Italian scientist Galileo Galilei, a brilliant astronomer who made many contributions to the world of science.
Italian scientist Galileo Galilei, a brilliant astronomer who made many contributions to the world of science.

Gravity is the reason behind books being dropped and suitcases feeling heavy. It’s also the reason our atmosphere sticks around and oceans staying put on the surface of the earth. Gravity is what pulls it all together, and we’re going to look deeper into what this one-way attractive force is all about.


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One of Newton’s biggest contributions was figuring out how to show that gravity was the same force that caused both objects like an apple to fall to the earth at a rate of 9.81 m/s2 AND the moon being accelerated toward the earth but at a different rate of 0.00272 m/s2.  If these are both due to the same force of gravity, why are they different numbers then? Why is the acceleration of the moon 1/3600th the acceleration of objects near the surface of the earth? It has to do with the fact that gravity decreases the further you are from an object. The moon is in orbit about 60 times further from the earth’s center than an object on the surface of the earth, which indicates that gravity is proportional to the inverse of the square of the distance (also called the inverse square law). So the force of gravity acts between any two objects and is inversely proportional to the square of the distance between the two centers.  The further apart the objects are, the less they force of gravity is between the two of them. If you separate the objects by twice the distance, the gravitational force goes down by a factor of 4.


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All objects are attracted to each other with a gravitational force. You need objects the size of planets in order to detect this force, but everything, everywhere has a gravitational field and force associated with it. If you have mass, you have a gravitational attractive force.  Newton’s Universal Law of Gravitation is amazing not because he figured out the relationship between mass, distance, and gravitational force (which is pretty incredible in its own right), but the fact that it’s universal, meaning that this applies to every object, everywhere.


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Lord Henry Cavendish in 1798 (about a century after Newton) performed experiments with a torsion balance to figure out the value of G. It’s a very small number, so Cavendish had to carefully calibrate his experiment! The reason the number is so small is because we don’t see the effects of gravity until objects are very massive, like a moon or a planet in size.


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How do astronomers find planets around distant stars? If you look at a star through binoculars or a telescope, you’ll quickly notice how bright the star is, and how difficult it is to see anything other than the star, especially a small planet that doesn’t generate any light of its own! Astronomers look for a shift, or wobble, of the star as it gets gravitationally “yanked” around by the orbiting planets. By measuring this wobble, astronomers can estimate the size and distance of larger orbiting objects.


Doppler spectroscopy is one way astronomers find planets around distant stars. If you recall the lesson where we created our own solar system in a computer simulation, you remember how the star could be influenced by a smaller planet enough to have a tiny orbit of its own. This tiny orbit is what astronomers are trying to detect with this method.


Materials


  • Several bouncy balls of different sizes and weights, soft enough to stab with a toothpick
  • Toothpicks
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Weight is nothing more than a measure of how much gravity is pulling on you. This is why you can be “weightless” in space. You are still made of stuff, but there’s no gravity to pull on you so you have no weight. The larger a body is, the more gravitational pull (or in other words the larger a gravitational field) it will have.


The Moon has a fairly small gravitational field (if you weighed 100 pounds on Earth, you’d only be 17 pounds on the Moon). The Earth’s field is fairly large and the Sun has a HUGE gravitational field (if you weighed 100 pounds on Earth, you’d weigh 2,500 pounds on the Sun!).


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At some point in the future you may ask yourself this question, “How can gravity pull harder (put more force on some things, like bowling balls) and yet accelerate all things equally?”
 
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If you could stand on the Sun without being roasted, how much would you weigh? The gravitational pull is different for different objects. Let’s find out which celestial object you’d crack the pavement on, and which your lightweight toes would have to be careful about jumping on in case you leapt off the planet.


Weight is nothing more than a measure of how much gravity is pulling on you. Mass is a measure of how much stuff you’re made out of. Weight can change depending on the gravitational field you are standing in. Mass can only change if you lose an arm.


Materials


  • Scale to weigh yourself
  • Calculator
  • Pencil
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What happens to gravity if you’re in a rocket moving up through the atmosphere to a satellite in orbit?


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First we’re going to assume the earth is like a ball in that it’s a perfect sphere, and also that the density of the earth is even and it depends only how far from the center of the earth you are. Let’s also assume the earth isn’t rotating. Once we have these things in mind, then the magnitude of the force of gravity acting on an object goes like this…


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There are three main differences between assuming the earth is round, uniformly dense, and not rotating as we did before.


First, the crust is not uniform. There are lumps and clumps everywhere that vary the density add up to make small variations in the force of gravity that we can actually measure with objects in free-fall motion. It’s actually how scientists find pockets of oil in the earth. They measure the surface gravity and plot it out, and if there’s a large enough deviation, it means there’s something interesting underground.


This image of the Mors salt dome in Denmark was studied for radioactive waste disposal. It’s a surface gravity survey that measures the acceleration due to gravity that shows something interesting is underground! The dots are the places where gravity was actually measured. You can read more about how gravity is measured from advanced lecture notes here. The unit of measurement for these deviations is called the “milligal” for Galileo, where 1 gal = 1,000 mgal = 1 cm/s3.  



 


Click here to go to next lesson on The Earth is not a Sphere.

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The second problem with our assumption sis that the earth is not a sphere. It’s flattened a bit at the poles and bulges out at the equator. The ring around equator is larger than a ring around the poles by 21 km, which makes the poles closer to the center of the earth than the equator! Free-fall at the poles is slightly more than free-fall at the equator.


But before you book a trip to skydive in Ecuador, Colombia, Brazil, Sao Tome, Gabon, the Republic of the Congo, the Democratic Republic of the Congo, Uganda, Kenya, Somalia, Maldives, Indonesia or Kiribati, let’s talk about the assumption we made… The earth really does rotate. That’s not a surprise. How does this affect the value of g then? The bottom line is that gravity changes with altitude from 9.78 to 9.84 m/s2., mostly due to the earth spinning, but some to the earth not being a perfect sphere.


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