July 21, 2009

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This lesson introduces Newton's Universal Law of Gravitation, including the equation. The strives to create an intuitive sense of the law and simply explain the equation that describes it.

- Mathematics > General
- Science > General
- Science > Astronomy
- Science > Earth Science
- Science > General Science
- Science > History of Science
- Science > Physics

- Grade 6
- Grade 7
- Grade 8

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This resource was reviewed using the Curriki Review rubric and received an overall Curriki Review System rating of 3, as of -0001-11-30.

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This resource received a 3* rating because it is part of the larger resource A Tour of the Universe, which received a rating of 3-Exemplary in the Curriki Review System. You can learn more about this larger resource by reading its review and comments.

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This lesson is designed for middle school students with no previous knowledge of astronomy or the history of astronomy. For this lesson, I spend a fair amount of time with the students playing with the cannon ball simulator in order to make sure they really start to understand what's going on with gravitational force. Also, there is a bit of notation and symbols that need to be introduced and a few calculations to be done, and this could take longer for some students than others.

Any

- Explain gravitational force
- Describe why the force changes depending on the mass of the objects and the distance between them
- Explain the difference between weight and mass

Why was the Scientific Revolution important and how did it contribute to progress?

Image of cannon and, if you have it, an apple (I find it helpful to drop the apple from various heights to work on the idea of gravity extending to the moon and discussing the variation of force).

Also, I use myself in the example for calculating mass, you will probably want to calculate the mass of a different object that is familiar to you students.

Books:

*The Story of Science Newton at the Center*by Joy Hakim. Published by Smithsonian Books, 2005. (Chapter 13)

[Note: This lesson in its entirety with images can be found as an attached pdf and doc file. The attached version has much nicer equations than the ones that appear here in the wiki version.]

- Describe gravity in words
- Develop the idea of the cannon ball falling into the Earth but having enough force to not crash into Earth
- Abstract the idea of the cannon ball to the Moon
- Explain the difference between mass and weight
- Calculate mass

Everyone should have read about Newton’s Universal Law of Gravitation last night. In general, what does this law state? [the Earth’s gravity pulls on everything; all objects have their own gravitational force and pull on everything else; it is gravity that keeps the planets, moons, stars in their orbits]. What is it that determines the amount of gravitational pull, because, obviously, the Earth doesn’t have the same pull as an apple...[The amount of attraction is determined by the mass and the distance between the two objects].

What is this thing we call mass, though? Why is it not your weight that affects your gravitational pull? Your mass contributes to your weight, but not the other way around. Your mass is the amount of matter in you, and your weight is calculated based on that amount of matter.

But, how does this really work? Newton’s truly brilliant idea was: if the force of gravity reaches to the top of the highest tree, might it not reach even further; in particular, might it not reach all the way to the orbit of the Moon! Then, the orbit of the Moon about the Earth could be a consequence of the gravitational force, because the acceleration due to gravity could change the velocity of the Moon in just such a way that it followed an orbit around the earth. But that’s a bit confusing...

This might make more sense if we do the following thought experiment: Imagine a cannon sitting on top of a mountain. We have the ability to control the force at which the cannon fires a cannon ball, thereby changing the velocity (speed + direction) of the cannon ball. If we simply fire the cannon ball from the cannon, the ball will eventually fall to Earth because of the gravitational force acting on the ball. But, if we increase the force of the cannon, thereby increasing the speed and velocity of the cannon ball the ball would travel completely around the Earth, always falling in the gravitational field but never reaching the Earth, which is curving away at the same rate that the ball falls. That is, the cannon ball would have been put into orbit around the Earth.

Newton realized that the orbit of the Moon followed the same concept: the Moon continuously "fell" in its path around the Earth because of the acceleration due to gravity, thus producing its orbit.

Newton’s Universal Law of Gravitation states: Gravity is an attractive force acting on everything in our universe. The greater the mass of an object, the greater its attraction to another object. Gravity weakens over distance (by the square of the distance – meaning if the distance doubles, the force becomes ¼ as strong). Newton summarized his Law in this equation:

Force_gravitational = G x m_1 x m_2 / d^2

Where:

G is the gravitational constant 6.67428x10^-11 m^3 kg^-1 s^-2

m_1 is the mass of the first object (kg)

m_2 is the mass of the second object (kg)

d is the distance between the two objects (m)

But, really, what is my mass compared to the Earth’s? Or yours? And, clearly, we’re not quite like the moon or a giant cannon ball since we’re standing on the Earth, so the distance between us is hardly anything. So, what is the gravitational for us?

Well, because the Earth is so massive and we reside on or near the surface of Earth, G x m_Earth / d^2 is the same for everyone, assuming m1 is the mass of Earth and d is the radius of Earth. Scientists have calculated G x m_Earth / d^2 = 9.8 m/s^2. Does that number look familiar to anyone? It should, it’s what we often refer to as gravity. In science, we refer to 9.8 m/s2 as g, which is the gravitational force on Earth.

But, what about m2? Where did it go in all of this? Don’t worry, it didn’t disappear!

What we’re left with in our equation is: F_gravitational = g x m2 = 9.8 x m2. But what’s m2 in this case? Well, that depends, it’s different for everyone in this room, because we could each be an m2. But, we could find out. How, you ask? Well, I’ve been keeping something from you, see, F_gravitational is more commonly known by another name: weight! So, I know my weight is 120 pounds, I need to convert that to kilograms to get the units right, which I did. I weigh roughly 54.43 kilograms. So, what is my mass? Well, what do I know? [F_g and g]

So, my equation now looks like:

F_gravitational = g x m_meredith

54.43 = 9.8 x m_meredith

5.55 kg = m_meredith

My mass on Earth is roughly 5.55kg. Over the next few lessons, we’ll be discussing why mass is so important to know. And because of that, I need each of you to calculate your own mass for our next lesson.

**Extension:**

If you have more time, another cool demonstration is to show how Fg changes over very short periods of time due to the fact that g is in terms of m/s^2. I like to demonstrate this outside for easier clean-up. Hold your apple about two inches above the ground and ask students what will happen if you drop it. Ask students why it will be pulled down toward the Earth. Drop the apple. )It should fall and bounce, maybe, but no real harm) Then remind them that what's pulling the apple down is not simply gravity, but the *force* of gravity, which means that the force will change if you change the variables. Hold the apple up about 5 feet off the ground and ask students what variable you're changing and what they expect to happen. (The variable you're changing is the time the apple is accelerating toward Earth. Because the time is increasing, the apple is accelerating more, and the force is increasing -- you may have to explain this last part). Drop the apple and notice any differences in the outcome. Finally, review the same questions from the last drop, but this time hold the apple from much higher (I prefer to use a 40 foot ladder). By this time, it should be sinking in that the time spent traveling towards Earth is causing the apple to accelerate more and thus increase the Force of gravity. Drop the apple and notice differences between the drops.

At the end of this lesson, students are asked to
complete he reading "Newton Moves" (Chapter 16) in *The Story of Science Newton at the Center* by Joy Hakim.

Also, students are asked to find two to three facts about Newton's life they find interesting and calculate their own mass. The assessment can be found as a separate wiki page here, where there is also a pdf and doc version available for download.

Newton's Universal Law of Gravitation Lesson (pdf)

Newton's Universal Law of Gravitation Lesson (doc)

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