00:01
We want to find the acceleration due to gravity on the surface of mercury and venus.
00:05
We can solve for this by pretending that there is an object at the surface of the planet, and since the planet is a sphere, we can take all the mass and put it at the center of the planet and find the gravitational force between the two objects.
00:24
Then using newton's second law, we can find the gravitational force or gravitational acceleration at the surface of each planet.
00:35
So let's go ahead and write fg is equal to fg.
00:44
So little g will be mg, which is the force due to gravity that we normally know.
00:53
F equals m g and this will be equal to newton's gravitational law which is g m let's call the object that we're looking at mass m and multiplied by let's do mercury first so m divided by r m squared notice how the masses of the object that we're looking at on the surface cancel out so it actually doesn't matter what object we put there as a test object, we'll always get the same gravitational acceleration.
01:33
So what we're trying to find is this g here, and we already have g on one side.
01:39
So we can just go ahead and plug in the radius of mercury, which i've conveniently written here, and the mass of mercury here, and we get a gravitational acceleration of 3 .70 meters per second squared...