Hi. It's Mr. Andersen and this AP Physics essentials 25. It is on gravitational field
strength which is a measure of the gravitational force placed on an object that is in a gravitational
field. And so you know that the moon orbits around the earth and stays there because of
this gravitational field. And so if we place it in orbit, watch how the force on those
two objects remains constant. The gravitational field strength is the same. But if we were
to play around with the phet simulation, if we move the moon closer to the earth, you
can see the force is increasing. It has greater strength. And as we move it away it becomes
less. How else could we change the gravitational field strength? Well we could increase the
mass of the moon. It is a greater force. We could increase the mass of the earth as well
and there is going to be a greater gravitational field strength and it is going to have catastrophic
consequences when we put it in orbit. And so remember, any object that has mass is going
to generate a gravitational field. And those field lines are going to point to the center
of that object. And so any object and we will just deal with spherical objects in AP Physics
1, is going to have a gravitational field. It is going to become greater the closer we
come to that object. And so if you want to calculate the gravitational field strength,
this equation works. And it was developed by Sir Isaac Newton. And it really only has
those two things that we saw in that video. It is the mass of the object and then the
radius or the distance between that object and a point. Now you might say there are three
things in this equation. The first one is a gravitational constant. We lots of times
refer to that as big G. But the other two things that are going to affect the gravitational
field strength are the mass of the object and then the radius, or the distance from
the object. And so in this class you should be able to calculate the gravitational field
strength of an object or sitting on the surface of a really large object like the planet.
And so gravitational field strength, this is our equation right here, there are three
parts to it. And so if we are measuring the gravitational field strength at a point separated
from that object, we need to know the mass of the object. We need to know the radius.
And note this, that when we are looking at the radius it is not from the surface of the
object. It is from the center of mass of both objects. In this case one is just a point.
And then the last one is going to be the gravitational constant or big G. And that is just 6.67 times
10 to the negative 11. And then we have a bunch of units coming after that. And so let
me give you an example problem. Let's say I want you to figure out the gravitational
field strength of a baseball. You can imagine it is going to be really, really small. There
is not much mass in it. But if you want to solve this problem I have not given you enough
information. You need to know what is the mass of that object. It is 1.45 kilograms.
And you also have to know how far away is it. And let's say it is 2.0 meters. And so
you maybe have forgotten what big G is, so we will put that right up there, 6.67 times
10 to the negative 11. And so you may want to pause the video right now and try to solve
this problem. Or you could just watch me do it. I am going to take those three values
and I am going to place them into my equation. So I am taking the big G times the mass divided
by the radius squared. And so when I solve that I get a gravitational field strength
or a G of 2.4 times 10 to the negative 12 newtons per kilogram. If we cancel out all
of those units we have got newtons on the top. We have kilograms on the top. But we
have kilograms squared on the bottom. So we are going to end up with one kilogram on the
top and the meters squared are going to cancel out. So that is going to be the gravitational
field strength of the baseball. Incredibly small. But it is still there. Let's say we
were to do this. Can you figure out the gravitational field strength of the earth? So we are sitting
on the surface of the earth. Can you figure out what is the strength of that force pulling
you or holding you on the planet? Well again you would need two more things. We are going
to need to know the mass of the earth. And it is pretty massive, 5.97 times ten to the
24 kilograms. And you also need to know how far are you from the center of the earth.
What is the radius of the earth? And it is 6.37 times 10 to the 6 meters. And so to solve
this problem you are going to do the same exact thing. We are going to plug it into
those equations, those values, and again it is worth doing. But if you do this, you are
going to get a value that you have seen before. The gravitational field strength is going
to be 9.81 newtons per kilogram. And so that is going to be the the gravitational field
strength as we get close to the planet. Again it is also numerically equal to the acceleration
due to gravity on our planet. And you might say it is going to be the same everywhere
on our planet. But it is not. If you look at the gravitational field strength on our
planet, this is a NASA image, it is going to vary depending on where you are, because
the earth is not consistent. It is not a consistent sphere with consistent density. It is going
to have differences in latitude and therefore the distance from the center of the earth.
There is going to be geological differences. What the earth is made up of. And so we can
study the gravitational field strength in different areas and it tells us a lot about
what the earth is actually made of. And so did you learn to calculate the gravitational
field strength of an object a certain distance away? And did you figure out how to approximate
the gravitational field strength if you are sitting on the surface of a really large object?
It is the same equation. It is pretty easy. And I hope that's helpful.