3.3-3.4 Universal Law of Gravitation and Planetary orbits

More of Newton’s observations By observation of the motion of planetary

bodies, Newton formulated the behaviour of gravity between two objects

Planets maintained circular orbits around the sun, suggesting that the sun generated gravity to keep them there

But the discovery of moons around other planets also illustrated that planets had a gravitational pull

I pull you, pull me? This suggested that objects affected each

other The larger mass of the sun and its ability to

override the gravitational pull of the earth suggested that the gravitational pull of an object was dependent on the mass of the object involved

The famous apple It is suggested that the famous apple that

started it all might have led Newton to consider the consequences of gravity at large distances

If gravity could cause an apple to fall from a shorter branch, and taller ones above it – could it affect other objects much further away – like the moon?

Newton’s cannon

Newton considered what would happen if a cannon were to fire consecutively faster cannonballs

There would be a point where the cannonball would move fast enough to curve away from the falling projectile

Orbit away The cannonball would be put into orbit Newton drew from the mathematical work

of another famous astronomer, Keppler, in order to derive the Universal Law of Gravitation

What are we looking at? Newton realized that this could occur

ANYWHERE and with ANYTHING that possessed mass

Hence the term “universal” in the name Gravity between two objects follows

Newton’s third law of motion: the pull on one object is matched equally but in the opposite direction on the other mass

Diagrammatically…

R = distance between centre of masses

m1

m2

F m1 on m2F m2 on m1

Force is dependent on: Both mass 1 and mass 2 Distance between masses Therefore: F = Gm1m2

r2

Where: G = 6.67 x 10-11 Nm2/kg2

Technically when you look at orbiting planets…

Planetary motion is not a perfect circle; in fact it is elliptical

But for the questions we will be dealing with, we assume uniform circular motion