One of the most significant intellectual achievements in the history of thought.

One of the most significant intellectual achievements in the history of thought.

• Every object attracts every other object.

• The force between two objects is proportional to their masses and inversely proportional to the square of the distance between their centers.

• The force acts along the line joining the two objects.

r

One of the most significant intellectual achievements in the history of thought.

• Every object attracts every other object.

• The force between two objects is proportional to their masses and inversely proportional to the square of the distance between their centers.

• The force acts along the line joining the two objects.

1 22

m mF = G

rr

One of the most significant intellectual achievements in the history of thought.

• Every object attracts every other object.

• The force between two objects is proportional to their masses and inversely proportional to the square of the distance between their centers.

• The force acts along the line joining the two objects.

1 22

m mF = G

r

G = 6.67x10-11 Nm2/ kg2 “Universal gravitational constant”

One of the most significant intellectual achievements in the history of thought.

• Every object attracts every other object.

• The force between two objects is proportional to their masses and inversely proportional to the square of the distance between their centers.

• The force acts along the line joining the two objects.

1 22

m mF = G

r

G = 6.67x10-11 Nm2/ kg2 “Universal gravitational constant” VERY VERY SMALL! SAME EVERYWHERE!

rE – Earth’s radius mE – Earth’s mass.

E E2 2E E

m m mF = G = G m = gm

r r

2E2E

mg = G = 9.80m/s

r

How does universal gravitation relate to the force of gravity on Earth?

rE – Earth’s radius mE – Earth’s mass.

E E2 2E E

m m mF = G = G m = gm

r r

2E2E

mg = G = 9.80m/s

r

How does universal gravitation relate to the force of gravity on Earth?

This force is commonly called weight W = mg.

Now we can see that the gravitational acceleration g is a consequence of the gravitational force.

UNIVERSAL GRAVITATION PROBLEMS – WE DO

1) Two satellites of equal mass orbit earth. Satellite A is 2 times farther from the center of earth than Satellite B. How does the gravitational force from the Earth on Satellite A compare to that on Satellite B?

UNIVERSAL GRAVITATION PROBLEMS – WE DO

1) Two satellites of equal mass orbit earth. Satellite A is 2 times farther from the center of earth than Satellite B. How does the gravitational force from the Earth on Satellite A compare to that on Satellite B?

FA = G FB = G

How do they differ?FA = ¼ FB

UNIVERSAL GRAVITATION PROBLEMS – WE DO

2) A 90 kg satellite orbits the earth at a distance of 300 km. The mass of the earth is 6.0 X 1024

kg and the radius of the earth is approximately 6.4 X 106

m. What is the gravitational force between the satellite and the earth?

UNIVERSAL GRAVITATION PROBLEMS – YOU DO

1) Two satellites of orbit earth. Satellite A has twice as much mass as Satellite B but has ½ the orbital distance. How does the gravitational force from the Earth on Satellite A compare to that on Satellite B?

2) Calculate the force of gravity between Earth (mass = 6.0 x 1024 kg) and the moon (mass = 7.4 x 1022 kg). The average Earth—moon distance is 3.8 x 108 m.