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Rocket Math and Propulsion - The Math Behind Rockets and Propulsion (Grades 5-8)
Programação
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The Mathematics Behind Rockets and Propulsion
Summer 2025
Collaborators: Jack Colvin (University of Chicago Intern)
Resources provided by Stevan Akerly (NSS Space Ambassadors Lead)
Loretta Hall (NSS Space Ambassador)
Kevin Simmons (NSS Space Ambassador & BLUECUBEAEROSPACE CEO)
Frances Dellutri (NSS Director of Education)
Background
Have you ever wondered how rockets soar so swiftly through the air and venture deep into space? While it may seem almost magical, rocket flight is powered by the precise language of mathematics. Propulsion—the process in which rockets burn fuel to generate thrust—relies on carefully calculated forces grounded in physics. Before we can design and build our own rockets, we must first understand what they are and how they work. In this lesson, we’ll explore the hidden world of Newtonian mechanics, uncovering how this foundational theory of motion makes space travel possible. Furthermore, we will look into the future and learn how we can use these same principles to imagine the next generation of rockets that could carry us one step closer to the cosmic unknown.
Lesson Goals:Understand basic propulsion and how it relates to Newton’s second and third laws of motion
Understand the problems with modern systems of propulsion
Think about possible alternatives to current propulsion systems that could be used going forward
Education Standards:
MS-PS2.3; 4
MS-PS3-A; B
MS-PS2.1
Common Core State Standards (CCSS_
ELA - Science and Technical Subjects:
Related Lessons
Rocket Engineering (HS & University): https://spacedge.nss.org/course/view.php?id=326
Rocket Math (HS & University): https://spacedge.nss.org/course/view.php?id=330
Rocketry: https://spacedge.nss.org/course/view.php?id=51
Recent Space Developments: https://spacedge.nss.org/course/view.php?id=47#section-2
Newton's Greatest Contribution to Mankind: https://spacedge.nss.org/course/view.php?id=255#section-2
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All rockets operate based on principles described by Newton’s Laws: a set of rules about how objects move proposed by the brilliant Issac Newton, a scientist often credited with the invention of modern physics itself. Specifically, we will look at how rockets use his second and third laws to push themselves forwards.
Free image from freeimages.com, depicting Sir Isaac Newton at work. https://www.freeimages.com/photo/isaac-newton-investigating-light-1763612
Newton’s second law of motion simply tells us that the more massive an object is, the more force it takes to accelerate it. In everyday terms, heavier objects are harder to push than lighter ones, a principle you’ve probably experienced firsthand on numerous occasions.
Activity One: Let’s test Newton’s Second Law!
Gather three objects of different masses – for example, a tennis ball, a soccer ball, and a basketball. First, compare them qualitatively: Which one feels the hardest to push? Which is the easiest?
For an extra challenge, try to quantify the relationship.
Measure the mass of each object.
Give each one a single push and measure how far it travels
Record your data in a table or turn it into a graph to show the connection between mass and motion.
Watch this video on the difference between mass and weight and explain the difference in your own words:DIFFERENCE OF WEIGHT & MASS | Animation
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Newton’s third law of motion is a little bit more complicated. It states that if you put a force on an object, it puts an equal and opposite force back on you. In other words, if you push something, it pushes back against you just as much. At first, this might sound wrong. When we push a ball forward, we don’t always feel ourselves being pushed back. But the push is still there. The ball is simply so much lighter than we are that a force that seems small and unnoticeable to us is capable of sending the ball rolling forward. Just like Newton’s second law, we experience this every day! When we push against a solid wall for example, we feel a backward force pressing against our arms. The stronger we push, the stronger the wall seems to resist that push. This is a real-life example of Newton’s third law in action!
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Aberto: quinta, 14 ago 2025, 00:00
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Now the question is: what do these laws have to do with rockets? As it turns out, rockets rely on them to move forward through a process called propulsion. This process begins with the rocket’s fuel source. A good fuel contains a large amount of stored chemical energy, which is released through a process called combustion—something we’ll explore in more detail later in our engineering lesson. For now, you can understand combustion simply as another term for burning something, in this case, our fuel source.
A simple Campfire is an example of a combustion reaction!
Image Credit: Britanica https://www.britannica.com/science/combustion/History-of-the-study-of-combustion
When fuel is burned through combustion, exhaust gases such as methane and carbon dioxide are produced. Rockets move forward by allowing these gases, which are extremely hot and thus are traveling extremely fast, to flow out of the rocket through an opening at the back end, called the nozzle. This is where Newton’s third law comes into play! As the fuel flows out of the rocket (the action force), it exerts an equal and opposite force on the rocket, which pushes the rocket forward (the reaction force).
Video Resource: How do combustion and propulsion work?
Watch the following video and answer these questions:
What is a combustion reaction? How are they used to power rocket engines?
What is the “Fire Triangle” and why is it important?
What is the importance of the rocket nozzle in propulsion?
_____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________Newton’s second law is just as important for understanding rockets. Rockets are enormous, weighing up to 2.34 million pounds. To put that in perspective, that’s about the same as 1,000 fully grown elephants. Because rockets are so huge, they also require a massive push in order to speed up enough to get off the ground. Therefore, rockets must burn huge amounts of fuel in order to get into the air and reach space.
Image 2: NASA. (1992). STS-45 Atlantis, OV-104, lifts off from KSC Launch Complex (LC) Pad. NASA Image Gallery. Retrieved 2025, from https://images.nasa.gov/details/s45-s-055.
But here’s the problem: fuel itself is heavy. The more fuel you add, the heavier the rocket becomes—and at a certain point, adding extra fuel can actually reduce performance because the rocket becomes too heavy to launch efficiently (again, due to Newton’s second law). This creates a major challenge for rocket engineers. Even modern liquid and solid fuel sources do not produce enough thrust per pound to allow for quick and efficient travel to deep space. The voyager missions, for example, have taken decades just to reach the outer edges of our solar system. Current methods of propulsion are thus extremely limited in their capacity for efficient space travel.
As we will see in our engineering lesson, rocket engineers have attempted to find solutions to this problem, such as building rockets in stages that can be discarded to reduce weight and maximizing rocket efficiency to try to squeeze out every last bit of energy from the fuel. However, in order to truly make way for interstellar travel, entirely new means of propulsion are likely necessary.
The above image is a NASA Figure showing breakdown of rocket weight between propellants and engine parts found at https://forum.nasaspaceflight.com/assets/50972.0/1915525.jpg. The most striking thing about this graphic is just how little the actual structure of the rocket itself contributes to the overall weight. Remarkably, over 90% of any rocket's pre-takeoff weight is simply propellant. This is why simply adding more and more fuel is an inefficient way of reaching further into space: fuel is just so heavy and so difficult to lift off the ground.
Video Resource: Fun with Model Rockets!
If you’d like, you can watch the following video of a dad and his son building and launching their own model rocket—a heartwarming moment that also perfectly demonstrates Newton’s 3rd law in action, just on a much smaller scale than a full-size rocket. My 6yr Old and I Designed and Built a Rocket
Finally, check out Estes Rockets if you would like to build your own model rockets!!!!!! https://estesrockets.com/?utm_medium=ppc&utm_source=adwords&utm_term=estes-
Aberto: domingo, 17 ago 2025, 00:00
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Stage One: Firing of Igniters: In this stage, igniters connected to the structure supporting the rocket fire red-hot sparks horizontally, providing the heat component of the "fire triangle" needed for the combustion reaction to begin.

Stage two: Ignition of main engine: In this stage, the main engine of the rocket (Stage 2) actually ignites before the boosters. You can tell what type of fuel is being used based on the color of the resulting flame: kerosene or gasoline light orange/yellow, whereas more efficient fuel types such as hydrogen produce more heat, and thus typically produce a blue flame.


Stage Three: Ignition of solid Boosters: Next, with the igniters still firing, the solid boosters light. This occurs in a far more dramatic manner, with columns of white smoke and white flames erupting from the booster engines.

Stage Four: Breaking Away! Finally, when enough upward thrust is generated, the bolts holding the shuttle to it supportive structure break explosively, sending the rocket careening towards the sky. Once up there, one can still differentiate between the blue and/or orange flames from the liquid fuel-based main engine, and the billowy white smoke from the booster engines.


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As mentioned in section 2 of this lesson, rocket engineers are beginning to look towards new source of propulsion due to the inefficiency of traditional combustion. One of the most promising such alternatives – already in use by many smaller spacecrafts and satellites – is harnessing the immense energy of the Sun. Many spacecrafts are equipped with solar panels, which can convert sunlight into electricity and charge engines that can push the craft forward. Others use solar sails, which use sunlight itself as a source of thrust. Sunlight is made up of countless tiny particles called photons. Solar sails are huge reflective surfaces which allow these photons to bounce off, transferring their kinetic energy to the spacecraft itself. Over time, these particles can gradually accelerate a craft.
The benefit to solar-powered sources of propulsion is that they weigh next to nothing and are completely rechargeable, as they obtain all of their energy from the sun! However, while the thrust they provide can build up over time, it is insufficient as a sole source of energy for a larger craft such as a rocket and would thus need to be supplemented by tradition fuel or some other source of propulsion.
Schweighart, B. (2024). Solar Sail Turntable With Sun. Nasa Image Archive. NASA. Retrieved from https://images.nasa.gov/details/ACS3_SolarSailTurntableWithSun.
Another alternative is ion propulsion. Instead of shooting out exhaust, ion engines accelerate tiny particles called ions to extremely high speeds, and shoot them out of the engine, pushing our rockets forward in the same way as traditional propulsion. Ion engines have been used since the 1990s to help launch satellites into orbit, however they have been yet to be implemented on larger spacecrafts. Similar to solar energy, ion propulsion is completely rechargeable but is also unable to be the sole source of thrust on a large spacecraft.
See the following video to learn more about ion propulsion! H9 Hall effect thruster simulation
NASA. (1970). Ion Thruster. Nasa Image Archive. Retrieved from https://images.nasa.gov/details/GRC-1970-C-02492
Yet another idea is nuclear propulsion. Atoms, the tiny particles that make up everything we can see and touch, have immense energy stored in their cores – densely packed collections of tiny particles called nuclei. Splitting these particles into smaller pieces releases this energy, which could be harnessed and used to power rockets in the near future. As of now, no rockets make use of nuclear propulsion. However, the technology has been experimented with extensively, first by the NERVA project in the 1950s and more recently by DRAKO in the 2020s. However, both of these projects were discontinued due to political and budgetary concerns. Nuclear propulsion technology, as with many of these alternate sources of propulsion, would not be used for the initial burst of thrust, but would rather give rockets extra power once already in space.
If you would like to learn more about how atomic energy is harnessed, watch the following video: Nuclear fission Atomic energy Animated and explanation with 3d program
Finally, even more futuristic possibilities exist. Lasers could be used to push rockets forward just like the sun: only with a more concentrated and controllable force. The most outlandish idea is the potential for a real-world version of a “warp-drive” as seen in science fiction movies. While we don’t have the technology to implement this idea yet, and likely won’t for many years, we can prove that it is possible using math, which by itself is pretty cool!
Kakaes, K. (2013, April 1). Faster-than-light drive. Popular Science. https://www.popsci.com/technology/article/2013-03/faster-light-drive/ -
Throughout this lesson, we’ve seen that rockets aren’t just feats of engineering or construction but are also triumphs of mathematics and physics that transform abstract equations into the power to access parts of the universe previously thought to be unreachable. We started by discovering Newton’s 2nd and 3rd laws, and how they shape and impact nearly everything in the world around us. We then connected these abstract concepts to rockets, and how engineers are able to use these principles to allow us to explore the cosmos. We discovered how thrust is generated and why even the smallest rockets still obey the same fundamental principles as the mighty Saturn V.
Finally, we looked into potential alternate sources of propulsion, from nuclear power and solar sails to abstract ideas like warp drives, showing that the mathematics of rockets is not only about designing rockets today, but also about imagining how to travel even further tomorrow.
If you would like to learn about rockets from the perspective of an engineer, visit our Rocketry Engineering lesson. If you would like to know more about the history of rocketry, and specifically Robert Goddard, the brilliant mind that pioneered modern rocketry, visit our biography about Goddard here (url), or the page for our Goddard 100 contest, celebrating his life's work and achievements here (url). Finally, visit the NSS Space Forum to learn more about rockets, propulsion, and any other recent developments on space science! -
NSS Blog: An online blog containing posts about many space-related topics, including rockets and propulsion
https://nss.org/category/blog/
NSS Space Forum: a forum containing videos produced by NSS space ambassadors about anything space realtedhttps://nss.org/nss-space-forums/
NASA Goddard Flight Center Website: A Website containing hundreds of math and engineering problems related to rocketry!
Math and Rockets in Sci Fi Movies (6:25 duration): A video discussing places where math and science show up in sci-fi movies!
https://spacemath.gsfc.nasa.gov/SpaceMath.html
A full video of a SpaceX Rocket Launch (15:42 duration)!
Build your own model rockets through Estes rockets!
https://estesrockets.com/? -
Send a Postcard to Space through NSS Supported Blue Origin Club For The Future initiative!
Visit: SpacEdge Academy Postcards in Space Course
