Good morning. Billy, we have two equations for the force of gravity,
what are they?
Flipping Physics
- The planet specific equation is, force of gravity equals the mass of the
object times the acceleration due to gravity.
The general equation for the force of gravitational attraction is
Newton’s Universal Law of Gravitation which is,
force of gravity equals the universal gravitational constant times mass 1 times mass 2 all divided by
r squared, where r is the distance between the centers of mass of the two objects.
- We can set these two equations equal to one another to find the acceleration due to gravity at any location.
In this lesson we are going to find the acceleration due to gravity near the surface of planet Earth.
In this case, Bo, what would mass 1 & mass 2 be equal to in Newton’s Universal Law of Gravitation?
- The two objects would be the mass of the object and the mass of the planet.
- Bobby, what would r, the distance between the centers of mass of the two objects, be equal to?
- r would be from the center of mass of the planet to the center of mass of the object.
So the radius of the planet plus the height the object is above the surface of the planet.
- The height an object is above the surface of a planet, or sea level, is called
altitude. And you can now see that.. [Class]: Everybody brought mass to the party.
Be careful, there are two masses in this equation therefore you need to specifically identify
which mass and say?
[Class]: Everybody brought the mass … of the object … to the party!
- That's right. - Everybody brought mass.
- We just solved for the acceleration due to gravity near the surface any planet.
We already know the acceleration due to gravity here on planet Earth is generally defined as
9.81 meters per second squared.
But let’s find the acceleration due to gravity at the top of Mount Everest.
In order to do so, we need some information.
The mass of the Earth is 5.9723 times ten to the 24th kilograms.
The radius of the Earth at Mount Everest is 6.3735 times 10 to the sixth meters.
Yes, the radius of the Earth is not constant because the Earth is not a perfect sphere.
The Earth is an oblate spheroid; it actually has a larger equatorial radius than polar radius.
The larger equatorial radius is caused by the rotation of the planet and the planet's own inertia.
So Yes, we need to use the radius of the Earth at Mt. Everest.
And the altitude of Mt. Everest, or the distance Mt. Everest is above sea level,
is 8848 m. Plugging those values into our equation gives us.
The acceleration due to gravity at the top of Mt. Everest is 9.77 meters per second squared.
So, notice the acceleration due to gravity, which is something we have previously considered to be
constant on the surface of planet Earth,
is actually not quite constant. But it is pretty darn close.
Billy, what are you doing?
- Okay, Javier Sotomayor is the men’s world record holder for the high jump. In 1993 in Salamanca, Spain,
he cleared a height of 2.45 meters.
The acceleration due to gravity there is 9.80 meters per second squared. If he performed the same jump,
instead, at the top of Mt. Everest, he would have been able to clear 2.46 meters instead.
That’s a roughly 1 centimeter higher! That’s awesome.
- But what about the oxygen tanks he would have to wear?
- And the temperature on Mt. Everest never gets above freezing.
- And the snow?
- And, where would he run?
- But still it would have been higher…
Thank you very much for learning with me today, I enjoyed learning with you.