Gravity Gravity
To demonstrate the relative weakness of gravity compared to other forces.
To explain the difference between Newtonian gravity and Einsteinian gravity.
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This section addresses, in whole or in part, the following National Science Education Standards:
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A Matter of Some Gravity
Introduction
There are four forces in nature. All other forces (friction, normal, centripetal, etc.) are manifestations of one or more of the four. The four are:
To be technically precise, the electromagnetic force was originally seen as two independent forces, the electric and magnetic forces. It was just more than a century ago that they were seen to be two aspects of the same force of nature. In more recent years, the weak nuclear force was also seen to be an aspect of a larger force of nature that combined it with the electromagnetic force, called the electroweak force. So three of the four are apparently, really, one force.
So what about gravity? Is it part of some grand unified force uniting all four forces? Don’t know. Nobody does.
In our everyday lives, and through the greatest part of human history, gravity was THE force of nature. It is all pervasive; from the moment we are born we have to fight gravity. There is no escaping it. Let’s take a look at it and its effects on us.
Vocabulary
G
g
inverse square law
warping of space
weighlessness
free-fall
The force of this force
All the forces of nature it is the weakest one. By far. Granted at macroscopic sizes we don’t feel the effects of the two nuclear forces though when any matter is within their limited, microscopic, atomic ranges of distances, the nuclear forces overpower everything else. Compared to the electromagnetic force, you shouldn’t even notice gravity! The electromagnetic force is 1039 times stronger than gravity. That’s a 1 followed by 39 zeros. If you have one dollar representing gravity, electromagnet force is represented by a thousand trillion trillion trillion dollars. That’s a 100 trillion trillion times more than the entire world’s gross domestic product, how much money the whole world made in 2005.
You can easily prove how weak gravity is. Hang a paperclip on a thread so it is vertical under the influence of gravity. Then bring a magnet slowly down from above the paper clip. At some point, magnetic force will overcome gravity and bring the clip to the magnet.
So if gravity is so darn weak, why is it so darn obvious?
As you will see when you read about the other forces, the electromagnetic force is a force between charged particles. All matter has positive and negative charges. Electromagnetism can have a positive, attractive force, a negative repulsive force, and even no force if there are neutral particles around. Consequently, there are many of each kind in any clump of matter and basically the sum total of all their forces cancel out. But gravity has only one kind, attractive. So while the average electromagnetic force is a 50-50 split between attraction and repulsion, gravity always pulls things together. And we notice it because it is that way all the time.
Gravity was not discovered by Sir Isaac Newton. Some aspects of gravity have been known by other scientists, ancient and contemporary to Newton. But Newton was the first to properly explain it and quantify it. Give it a numerical basis as well as a proper understanding of where it comes from and what it does. It’s probably just a legend that a falling apple conked Newton on the head, making sense of gravity. But he did explain how the apple and the moon are both governed by the law.
What Gravity IS
There are two key points to know about gravity. First, it is universal. Gravity doesn’t stop at a certain range. It may be negligible and less important in the situation but it is never absent. Second, it is a mutual force. It doesn’t exist independently, it is always between TWO objects pulling on each other with the same amount of force.
There is therefore gravity between you and me, wherever we are. There is gravity between you and a bus, you and the Earth, you and the Moon, you and the next galaxy, you and a quasar near the edge of the universe. And all the pairs are pulling on each other with the same identical amount of force. Whatever gravity you feel from me, I feel from you. Your gravitational effect on the Earth equals what the Earth does on you.
How much gravity is there?
How MUCH gravity there is between each of the mutual pairings DOES vary. It depends on two factors, the amount of mass BOTH objects have, and the distance between them.
Newton determined that the amount of gravity increases by the product of the two masses, and decreases by the distance between them, squared. Expressed as an equation,
| Fg ≈ m1 * m2
r2 |
The m’s are the masses of the two objects, you and the moon, for example. Notice that the masses are multiplied, not added. Thus the gravitational force can’t be zero as long you have two masses, which there always are. Double one mass, gravity doubles. Double one and halve the other, the gravity doesn’t change. But our human masses are pretty small. So the amount of gravity, even when we are within touching distance, is pretty small. Maybe it would make a difference two a couple of astronauts in deep space but on Earth, well, we’re just not apparently attracted to each other. Sorry.
But the amount of gravity does go down, and rapidly, with increasing distance. Double the distance and gravity goes down by 2-squared, or to 1/4th of the original value. Move ten times farther away and gravity is just 1%, 1/100th of what you originally had. This is an example of something called the inverse square law. The distribution of light from a light source, heat from the sun, and the force of electrically charged particles and magnets, all are examples of an inverse square relationship. Effects weaken very rapidly….but they never go to zero except at an infinite distance away.
This is why even the biggest sources of gravity, i.e, BIG MASSIVE BODIES, if they are far away are not usually any great influence on us in our daily lives. Over the long term, yeah, maybe.
And vice versa. You don’t matter much to the residents of the Andromeda Galaxy. The force you feel from them is as weak as the force they feel from you. It doesn’t matter if you or the Andromedans are focus of interest, it doesn’t matter if that equation has m1 * m2, or m2 * m1, the products are the same. The forces are mutual and equal. And it doesn’t matter if you measure from here or from there. “r” is “r”.
The
mutual aspects of gravity
But if the forces are equal, why is it that you can jump up and the Earth pulls you down? Well, it doesn’t actually. You jump up and you are pushing on the Earth, right? By Newton’s Third Law, there is an equal and opposite reaction to your action. You do push the Earth away…but…there’s a real big difference between the mass of you and the mass of Earth!
Recall Newton’s Second Law, F = m*a.
Since the forces of gravity on you and by you are equal, myou*ayou = mearth*aearth.
But the mass of Earth is millions of times more than your mass! To keep the equations balanced and equal, the Earth’s acceleration must be millions of times LESS than your acceleration.
So you may jump up a half of a meter and fall that much back. But the Earth moves that half meter….divided by some number of millions. It’s a lot more noticeable to you than to the Earth.
The
real numbers about gravity
Let’s get the hard math part out of the way now.
Force in metrics is in Newtons (named, of course, for Sir Isaac).
Mass is in kilograms and distance in meters.
If you stick in standard values for you and the Earth, at a distance to the center of the Earth, you won’t get your weight correct (weight being the value of the force of gravity on you). The equation needs an additional fudge factor, to get the value straight and make the units on the right equal Newtons on the left. That factor is called the gravitational constant, G. “Capital G” equals 6.6742 x 10-11 and has units of N*m2/kg2. Our equation should read:
|
r2
|
For more of this equation, its values and the various things that happen when you change masses and distances, go here: http://www.physicsclassroom.com/Class/circles/U6L3c.html
As explained earlier, everything falls at the rate of 9.8 meters per second per second, something called the gravitational acceleration, or g. This value is what you get if you substitute the value of the mass and radius of Earth into the equation and forget about the other mass (you). 5.9736 x 1024 kg. The radius is 6.3781 x 106 meters. You can do the mass. When you fall off the ladder, jump out of an airplane, you fall at this rate, and this is called free-fall.
Then, as in the section on forces and motions, your weight is just your mass m * g. But that’s the m we took out of the equation above.
Gravity in space
What about anything else the Earth affects? Like the Moon?
The Moon is about 60 times farther way. So the mutual gravitational acceleration between Earth and Moon is about 1/3600, or 9.8*0.01/3600, or about 3 millimeters per second squared. But that’s all the Moon needs to be kept in orbit around the Earth.
The Earth and Moon.
Images courtesy of
NASA, JPL.
Image # :
PIA00342 (left),
Image # :
P-19891(right)
Another take on the history of Sir Isaac explaining the moon’s orbital motion can be found here: http://www.physicsclassroom.com/Class/circles/U6L3b.html Be sure to click on the fun Animation graphic, too!
The gravity ON the Moon is less, too, because it has a smaller size and mass. If you substitute a mass of 1/100th of the Earth and a radius about 1/4th that of Earth, you get a g value for the Moon 1/6th as much as Earth’s or 1.56 meters per second squared. A 200 pound person will be just a 32 pounder on the Moon.
Hammer and Feather video
Hammer and feather video
Hammer and feather video
How about effects of the Moon and other bodies on the Earth? The Moon is the closest so you would think it should have a pretty good effect on us. But how about that big ol’ Sun? The Sun is 3,330,000 times more massive than Earth and another factor of a 100 times more compared to the Moon, but it is more than 400 times farther away. The Sun raises tides in the oceans of an average of a foot (1/3rd meter). The Moon’s tides on us is 3 times more. The tides raised by the nearest planet, Venus? Hardly noticeable, and big planet Jupiter, about the same. There is more gravitational pull on you from the doctor that delivered you in the hospital, or the city bus passing the hospital, than from any other object in space.
But perhaps you thought in space everything is weightless? That can be true! But that doesn’t mean there is no gravity! Astronauts in orbit in the Space Station are only about 250 miles (400 km) above the Earth surface. Add that distance to the “r” factor and you still have about 90% of the gravity at Earth’s surface. So how come they float around? They are falling towards Earth because now there is no ground to stop their fall. But the station is also going perpendicular to that fall so instead of falling DOWN, the station and occupants fall AROUND the Earth. Hence, there is gravity but no weight! Free fall, with a twist!
Astronaut Bruce McCandless on an untethered
EVA.
Image courtesy of Great Images in
NASA.
Go here to see how gravity changes as you move away from Earth…. http://www.physicsclassroom.com/Class/circles/U6L3e.html
You are in weightless for an instant when you jump up, when you reach the peak of your jump before you start to free-fall downwards. You can even feel a bit lighter in a fast elevator going down in some tall sky scraper. You are closer to free-fall, and weightlessness there, and can get a longer moment of it if you jump up during the elevator’s most speedy part of its descent. Also, at the top part of a roller coaster ride when the coaster seat beneath starts to fall near the rate of gravitational free-fall. Certain NASA planes, where the pilot puts the plane into free fall allow trainees to get up to 30 seconds of apparent weightlessness. See here for more “amusement park free fall physics”: http://www.learner.org/exhibits/parkphysics/freefall.html
Astronauts Experience Weightlessness in the
KC-135 Vomit Comet
Image courtesy of Great Images in
NASA.
Other gravity aspects
Gravity has undergone an ‘improvement’ since the days of Newton. Just a hundred years ago, Einstein came up with his theories of relativity. Among the aspects of those theories was that gravity was no longer ‘just a force’. In fact, Einstein showed that you could interpret gravity as a warping of space.
Think of a pool table. Normally flat and smooth. But now, every place there is billiard ball, the table sinks downwards, like it was rubber. That’s warping of space.
Now shoot a marble on this flexible pool table. When the marble gets near any ball, it changes its path because the table underneath the marble is bent ‘downwards’. It just doesn’t fall; it still has its forward motion. So the marble’s path bends and curves away from being straight. If it doesn’t go too deep into this ‘well’, it will resume a straight path when it gets out of the well.
As far as the marble is concerned, a force pulled it out of its original path but in the Einsteinian universe, it simply traveled a path of least resistance through the well and out again.
If the marble had fallen too deeply into the well, it would have been trapped, like a satellite, or even crash landed at the bottom of the well, like a meteorite. And we haven’t even discussed about the well that moves along with the marble!
If there is enough mass, then the well becomes so deep that anything that falls close enough can never get enough energy to escape it. Even mass-less objects like photons of light. This is the way a ‘black hole’ works, but that’s a subject for an astronomy class.
Review Questions
Find the values for the mass of Mars and Earth and calculate the force in Newtons between them at their closest distances (this is found by subtracting Earth’s average orbital distance from Mars’). How does that compare with your weight in Newtons on Earth?
If the distance between two masses is suddenly 5 times closer than before, how will the amount of gravity change?
Explain how weightlessness occurs.
Demonstrate the relative weakness of gravity compared to other forces, especially the electromagnetic force.
Explain the difference between Newtonian gravity and Einsteinian gravity.
Define
G
g
inverse square law
warping of space
weighlessness
free-fall
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Content provided by Mr. Larry Krumenaker, Georgia Perimeter College
Gravity icon from http://www.icteachers.co.uk/children/sats/gravity.htm
Page created by Pamela J.W. Gore
Georgia Perimeter College,
Clarkston, GA
Page created March 7, 2007
Modified May 27, 2007