At-home STEM Activities: Kepler's Laws of Planetary Motion and DIY Gravity Well
We’re spending this week looking at planets!
In the mid-1500s, Polish astronomer and mathematician Nicolaus Copernicus proposed that the planets moved around the Sun in uniform circles.
Nicolaus Copernicus
Copernican model of the solar system
But Copernicus’s planetary model wasn’t immediately accepted in the scientific community. In fact, a lot of scientists thought Copernicus’s model was wrong, including Danish astronomer Tycho Brahe. Brahe thought all the planets moved around the Sun, except for Earth. In Brahe’s model, the Earth was stationary, the Moon and Sun revolved around the Earth, and the other planets revolved around the Sun.
Tycho Brahe
Tychonian Model of the solar system—The Earth is the black dot in the center, with the sun and moon shown in orbit around it. The rest of the planets revolve around the sun, and the whole system is surrounded by a sphere of stars.
Johannes Kepler
However, Brahe’s assistant, German astronomer Johannes Kepler, thought Brahe’s model was wrong—Kepler was fully convinced the Copernican model was correct. Brahe was known for his precise and detailed observations of the sky, so by analyzing Brahe’s observational notes of Mars, Kepler was able to come up with a new (and true!) model of the solar system.
Kepler’s model was heliocentric, which means all the planets orbit the Sun, like Copernicus’s. Unlike Copernicus’s model, though, Kepler claimed the planets traveled in elliptical paths.
Planetary orbits, as proposed by Kepler Image via anatomynote.com
Not only was Kepler able to develop an accurate model of the solar system, he came up with three Laws of Planetary Motion, which can be summarized as
1. Planets follow an elliptical orbit.
an ellipse is like a stretched out circle. For a Circle, every point on the circle is the same distance from the circle’s center. For an Ellipse, the two points inside are called the foci (an individual is a focus) and the sum of the distance between the foci and any point on the ellipse is constant. The closer the two foci are to each other, the closer the ellipse becomes to a circle. Image via CK12.org
2. For each planet, if we draw a line from the planet to the Sun, it will sweep out the same size area in the same amount of time.
Here, the planet it travelling the same amount of time along it's orbit (The curved path). The Green wedges all have the same area. Notice that as the planet gets closer to the sun, it travels a further distance. So what Kepler’s 2nd Law of Planetary Motion is saying is that A planet moves faster when it’s closer to the Sun and slower when it’s farther away. Image via CK12.org
3. The amount of time it takes for a planet to complete one full orbit around the Sun is called a period. If you square the ratio of any two planets’ periods, it will be equal to the cube of the ratio of the average distance of each planet to the Sun.
Here, T is the planet’s period and r is the average distance to the Sun. The subscripts denote if we’re talking about Planet 1 or planet 2.
If we move around this equation a little bit, we get:
So Kepler’s Third Law of Planetary Motion says that for any planet, if you square its period and cube its distance from the Sun, then divide the two numbers, you’ll get the same number for every planet in the solar system.
Check out this video for a little more information about Kepler’s Laws of Planetary Motion:
Now that we have a better idea of how planets orbit the Sun, let’s simulate planetary motion by making our own gravity well!
DIY Gravity Well
Materials:
Large bowl
Stretchy fabric, like a cotton blend t-shirt
Rubber band, big enough to go around the bowl, or binder clips
Heavy ball, like a golf ball or something similar
Marble, round bead, or something similar
Instructions:
1. Place the stretchy fabric over the top of the bowl. Stretch the fabric tightly and use the rubber band or binder clips to hold it in place.
2. Place the heavy ball in the center of the fabric.
3. First place the marble on the side and let it go. What path does it follow?
4. Next, roll the marble along the side of the bowl. What path does it follow now?
So how does this simulate planetary orbit?
We can think about gravity as the pulling of the stretchy fabric. When we place the heavy ball, our Sun, in the middle of the fabric it bends the cloth. So when we let our little marble planet go in the gravity well, the heavy ball’s gravity is pulling the marble towards it. When we gave our marble a little push, though, it started to orbit the ball in an elliptical path.
Our set-up is on such a small scale, that that marble quickly collides with the heavy ball, but on a massive scale, like with a planet and the Sun, an initial velocity allows the planet to stay orbiting the Sun.
Take this activity further by changing the scale on your gravity well. Try stretching fabric over a hula hoop or building a frame with PVC pipes. Change the size of the balls—what happens when the balls are really different in size? What about if the balls are really close in size?
