Johannes Kepler explained what was happening with the planetary motion, but Newton was not satisfied with that. He wanted to figure out why the planets act the way they do. He knew that there must be a cause of the elliptical motion—he knew there was a force that governed this motion. Knowing that a force must be present to change the direction of motion, he deduced that there was a force that the Sun exerted on the planets to pull them into an orbit. After much deliberation, he found out that the laws that dictated the motion on Earth also applied to those on a much larger scale, but that force of gravity was somehow diluted because of distance. Using the apple example, he showed that the acceleration of the moon toward the Earth was proportional to the inverse of the square of the distance from the center of the earth. Watch this video to find out more.
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Description |
Narration |
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Slide 1 shows a hand holding an atom. As the narrator speaks what he says shows on the slide. |
This lesson is about Newton's law of universal gravitation. Every particle of matter is composed of atoms. |
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Slide 2 shows an image of electrons around a nucleus. As the narrator speaks what he says shows on the slide. |
Every atom is composed of electrons circling around the nucleus. |
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A diagram is showing protons in yellow, neutrons in orange and the electrons moving around the outside. Each part of the diagram is labeled. As the narrator speaks what he says shows on the slide. |
Every nucleus is composed of protons and neutrons. OK, we see a diagram there. You'll notice that we have the protons of the positive yellow's. The neutrons of the neutral orange. And then you have the electrons moving around the outside. |
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The number 4 is walking with eyes on it in the top right corner of the slide. As the narrator speaks what he says shows on the slide. |
In nature, there are four unique forces that exist. They are called the fundamental forces of nature. |
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A green circle with a face on it is holding weights over his head in the top left corner of the slide. As the narrator speaks what he says shows on the slide. |
The strong nuclear force is responsible for keeping the nucleus together in an atom. It is the strongest of the four forces, but has a very short range, diameter of the nucleus. The force is carried by gluons. The second strongest force is the electromagnetic force, and is responsible for the charge of a particle. |
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An image of a light bulb is at the bottom of the slide. As the narrator speaks what he says shows on each slide. |
The electromagnetic force has an infinite range and is carried by photons. The weak force is responsible for changing quarks, which allows protons to turn into neutrons. The weak force is a very short range, approximately 0.1% the width of a proton. The force is carried by bosons, which are w and z particles. The gravitational force is responsible for the attraction of the objects that have mass. It is the weakest of the four forces-- 10 to the negative 40th of the strong force. The force is carried by what we call gravitons. All other forces are non-fundamental. Newton provided an understanding of gravity. The only known force in his time, and founded what we call his last law. Newton's law of universal gravitation, which tells us that every particle in the universe attracts every other particle. A force of gravity is proportional to the product of their masses and inversely proportional to the distance between the masses squared. This relationship had one fault. The units didn't work out. So if we'd kept the just as Sir Isaac Newton once did, we'd see that the units do not work out. Because of this, Newton had to place a constant into the equation. He named the constant the Universal Gravitational constant, or capital G. It was found out much later that g is equal to 6.673 times 10 to the negative 11th Newton meters squared divided by kilograms squared, and is the same throughout the universe. There is the variable form of the formula, f equals Gm1m2 divided by r2 or the distance squared. m1 and m2 are the masses of the objects in question. r is the radial distance between the two objects center of mass as you see there. When distances get to be large like between planets, a new non-SI unit is used. This is what we call astronomical units. The distance from the Earth to the sun is 1 AU. 1 AU is 1.5 times 10 to the 11th meters. We know that weight is a force caused by gravity. We can find our weight using this law. So if we set weight equal to GM on earth, the m of you, divide it by r2, we see that the mass of you times G, which is equal to the weight, is equal to the gravitational constant times the mass of the Earth times the mass of you divided by the distance between the Earth and you squared. So if we cancel out the two common factors here, which is the mass of you, we find that G on any planet can be solved by the same law, which is the G of that planet, or the gravity, is equal to the gravitational constant times the mass of that planet divided by the radial distance squared of that planet. M is the larger of the two masses involved. The acceleration due to gravity, g, is caused by a net force gravity. |
Question
Newton's epiphany supposedly happened when an apple fell on his head. He compared the gravitational pull on the apple to the gravitational pull on the Moon. The acceleration of the apple was found to have a magnitude of 9.81 m/s2 and the acceleration of the Moon (toward the Earth) was found to be 0.00272 m/s2. How can this be explained comparing distance between the objects involved?
Because the Moon is 60 times as far away from the center of the Earth than the apple was when it fell, the acceleration of gravity on the Moon is \(\small\mathsf{ \frac{1}{60^2} }\)th of the acceleration on the apple.
\(\small\mathsf{ \frac{g_{moon}}{g_{apple}} = \frac{0.00272 \text{ m/s}^2}{9.81 \text{m/s}^2} = \frac{1}{3600} }\).
