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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