Embedded Files
by Cindy Li
project overview
project overview
It was difficult to predict and study physics in the universe, for that mysterious outer space was never reached by human beings until the 20th century. This project will investigate how physics is applied in universe; specifically how objects are orbiting under the universal gravity law. The project is divided into two parts: a short research document and three separate space simulations.
The short research document summarizes the general physics phenomenon and concepts in the universe, which some of them are distinctly different from physics on Earth, while others are similar. While the snap simulations delivers an easier, more direct way for audiences to see the physics in universe. Hope you will enjoy:)
I. Research document
I. Research document
- composition of universe
The universe is composed completely of dark energy, dark matter, and ordinary matter.
Dark energy is an unknown form of energy that is hypothesized to permeate space, which an explanation for why the expansion of the universe is accelerating remains elusive. Dark matter is a hypothetical kind of matter that is invisible to the entire electromagnetic spectrum, and it accounts for most of the matter in the universe. While ordinary matter is any matter that takes up space and mass, which commonly exists in four states: solid, liquid, gas, and plasma.
2. physics in space
2. physics in space
Objects in space follow the laws of rules of physics, just like objects on Earth do. Objects in space have inertia. That is, they travel in a straight line unless there is force that makes them stop or change. The movement of things in space is influenced by gravity.
3. gravity in space
3. gravity in space
There is gravity everywhere. It gives shape to the orbits of the planets, the solar system, and even galaxies. Gravity from the Sun reaches throughout the solar system and beyond, keeping the planets in their orbits. Gravity from Earth keeps the Moon and human-made satellites in orbit.
It is true that gravity decreases with distance, so it is possible to be far away from a planet or star and feel less gravity. But that doesn't account for the weightless feeling that astronauts experience in space. The reason that astronauts feel weightless actually has to do with their position compared to their spaceship. We feel weight on Earth because gravity is pulling us down, while the floor or ground stop us from falling. We are pressed against it. Any ship in orbit around the Earth is falling slowly to Earth. Since the ship and the astronauts are falling at the same speed, the astronauts don't press against anything, so they feel weightless.
One of the examples of being weightless is that one can feel something very like the astronaut feels for a moment in a fast-moving elevator going down or in a roller coaster, when one starts going down a big hill. You are going down rapidly, but so is the roller coaster or the elevator so for a second one feels weightless.
4. How do scientists know that the path of an object in space will be?
4. How do scientists know that the path of an object in space will be?
Scientists know the basic laws of physics or movement rules that objects in space follow. Because of this, if a scientist knows how big something is (how much mass an object has) how fast it’s going, the direction it's going and what it will be going near, that scientists can figure out what its flight will look like.
A very basic principle of physics says that if something is going in a straight line it has something called inertia that will keep it going in a straight line at the same speed unless a force makes it change or stop. The bigger (more massive) something is, the more inertia it has and the harder it is to stop it or change its course. That’s why if one drops a bowling ball on a glass table, it will keep going through the table, while a marble will be stopped by it.
Gravity is the most important force affecting movement in space. The strength of gravity’s pull between two objects depends on how big they are and how close they are (generally one object is a lot bigger than the other, and so most of the gravitational pull comes from one to the other).
If a scientist knows how big something is, how fast it is moving, and how close it is to other things with gravity it is, the scientist can get out a calculator and a math book to see how gravity and inertia will act on the object. These two factors (gravity and inertia) will usually completely determine the path of the object.
5. What is an orbit?
5. What is an orbit?
An orbit is a regular, repeating path that an object in space takes around another one. An object in an orbit is called a satellite. A satellite can be natural, like the moon, or human-made.
In our solar system, the Earth orbits the Sun, as do the other eight planets. They all travel on or near the orbital plane, an imaginary disk-shaped surface in space. All of the orbits are circular or elliptical in their shape. In addition to the planets’ orbits, many planets have moons which are in orbit around them.
6. What travels an orbit?
6. What travels an orbit?
Almost all of our neighbors in space are in orbit around something. All of the planets are in a circular or elliptical orbit around the Sun. Our moon and the moons of the other planets are in orbit around their planets. Comets are in an irregular orbit around the Sun. Most asteroids in our solar systems are orbiting the Sun in a band between Mars and Jupiter. Most human-made spacecraft in space are orbiting Earth. Almost all of the rest, even ones we think of as traveling to other planets, are in orbit around the Sun.
Even our Sun is traveling around the center of the Milky Way galaxy. The huge amount of matter there acts as a gravitational center for the other stars in the Milky Way. They travel around the center of the Milky Way as our planets go around the Sun.
There are a few things that we are familiar with, though, that aren't in orbits. When a meteorite enters our atmosphere and becomes a "shooting star," it is no longer in an orbit. Some space probes like Voyager have achieved escape velocity and broken away from the pull of the Sun's gravity and left the solar system. These space probes are not in orbit around a planet or the Sun, or they would stay near a planet or continue in a loop around the Sun.
7. What cause an orbit to happen/form?
7. What cause an orbit to happen/form?
Orbits are the result of a perfect balance between the forward motion of a body in space, such as a planet or moon, and the pull of gravity on it from another body in space, such as a large planet or star. An object with a lot of mass goes forward and wants to keep going forward; however, the gravity of another body in space pulls it in. There is a continuous tug-of-war between the one object wanting to go forward and away and the other wanting to pull it in.
These forces of inertia and gravity have to be perfectly balanced for an orbit to happen. If the forward movement (inertia) of one object is too strong, the object will speed past the other one and not enter orbit. If inertia or momentum is much weaker than the pull of gravity, the object will be pulled into the other one completely and crash.
8. How do objects in space travel?
8. How do objects in space travel?
Objects in space follow the laws or rules of physics, just like objects on Earth do. Things in space have inertia. That is, they travel in a straight line unless there is a force that makes them stop or change. The movement of things in space is influenced by gravity. Gravity is an important force that can change the course of bodies in space or pull them off of one course, or even cause them to crash together.
While some objects in space travel in irregular paths, most (especially our near neighbors in space) tend to travel in orbits around the Sun or around planets. The orbits are usually close to circular, but are actually slightly flattened ellipses.
9. Once a ship is in orbit, do we have to do anything to keep it there?
9. Once a ship is in orbit, do we have to do anything to keep it there?
Yes. Satellite orbits will degrade (slow and fall slightly) over time. As a ship travels for a long time, it goes through space, which is almost but not completely empty. The collective force from millions of tiny collisions with floating matter in space will decrease an orbiting object's speed. This force is very small since the floating matter is usually nothing more than dust and occasional clouds of gas. Overall, the effect of all these tiny forces hitting the satellite will act like drag or resistance on a plane flying in our atmosphere.
Drag is the slowing or resistance force caused by air. If one tries to swing their arm around their body with their palm facing the direction their hand is moving, they will feel the wind on their palm. This is an example of feeling the drag force. The faster one’s hand moves, the harder the air molecules hit their hand, and more drag force will be exerted on their hand. If one’s hand is not moving at all compared to the air, then there isn’t any drag force acting on it. The drag force on an object, like the hand, is directly proportional to its speed. That means that as the speed goes up the force goes up, and as the speed goes down, the drag force goes down.
Back to satellites in space.If space were a perfect vacuum, which means that there was nothing in it, it is true that everything would stay in orbit because of inertia. However, space isn’t a perfect vacuum. Even though that dust and dirt and gas that hits the satellite is very thin and spread out, its effect is like an extremely thin atmosphere. Even though any orbiting object is moving at thousands of miles per hour (speeds which would cause an object to break apart and burn up if it was in the atmosphere being hit by bazillions of air molecules) too few particles are hitting it to cause a significant drag force. However, over long periods of time, the effect of the particles colliding with the orbiting object are significant and slow the ship. For instance, NASA scientists estimate that the space shuttle, about the size of a passenger plane, can stay in orbit for about a month before this force causes it to slow enough that it falls out of its orbit. Note: Sometimes NASA scientists dip a satellite into the atmosphere of a planet on purpose so that drag will slow it. This is called aerobraking.
10. Universal gravitational force equation (Newton’s Law of Universal Gravitation)
10. Universal gravitational force equation (Newton’s Law of Universal Gravitation)
The Law of Universal Gravitation states that every point mass attracts every other point mass in the universe by a force pointing in a straight line between the centers-of-mass of both points, and this force is proportional to the masses of the objects and inversely proportional to their separation (distance). This attractive force always points inward, from one point to the other. The Law applies to all objects with masses, big or small. Two big objects can be considered as point-like masses, if the distance between them is very large compared to their sizes or if they are spherically symmetric. For these cases the mass of each object can be represented as a point mass located at its center-of-mass.
While Newton was able to articulate his Law of Universal Gravitation and verify it experimentally, he could only calculate the relative gravitational force in comparison to another force. It wasn’t until Henry Cavendish’s verification of the gravitational constant that the Law of Universal Gravitation received its final algebraic form:
F=GMm/r2
where F represents the force in Newtons, M and m represent the two masses in kilograms, and rr represents the separation in meters. G represents the gravitational constant, which has a value of 6.674⋅10−11N(m/kg)26.674⋅10−11N(m/kg)2. Because of the magnitude of G, gravitational force is very small unless large masses are involved.
II. SIMULATIONS
II. SIMULATIONS
1-body space simulation
1-body space simulation
Snap published link: https://snap.berkeley.edu/project?user=cindyli&project=1-body%20simulator
Screenshot of the 1-body simulator:
Code for this simulation:
Body-diagram & formula derivation:
Analysis:
Conducting a 1-body simulation is relatively easy. There are four variables: a, g, Vy, and Vx. Since the planet in the center is stationary, we only need to focus on the moving planet. a is the acceleration: which in this case can be shorten in the form of g/d^2. Respectively, Vy and Vx is the change of position x and position y. While g is the constant for the universal gravitation laws. Because this is merely a simulation, I decide to make g 100 (a random number that works in the simulation).
It is clear to see that planet 2 is orbiting around the center planet. Which in the actual universe, the planet is going to behave like the simulation. One of the potential source of errors is the over-simplification of my code, which leads to the non-accurate representation of the actual universe. However, the simulation can give a general overview of the orbiting planet.
2-body space simulations
2-body space simulations
Screenshot of the 2-body simulator (net momentum = 0):
Code for the simulation:
Body diagram & formula derivation:
Analysis:
This simulation is slightly more complicated than the 1-body simulator. Because both of the planets are moving, and they have gravity forces attracted to each other. The picture shown above is my work in deriving the acceleration of these two planets.
I purposefully set the net momentum of two objects zero, which indicate that the momentum is conserved. However, based on the simulation, each orbit is getting smaller and smaller by size. This refers that the total energy is not conserved and is eventually losing. Again, it's probably because of the over-simplification of the code, so that it inaccurately predicts the actual space:(
Screenshot of the 2-body simulator (when the net momentum is positive)
Code for the simulation:
Analysis:
As you can see from the screenshot, two planets collide to each other and then explode. This indicates the error of energy-consuming during the process of orbiting. Because Vx from both planets are positive, therefore both of the planets are moving from left to right.
Additionally, the simulation shows that when two planets get close to each other, they both speed up. In reality, if two planets pass closely by one another in orbit, one can perturb the other, resulting in a massive orbital change. These two planets could collide.
Screenshot of the 2-body simulator (with elliptical orbits):
Code for this simulation:
Analysis:
This time, I change the the Vx of planet D, so that the net momentum is changing as well. Both planets have seemingly elliptical orbits. Each planet speeds up when they get close to each other. While the other parts still behave similarly compared to the previous code.
3-body space simulation
3-body space simulation
Snap published link: https://snap.berkeley.edu/project?user=cindyli&project=3-body%20simulator
Screenshot of the simulation:
Code for this simulation:
Body-diagram & formula derivation:
Analysis:
The 3-body diagram is very challenging for me because there are too many variables, and it was really difficult to conduct complicated operations on Snap so that I had to create several intermediate variables. I did not make the net momentum zero so the orbits of these three planets cannot remain the same.
In summary, the reasons that lead to the weirdness of the code might be:
Computational inaccuracies with the model, especially when the planets get close (mathematically, as d^2 gets very small, 1/d^2 gets huge)
Initial conditions not right for a “good” orbit. And yes, apart from the computational issues above, this system would absolutely behave this way (although much more slowly at huge distances). And the real world system would be just a sensitive to initial conditions. If the velocities start too big, they will separate, never to return. If too small or in wrong direction, they’ll smash into each other. I suspect that by playing around with the initial velocities, you’ll eventually find a configuration that lasts for 10-15 orbits before the numerical issues cause them to collide.
If the orbits want to be remaining the same, the initial momentum net force should be 0.
The over-simplified code makes some error in the simulation: the energy is eventually losing (because the orbit is getting smaller and smaller eventually)
conclusion & takeaways
conclusion & takeaways
This project helps me develop my logic skills in practicing block coding. The central coding idea is to use the Universal Gravitation Laws, which is applicable in the space as well. As a huge portion of universe remain unknown and mysterious, it is still worth to try to predict the system and study for the pattern in universe. Thanks to Dave and his patient instruction, it was a really fun experience making simulations:). This project not only helped me grasp physics related concepts but also made it clearer and more direct.
Works Cited
Works Cited
Boundless Physics. “Newton’s Law of Universal Gravitation”. https://courses.lumenlearning.com/boundless-physics/chapter/newtons-law-of-universal-gravitation/ Retrieved May 20, 2020.
Dave Otten. “Orbit Simulator”. https://snap.berkeley.edu/project?user=daveotten&project=Orbit%20Simulator Retrieved April 20, 2020.
Fritzsche, Hellmut. "electromagnetic radiation | physics". Encyclopædia Britannica. p. 1. Retrieved May 10, 2020.
"Hubble sees galaxies galore". spacetelescope.org. Retrieved May 25, 2020.
Itzhak Bars; John Terning (November 2009). Extra Dimensions in Space and Time. Springer. pp. 27–. ISBN 978-0-387-77637-8. Retrieved May 1, 2020.
Northwestern University. “Space Environment Project”. http://www.qrg.northwestern.edu/projects/vss/docs/space-environment/zoom-travel.html. Retrieved April 15, 2020.
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