Law of Universal Gravitation

The Law of Universal Gravitation every object in the universe attracts every other object in the universe with a force that has a magnitude which is directly proportional to the product of their masses and inversely proportional to the distance between their centers squared.

What does it all mean? G is the gravitational constant, 6.67 x 10-11 Nm2/kg2 M1 is the mass of the first body in kg M2 is the mass of the second body in kg R is the distance from the center of M1 to the center of M2

Big G, little g??? G is the universal gravitational constant- same for any pairs of particles, anywhere in the universe Little g is acceleration due to earth’s gravity, measured at the surface of the earth F=ma=mg If you enter the values for the mass of earth and the avg radius of earth, we get the 9.8m/s2

Gravitational Force Always directed to center of object (usually earth) and is a vector Related to inverse square of distance from center of earth

Weight Weight is the gravitational force that the earth (or another planet) exerts on an object If it’s a force, what are the units? Is it vector or scalar? Which direction?

Weight as Force If F=ma and weight is the force exerted by earth’s gravity… On surface of the earth: Weight =F=ma=mg If you are not on surface of earth… Weight=G* Mem r2

Weight on other planets If you’re not on earth, you can calculate weight on other planets by replacing Me with the mass of the other planet

Apparent Weight If you were standing on a scale in an elevator, as it accelerates up or down, the reading on the scale would change If you have any vertical acceleration, you need to add that F=ma to your sum of forces in the y direction So apparent weight: F=mg+ma (be careful of sign of a) In free fall, a=-g so your apparent weight will=0