the Moon along with the Earth should that prove necessary.

It has been suggested (cf. Ward and Brownlee, 2000) that the presence of the Moon maintains the Earth’s obliquity in a relatively narrow band about its present value and is thus necessary to preserve the Earth’s habitability. Given that the Moon’s mass is 1/81 that of the Earth, a similarly small increment of the number of encounters should be sufficient to keep it in the Earth’s environment.

The fate of Mars in this scenario remains unresolved. By the time this migration question becomes urgent, Mars (and perhaps other bodies in the solar system) may have been altered for habitability, or at least become valuable as natural resources. Certainly, the dynamical consequences of significantly re-arranging the Solar System must be evaluated. For example, recent work by Innanen et al. (1998) has shown that if the Earth were removed from the Solar System, then Venus and Mercury would be destabilized within a relatively short time. In addition, the Earth will traverse various secular and mean-motion resonances with the other planets as it moves gradually outward. A larger flux of encounters might be needed to escort the Earth rapidly

Journal reference: Astrophys.Space Sci.275:349-366,2001
Astronomical Engineering: A Strategy For Modifying Planetary Orbits, Springer Link
Cite as: arXiv:astro-ph/0102126
(or arXiv:astro-ph/0102126v1 for this version)

Physics teaching methods

www.physport.org Teaching Methods

Flipped classroom

The flipped classroom intentionally shifts instruction to a learner-centered model. Students take responsibility to learn the content at home, usually through video lessons prepared by the teacher or third parties, and readings from textbooks.  In-class lessons include activity learning, homework problems, using manipulatives, doing labs, presentations, project-based learning, skill development, etc.

An early example of this was called Peer Instruction by Harvard Professor Eric Mazur, in the early 1990s.


Physlets (Physics apps, flash, JAVA, HTML5)

Any interactive computer simulations for teaching and learning physics, chemistry, math, and other sciences. They help make the visual and conceptual models of expert scientists accessible to students.


PhET Interactive Simulations

PhET are modern, refined Physlets. A suite of research-based interactive computer simulations for teaching and learning physics, chemistry, math, and other sciences. They are animated, interactive, and game-like environments where students learn through exploration. They emphasize the connections between real-life phenomena and the underlying science, and help make the visual and conceptual models of expert scientists accessible to students.


Teaching with Clickers/Classroom response systems

A classroom response system (sometimes called a personal response system, student response system, or audience response system) is a set of hardware and software that facilitates teaching activities such as the following.

  • A teacher poses a multiple-choice question via an overhead or computer projector.
  • Each student submits an answer to the question using a clicker.
  • Software collects the answers and produces a bar chart showing how many students chose each of the answer choices.
  • The teacher makes “on the fly” choices in response to the bar chart.


Ranking Task Exercises in Physics

Conceptual exercises that challenges readers to make comparative judgments about a set of variations on a particular physical situation. Exercises encourage readers to formulate their own ideas about the behavior of a physical system, correct any misconceptions they may have, and build a better conceptual foundation of physics.


Interactive Lecture Demonstrations (ILDs)

See Interactive Lecture Demonstrations, Active Learning in Introductory Physics, by David R. Sokoloff (Author), Ronald K. Thornton (Author)

Start with a scripted activity in a traditional lecture format. Because the activity causes students to confront their prior understanding of a core concept, students are ready to learn in a follow-up lecture. Interactive Lecture Demonstrations use three steps in which students:
Predict the outcome of the demonstration. Individually, and then with a partner, students explain to each other which of a set of possible outcomes is most likely to occur.
Experience the demonstration. Working in small groups, students conduct an experiment, take a survey, or work with data to determine whether their initial beliefs were confirmed (or not).
Reflect on the outcome. Students think about why they held their initial belief and in what ways the demonstration confirmed or contradicted this belief. After comparing these thoughts with other students, students individually prepare a written product on what was learned.


GIFs: Using short, step-by-step animations to help students visualize a complex process.

There are many scientific phenomenon traditionally taught with textbook and lecture. These have static diagrams, and for many students it is hard to visualize the process. As such, with GIFs specifically targeted to the idea or equation at hand, it becomes easier for students to grasp the essential ideas.

For instance, one can model an electric series circuit with two resistors with math, a circuit diagram, or a GIF. With the GIF we can see how the battery adds potential energy to the electrons in a circuit, while the electrons lose this potential energy as they go through any circuit element with resistance.

Rtotal = R1 + R2

V = I/R = I / Rtotal






Cooperative Group Problem-solving – Students work in groups using structured problem-solving strategy. In this way they can solve complex, context-rich problems which could be difficult for them to solve individually. This was developed by the University of Minnesota Physics Education Research Group.

Students in introductory physics courses typically begin to solve a problem by plunging into the algebraic and numerical solution — they search for and manipulate equations, plugging numbers into the equations until they find a combination that yields an answer (e.g. the plug-and-chug strategy). They seldom use their conceptual knowledge of physics to qualitatively analyze the problem situation, nor do they systematically plan a solution before they begin numerical and algebraic manipulations of equations. When they arrive at an answer, they are usually satisfied — they rarely check to see if the answer makes sense.

To help students integrate the conceptual and procedural aspects of problem solving so they could become better problem solvers, we introduced a structured, five-step problem solving strategy. However, we immediately encountered the following dilemma:

If the problems are simple enough to be solved moderately well using their novice strategy, then students see no reason to abandon this strategy — even if the structured problem-solving strategy works as well or better.

If the problems are complex enough so the novice strategy clearly fails, then students are initially unsuccessful at using the structured problem-solving strategy, so they revert back to their novice strategy.

To solve this dilemma, we (1) designed complex problems that discourage the use of plug-and-chug strategies, and (2) introduced cooperative group problem solving. Cooperative group problem solving has several advantages:

  1. The structured problem-solving strategy seems too long and complex to most students. Cooperative-group problem solving gives students a chance to practice the strategy until it becomes more natural.
  2. Groups can solve more complex problems than individuals, so students see the advantage of a logical problem-solving strategy early in the course.
  3. Each individual can practice the planning and monitoring skills they need to become good individual problem solvers.
  4. Students get practice developing and using the language of physics — “talking physics”.
  5. In their discussion with each other, students must deal with and resolve their misconceptions.
  6. In subsequent, whole-class discussions of the problems, students are less intimidated because they are not answering as an individual, but as a group.

Of course, there are several disadvantages of cooperative-group problem solving. Initially, many students do not like working in cooperative groups. They do not like exposing their “ignorance” to other students. Moreover, they have been trained to be competitive and work individually, so they lack collaborative skills.


Just-in-Time Teaching: Students answer questions online before class, promoting preparation for class and encouraging them to come to class with a “need to know.


Context-Rich Problems: Students work in small groups on short, realistic scenarios, giving them a plausible motivation to solve problems.


Open Source Physics Collection: Open source code libraries, tools, and compiled simulations.


Tutorials in Introductory Physics: Guided-inquiry worksheets for small groups in recitation section of intro calculus-based physics. Instructors engage groups in Socratic dialogue.


RealTime Physics: A series of introductory laboratory modules that use computer data acquisition tools to help students develop physics concepts and acquire lab skills.


Modeling Instruction – Instruction organized around active student construction of conceptual and mathematical models in an interactive learning community. Students engage with simple scenarios to build, test and apply the handful of scientific models that represent the content core of physics.


Force Concept Inventory – “The FCI is a test of conceputal understanding of Newtonian mechanics, developed from the late 1980s. It consists of 30 MCQ questions with 5 answer choices for each question and tests student understanding of conceptual understanding of velocity, acceleration and force. Many distracters in the test items embody commonsense beliefs about the nature of force and its effect on motion. ” Developed by Hestenes, Halloun, Wells, and Swackhamer (1985.) Sample question:

FCI Force Concept Inventory


How to teach AP Physics


ASU Modeling Instruction



Particle Physics lesson

particles colliding LHC

Your job: Produce a document, with pictures, putting together what you have learned today. Ways that you can do this:

* Handwrite

* Create a PowerPoint presentation

* Google Docs (typing or voice-to-text)

* Create a poster – pencils, colored pencils, pens, markers.


Inside atoms we have protons, neutrons and electrons. Now we learn that protons and neutrons are not “solid”. They are built from smaller subatomic particles!

The particle zoo


Animation: Atoms to Quarks


Videos: Out Of Sight – Building From Quarks To Atoms to Molecules


CERN: Two protons collide and create new particles


CK-12 Chemistry Fundamental Particles


At the end of this website launch and explore the “CK-12 Interactive”


Advanced topics

Quarks are particles within protons and neutrons.

How do point particles create atoms with size?

Labs (Physics)

Physics labs

Welch Labs plotting imaginary

Image from Imaginary Numbers Are Real, Welch Labs


Build projects

Hovercraft build project


Traditional physics labs


Reaction time lab

Finding the coefficient of friction lab

Inertial balance lab

Magnetism labs

Why Is There a Tidal Bulge Opposite the Moon?


Virtual labs


Science Sims @ CCNY

BU Physics ~ Duffy HTML5 sims

HTML 5 Physics Lab Simulations: The Physics Aviary

Open Source Physics sims

The Physics Classroom interactives


Coding labs

Programming Labs for Physics




Earth’s magnetic field

Earth’s Magnetic Field

The Earth has a magnetic field. When we use a compass, we make use of this field. So we’re tempted to view the Earth as a big rock with a giant bar magnet stuck through it.

But this isn’t at all how it really works: The Earth has a molten metal core, surrounded by a highly metallic shell of magma.  Electrons move through this metal  – and the motion of electrons – as will learn in this chapter – creates a magnetic field!

The Earth itself is slowly spinning, so we end up with slow-moving currents within the Earth. These currents affect the flow of electrons, thus affecting the resulting magnetic field.

Here is the “obvious” model of Earth’s magnetic field (it’s wrong)


The red pointer in a compass is attracted by Earth’s own magnetism (sometimes called the geomagnetic field—”geo” simply means Earth).

As English scientist William Gilbert explained about 400 years ago, Earth behaves like a giant bar magnet with one pole up in the Arctic (near the north pole) and another pole down in Antarctica (near the south pole).

Earth’s magnetic field is actually quite weak compared to the “macho” forces like gravity and friction that really dominate our lives.

For a compass to be able to show up the relatively tiny effects of Earth’s magnetism, we have to minimize the effects of these other forces.

That’s why compass needles are :

* lightweight (so gravity has less effect on them)

* mounted on frictionless bearings (so less resistance for the magnetic force to overcome)



“Where the Earth’s magnetic field comes from, Chris Rowan

The Earth’s magnetic field may approximate to a simple dipole, but explaining precisely how that dipole is generated and maintained is not simple at all. The field originates deep in the Earth, where temperatures are far too high for any material to maintain a permanent magnetisation.

The dynamism that is apparent from the wandering of the magnetic poles with respect to the spin axis (secular variation), and the quasi-periodic flips in field polarity, also suggest that some process is actively generating and maintaining the geomagnetic field. Geophysicists therefore look to the most dynamic region in the planetary depths, the molten outer core, as the source of the force that directs our compass needles…

The Earth’s interior generates a magnetic field. It reaches out into space.



This magnetic field protects us from some types of radiation

Earth’s North geographic pole has a South magnetic field

The “north” pole of a compass – by definition – is pulled to a “south” magnetic pole.

If we hold a compass in our hands, and call the part pointing to the land of Polar bears “north”, then we’d have to call the part attracting it “south.”

Earth North Geographic Pole South Magnetic Pole

How a planet becomes a magnet

Earth’s magnetic field single-handedly protects life on this planet from a deadly case of solar wind-burn, By Bernie Hobbs


Magnetic field reversals

The magnetic field of the Earth is not stable; it has flip-flopped throughout geologic time.

Evidence: (to be added)

“In the meantime, scientists are working to understand why the magnetic field is changing so dramatically. Geomagnetic pulses, like the one that happened in 2016, might be traced back to ‘hydromagnetic’ waves arising from deep in the core1. And the fast motion of the north magnetic pole could be linked to a high-speed jet of liquid iron beneath Canada2.”

Earth’s magnetic field is acting up and geologists don’t know why. Nature Jan 19

Geomagnetic acceleration and rapid hydromagnetic wave dynamics in advanced numerical simulations of the geodynamo, Aubert, Julien, Geophys. J. Int. 214, 531–547 (2018).

An accelerating high-latitude jet in Earth’s core. Livermore, P. W., Hollerbach, R. & Finlay, C. C. Nature Geosci. 10, 62–68 (2017).


App: The solar wind and Earth’s magnetic field


Learning about Earth’s magnetic field: ESA’s Swarm mission


The Physics of Interstellar Travel

Why should humanity eventually colonize the stars?

“Ask ten different scientists about the environment, population control, genetics and you’ll get ten different answers, but there’s one thing every scientist on the planet agrees on. Whether it happens in a hundred years or a thousand years or a million years, eventually our Sun will grow cold and go out. When that happens, it won’t just take us. It’ll take Marilyn Monroe and Lao-Tzu, Einstein, Morobuto, Buddy Holly, Aristophanes .. and all of this .. all of this was for nothing unless we go to the stars.”

– Writer J. Michael Straczynski, from a character’s speech (Commander Sinclair) in Babylon 5, season 1, “Infection”

This a resource for a future lesson on physically possible ways of interstellar travel.


Lawrence H. Ford and Thomas A. Roman. Sci Am article.


Ways that currently only exist in science fiction:

In Star Trek, spaceships have a warp drive.

In Star Wars, spaceships have a hyperdrive, to send a ship through hyperspace.

Some sci-fi novels postulate a technology called a jump drive – This allows a starship to be instantaneously teleported between two points.

In Stargate the characters use a traversable wormhole – the idea is based on the Einstein–Rosen bridge.

Current space travel technology

Rockets powered by chemical reactions

New Horizons mission has rocket thrusters fueled with hydrazine. Chemical reaction powered rockets are good for manned or unmanned missions within our solar system.

Ionic propulsion

This is the slowest method, but also the most efficient, as it needs much less fuel. Uses engines such as the Hall-effect thruster (HET). Used in European Space Agency’s (ESA) SMART-1 mission. Good for unmanned missions within our solar system.


Matt Williams writes

Nuclear Thermal and Nuclear Electric Propulsion (NTP/NEP)

Another possibility for interstellar space flight is to use spacecraft equipped with nuclear engines, a concept which NASA has been exploring for decades. In a Nuclear Thermal Propulsion (NTP) rocket, uranium or deuterium reactions are used to heat liquid hydrogen inside a reactor, turning it into ionized hydrogen gas (plasma), which is then channeled through a rocket nozzle to generate thrust.

A Nuclear Electric Propulsion (NEP) rocket involves the same basic reactor converting its heat and energy into electrical energy, which would then power an electrical engine. In both cases, the rocket would rely on nuclear fission or fusion to generates propulsion rather than chemical propellants, which has been the mainstay of NASA and all other space agencies to date.

Although no nuclear-thermal engines have ever flown, several design concepts have been built and tested over the past few decades, and numerous concepts have been proposed. These have ranged from the traditional solid-core design – such as the Nuclear Engine for Rocket Vehicle Application (NERVA) – to more advanced and efficient concepts that rely on either a liquid or a gas core.

However, despite these advantages in fuel-efficiency and specific impulse, the most sophisticated NTP concept has a maximum specific impulse of 5000 seconds (50 kN·s/kg). Using nuclear engines driven by fission or fusion, NASA scientists estimate it would could take a spaceship only 90 days to get to Mars when the planet was at “opposition” – i.e. as close as 55,000,000 km from Earth.

But adjusted for a one-way journey to Proxima Centauri, a nuclear rocket would still take centuries to accelerate to the point where it was flying a fraction of the speed of light. It would then require several decades of travel time, followed by many more centuries of deceleration before reaching it destination. All told, were still talking about 1000 years before it reaches its destination. Good for interplanetary missions, not so good for interstellar ones.

Realistic extensions of current technology

Fusion Rockets

[One could use] thermonuclear reactions to generate thrust. For this concept, energy is created when pellets of a deuterium/helium-3 mix are ignited in a reaction chamber by inertial confinement using electron beams (similar to what is done at the National Ignition Facility in California). This fusion reactor would detonate 250 pellets per second to create high-energy plasma, which would then be directed by a magnetic nozzle to create thrust.

Like a rocket that relies on a nuclear reactor, this concept offers advantages as far as fuel efficiency and specific impulse are concerned. Exhaust velocities of up to 10,600 km/s are estimated, which is far beyond the speed of conventional rockets. What’s more, the technology has been studied extensively over the past few decades, and many proposals have been made.

For example, between 1973 and 1978, the British Interplanetary Society conducted feasibility study known as Project Daedalus. Relying on current knowledge of fusion technology and existing methods, the study called for the creation of a two-stage unmanned scientific probe making a trip to Barnard’s Star (5.9 light years from Earth) in a single lifetime.

The first stage, the larger of the two, would operate for 2.05 years and accelerate the spacecraft to 7.1% the speed of light (o.071 c). This stage would then be jettisoned, at which point, the second stage would ignite its engine and accelerate the spacecraft up to about 12% of light speed (0.12 c) over the course of 1.8 years. The second-stage engine would then be shut down and the ship would enter into a 46-year cruise period.

Project Daedalus spacecraft, by Adrian Mann

According to the Project’s estimates, the mission would take 50 years to reach Barnard’s Star. Adjusted for Proxima Centauri, the same craft could make the trip in 36 years. But of course, the project also identified numerous stumbling blocks that made it unfeasible using then-current technology – most of which are still unresolved.

For instance, there is the fact that helium-3 is scare on Earth, which means it would have to be mined elsewhere (most likely on the Moon). Second, the reaction that drives the spacecraft requires that the energy released vastly exceed the energy used to trigger the reaction. And while experiments here on Earth have surpassed the “break-even goal”, we are still a long way away from the kinds of energy needed to power an interstellar spaceship.

Speculative technologies for space travel

Fusion Ramjet

Also known as the Bussard Ramjet, this theoretical form of propulsion was first proposed by physicist Robert W. Bussard in 1960. Basically, it is an improvement over the standard nuclear fusion rocket, which uses magnetic fields to compress hydrogen fuel to the point that fusion occurs. But in the Ramjet’s case, an enormous electromagnetic funnel “scoops” hydrogen from the interstellar medium and dumps it into the reactor as fuel.

As the ship picks up speed, the reactive mass is forced into a progressively constricted magnetic field, compressing it until thermonuclear fusion occurs. The magnetic field then directs the energy as rocket exhaust through an engine nozzle, thereby accelerating the vessel. Without any fuel tanks to weigh it down, a fusion ramjet could achieve speeds approaching 4% of the speed of light and travel anywhere in the galaxy.

However, the potential drawbacks of this design are numerous. For instance, there is the problem of drag. The ship relies on increased speed to accumulate fuel, but as it collides with more and more interstellar hydrogen, it may also lose speed – especially in denser regions of the galaxy. Second, deuterium and tritium (used in fusion reactors here on Earth) are rare in space, whereas fusing regular hydrogen (which is plentiful in space) is beyond our current methods.

Antimatter-Matter annihilation powered rocket

Fans of science fiction are sure to have heard of antimatter. But in case you haven’t, antimatter is essentially material composed of antiparticles, which have the same mass but opposite charge as regular particles. An antimatter engine, meanwhile, is a form of propulsion that uses interactions between matter and antimatter to generate power, or to create thrust.

In short, an antimatter engine involves particles of hydrogen and antihydrogen being slammed together. This reaction unleashes as much as energy as a thermonuclear bomb, along with a shower of subatomic particles called pions and muons. These particles, which would travel at one-third the speed of light, are then be channeled by a magnetic nozzle to generate thrust.

The advantage to this class of rocket is that a large fraction of the rest mass of a matter/antimatter mixture may be converted to energy, allowing antimatter rockets to have a far higher energy density and specific impulse than any other proposed class of rocket. What’s more, controlling this kind of reaction could conceivably push a rocket up to half the speed of light.

Pound for pound, this class of ship would be the fastest and most fuel-efficient ever conceived. Whereas conventional rockets require tons of chemical fuel to propel a spaceship to its destination, an antimatter engine could do the same job with just a few milligrams of fuel. In fact, the mutual annihilation of a half pound of hydrogen and antihydrogen particles would unleash more energy than a 10-megaton hydrogen bomb.

It is for this exact reason that NASA’s Institute for Advanced Concepts (NIAC) has investigated the technology as a possible means for future Mars missions. Unfortunately, when contemplating missions to nearby star systems, the amount if fuel needs to make the trip is multiplied exponentially, and the cost involved in producing it would be astronomical (no pun!).

How Long Would It Take To Travel To The Nearest Star?

NASA PDF PowerPoint: Realistic Interstellar Travel

Ask Ethan: Is Interstellar Travel Possible? Forbes


What technologies would we need to develop?

Chemical rocket spaceships

Solar sail spaceships

Nuclear fission powered spaceships

Nuclear fusion powered spaceships

Matter-Anti-matter spaceships

How long would it take a spaceship to get from one star to another?

To get to the center of our galaxy?


The Big Problem With Interstellar Travel, YouTube, RealLifeLore

Interstellar Travel: Approaching Light Speed. Jimiticus

Interstellar Travel – Speculative Documentary HD

Warp drive

Many people are familiar with warp drive as a form of FTL (Faster Than Light travel.) Its most popular use is in the science-fiction series Star Trek. According to the laws of physics could this potentially be possible?

Possibility of a real life warp drive, The Alcubierre drive. (KaiserScience)

Warp Drive Research Key to Interstellar Travel, Scientific American


External resources and articles

Physics of interstellar travel Michio Kaku

Space.com articles on interstellar travel

Pros and Cons of Various Methods of Interstellar Travel, Universe Today

Space.StackExchange – [interstellar-travel]

Concepts for Deep Space Travel: From Warp Drives and Hibernation to World Ships and Cryogenics“, Current Trends in Biomedical Engineering and Biosciences


Learning Standards

Massachusetts Curriculum Frameworks Science and Technology/Engineering (2016) 

6.MS-ESS1-5(MA). Use graphical displays to illustrate that Earth and its solar system are one of many in the Milky Way galaxy, which is one of billions of galaxies in the universe.

A Framework for K-12 Science Education: Practices, Crosscutting Concepts, and Core Ideas (2012)

By the end of grade 8. Patterns of the apparent motion of the sun, the moon, and stars in the sky can be observed, described, predicted, and explained with models. The universe began with a period of extreme and rapid expansion known as the Big Bang. Earth and its solar system are part of the Milky Way galaxy, which is one of many galaxies in the universe.

Next Generation Science Standards

4-PS3 Energy, Disciplinary Core Ideas, ETS1.A: Defining Engineering Problems

 Possible solutions to a problem are limited by available materials and resources (constraints). The success of a designed solution is determined by considering the desired features of a solution (criteria). Different proposals for solutions can be compared on the basis of how well each one meets the specified criteria for success or how well each takes the constraints into account. (secondary to 4-PS3-4)

Common Core State Standards Connections: ELA/Literacy

RST.6-8.8 Distinguish among facts, reasoned judgment based on research findings, and speculation in a text. (MS-LS2-5)

RI.8.8 Trace and evaluate the argument and specific claims in a text, assessing whether the reasoning is sound and the evidence is relevant and sufficient to support the claims. (MS-LS-4),(MS-LS2-5)

WHST.6-8.2 Write informative/explanatory texts to examine a topic and convey ideas, concepts, and information through the selection, organization, and analysis of relevant content. (MS-LS2-2)