Newton’s Law of Universal Gravitation

Formula and Explanation

Newton’s Law of Universal Gravitation

• To calculate the force of gravitation • F = G m1m2

d2

• m1 and m2 = the mass of the objects in kgG = gravitational constant of 6.67 x 10 -11 N*m2/kg2 d is the distance between the objects in mF = gravitational force between the 2 objects

Gravitational Force

• If the value of the constant gravitational force G were to increase by a factor of 10, we would be crushed

• If G were to decrease by a factor of 10, we would be able to jump over a tall building

Sample Problem 1

• Determine the force of gravitational attraction between the earth (m = 5.98 x 1024 kg) and a 70-kg physics student if the student is standing at sea level, a distance of 6.38 x 106 m from earth's center.

• F = Gm1m2 = (6.67 x 10 -11 N*m2/kg2 )*(5.98 x 1024 kg )*(70kg) d2 (6.38 x 106m)2

• F = 686N

Sample Problem 2

• Determine the force of gravitational attraction between the earth (m = 5.98 x 1024 kg) and a 70-kg physics student if the student is in an airplane at 40000 feet above earth's surface. This would place the student a distance of 6.39 x 106 m from earth's center.

• F =Gm1m2 = (6.67 x 10 -11 N*m2/kg2 )*(5.98 x 1024 kg )*(70kg) d2 (6.39 x 106m)2

• F = 684 N