Johannes Kepler, a German mathematician and astronomer in the 1600s, was one of the key players of his time in astronomy. Among his best discoveries was the development of three laws of planetary orbits. He worked for Tycho Brahe, who had logged huge volumes of astronomical data, which was later passed onto to Kepler. Kepler took this information to design and develop his ideas about the movements of the planets around the Sun.

Kepler’s 1st Law states that planetary orbits about the Sun are not circles, but rather ellipses. The Sun lies at one of the foci of the ellipse.

Well, almost.

Newton’s Laws of Motion state that the Sun can’t be stationary, because the Sun is pulling on the planet just as hard as the planet is pulling on the Sun. They are yanking on each other. The planet will move more due to this pulling because it is less massive. The real trick to understanding this law is that both objects orbit around a common point that is the center of mass for both objects. If you’ve ever swung a heavy bag of oranges around in a circle, you know that you have to lean back a bit to balance yourself as you swing around and around. It’s the same principle, just on a smaller scale.

Please login or register to read the rest of this content.

Kepler’s Laws of planetary orbits explain why the planets move at the speeds they do. You’ll be making a scale model of the solar system and tracking orbital speeds.

Kepler’s 1st Law states that planetary orbits about the Sun are not circles, but rather ellipses. The Sun lies at one of the foci of the ellipse. Kepler’s 2nd Law states that a line connecting the Sun and an orbiting planet will sweep out equal areas in for a given amount of time. Translation: the further away a planet is from the Sun, the slower it goes.
Please login or register to read the rest of this content.

If one of Kepler’s Laws describe the orbits of satellites as being an elliptical orbit, you might be wondering what an ellipse is! Here’s a really neat way to make an ellipse using a pencil and a rubber band:

 

Click here to go to next lesson on Applying Kepler’s Laws.

[/am4show]

Let’s try a few practice problems so you get more familiar with how to use and apply Kepler’s Laws to real world physics problems…

Please login or register to read the rest of this content.

A satellite is an object that orbits the sun, earth or other massive body like a planet, moon, asteroid, or even galaxy. There are two kinds of satellites: natural, like the moon, and man-made, like the Hubble Space Telescope.

Please login or register to read the rest of this content.

But physics doesn’t care if a satellite is man-made or not. The laws of physics and math equations still apply no matter where the satellite came from.

Please login or register to read the rest of this content.

An important concept to understand is that a satellite is a projectile, meaning that only the force of gravity is acted on it (once it’s launched). In order to maintain it’s orbit, a satellite needs to fall continuously at the same rate that the earth is curving away from it.

Please login or register to read the rest of this content.

The Hubble Space Telescope (HST) zooms around the Earth once every 90 minutes (about 5 miles per second), and in August 2008, Hubble completed 100,000 orbits! Although the HST was not the first space telescope, is the one of the largest and most publicized scientific instrument around. Hubble is a collaboration project between NASA and the ESA (European Space Agency), and is one of NASA’s “Great Observatories” (others include Compton Gamma Ray Observatory, Chandra X-Ray Observatory, and Spitzer Space Telescope). Anyone can apply for time on the telescope (you do not need to be affiliated with any academic institution or company), but it’s a tight squeeze to get on the schedule.

Hubble’s orbit zooms high in the upper atmosphere to steer clear of the obscuring haze of molecules in the sea of air. Hubble’s orbit slowly decays over time and begins to spiral back into Earth until the astronauts bump it back up into a higher orbit.

But how does a satellite stay in orbit? Try this experiment now:

Materials:

• marble
• paper
• tape

Please login or register to read the rest of this content.

Kepler’s Law of Periods relates the period T of any planet around the sun to the cube of the semi-major axis a of the orbit:

Please login or register to read the rest of this content.

A satellite is an object that does around a planet, a star, or other similar object. Here’s how you can figure out the net force of a satellite as well as the velocity of the satellite, since the only force applied to the satellite is from gravity:

Please login or register to read the rest of this content.

For a satellite orbiting around the earth at a given distance. What is the speed and acceleration of the satellite? Do you think you need to know the masses of the satellite and the earth, or just one?

Please login or register to read the rest of this content.

Here’s an overview of all the equations we’ve been using so far for our study in uniform circular motion:

Please login or register to read the rest of this content.

How fast does the moon travel around the earth? And how far away is the moon really? Here’s a way to figure out!

Please login or register to read the rest of this content.

Callisto is one of Jupiter’s moons. Would it be really cool to be able to approximate the size of Jupiter based on watching the motion of Callisto? For example, if you knew how long it took Callisto to orbit around Jupiter, and the furthest distance it traveled away from it (both of which you could measure from a backyard telescope)? Here’s how:

Please login or register to read the rest of this content.

One of the questions I get asked a lot is how fast does the International Space Station travel around the Earth? Here’s how to figure this out (hint: it’s a lot like the one we did previously with Jupiter and Callisto!)

Please login or register to read the rest of this content.

Comet Hally takes 76 years to orbit around the sun, and in 1986 it came as close as it possibly could to the sun (89,000,000 km). Can we figure out how far the comet gets from the sun based on this information? Sure! Here’s how:

Please login or register to read the rest of this content.

So, here’s a question. If you are “weightless” in space, do you still have mass? Yes, the amount of stuff you’re made of is the same on Earth as it is in your space ship. Mass does not change but since weight is a measure for how much gravity is pulling on you, weight will change. Did you notice that I put weightless in quotation marks? Wonder why?

Please login or register to read the rest of this content.

Now let’s have fun with an elevator and a bathroom scale, since we can’t easily jump ourselves into orbit.

Please login or register to read the rest of this content.

Now let’s bust the myth of weightlessness in space for good…

Please login or register to read the rest of this content.

A binary system exists when objects approach each other in size (and gravitational fields), the common point they rotate around (called the center of mass) lies outside both objects and they orbit around each other. Astronomers have found binary planets, binary stars, and even binary black holes.

The path of a planet around the Sun is due to the gravitational attraction between the Sun and the planet. This is true for the path of the Moon around the Earth, and Titan around Saturn, and the rest of the planets that have an orbiting moon.

Materials

• Soup cans or plastic containers with holes punched (like plastic yogurt containers, butter tubs, etc.)
• String
• Water
• Sand
• Rocks
• Pebbles
• Baking soda
• Vinegar

Please login or register to read the rest of this content.

Today you get to learn how to read an astronomical chart to find out when the Sun sets, when twilight ends, which planets are visible, when the next full moon occurs, and much more. This is an excellent way to impress your friends.

The patterns of stars and planets stay the same, although they appear to move across the sky nightly, and different stars and planets can be seen in different seasons.

Materials:

• Printout of Stargazer’s Almanac
• Pencil
• Tape and scissors (optional)
• Ruler

Please login or register to read the rest of this content.

If you watch the moon, you’d notice that it rises in the east and sets in the west. This direction is called ‘prograde motion’. The stars, sun, and moon all follow the same prograde motion, meaning that they all move across the sky in the same direction.

However, at certain times of the orbit, certain planets move in ‘retrograde motion’, the opposite way. Mars, Venus, and Mercury all have retrograde motion that have been recorded for as long as we’ve had something to write with. While most of the time, they spend their time in the ‘prograde’ direction, you’ll find that sometimes they stop, go backwards, stop, then go forward again, all over the course of several days to weeks.

Here are videos I created that show you what this would look like if you tracked their position in the sky each night for an year or two.

Please login or register to read the rest of this content.

Click here to go to next lesson on Potential Energy in the Stars.

In our physics problems so far, we’ve kept the objects close to the earth so that the acceleration due to gravity g remains constant, and we defined the potential energy of an object on the surface of the earth to be zero. What if we look up and see three stars in a system and want to find out the gravitational potential energy of the system?

Please login or register to read the rest of this content.

Let’s determine the gravitational potential energy of the earth-moon system as well as the speed needed to escape the Earth’s gravitational pull:

Please login or register to read the rest of this content.

Here’s how you put it all together and figure out the total energy of the system. This is useful when you’re trying to figure out something that you can’t otherwise solve for… let me show you with a set of videos here. Remember, for satellites the only force we have on the object is due to gravity, so the external work force term always goes to zero like this:

Please login or register to read the rest of this content.

A geosynchronous orbit is an orbit that a satellite has when viewed from the earth, looks like the satellite is stationary.

Please login or register to read the rest of this content.

How do you find the gravitational potential energy between two objects that are really far apart, like two stars or two galaxies? Here’s how:

Please login or register to read the rest of this content.

Imagine you and I are racing rocketships in orbit around the Earth. I can slow down and still beat you around the Earth. Want to see how?

Please login or register to read the rest of this content.

Einstein once said: “I was sitting in a chair in the patent office at Bern when all of the sudden a thought occurred to me: If a person falls freely, he will not feel his own weight. I was startled. This simple thought made a deep impression on me. It impelled me toward a theory of gravitation.”

This led Einstein to develop his general theory of relativity, which interprets gravity not as a force but as the curvature of space and time. This topic is out of the scope for our lesson here, but you can explore more about it in this lesson.

The fundamental principle for relativity is the principle of equivalence, which says that if you were locked up in a box, you wouldn’t tell the difference between being in a gravitational field and accelerating (with an acceleration value equal to g) in a rocket.

The same thing is also true if you were either locked in a box, floating in outer space or in an elevator shaft experiencing free-fall. Any experiments you could do in either of those cases wouldn’t be able to tell you what was really happening outside your box. The way a ball drops is exactly the same in either case, and you would not be able to tell if you were falling in an elevator shaft or drifting in space.

Please login or register to read the rest of this content.