View
223
Download
1
Category
Tags:
Preview:
Citation preview
Newton’s Law of Universal Gravitation
By: Heather Britton
Newton’s Law of Universal Gravitation
Johannes Kepler (1571 - 1630) - a German scientist that researched and calculated the motions of the planets using the sun as the center of the system
He came up with three laws that describe his observations
Newton’s Law of Universal Gravitation
1. The paths of the planets are elipses with the center of the sun at one focus
2. Imaginary lines from the sun to a planets orbit sweep out. The lines have equal areas in equal time intervals. Thus planets move fastest when closest to the sun and slowest when farthest away
Newton’s Law of Universal Gravitation
3. The ratio of the squares of the periods of any two planets revolving around the sun is equal to the ratios of the cubes of their average distance from the sun
(Ta/Tb)2 = (ra/rb)3
The above equation may be used for any body revolving around another body in space
Newton’s Law of Universal Gravitation
T = the period of revolution
period - how much time an objects takes to complete one revolution
r = the distance between the two centers of the objects
Newton’s Law of Universal Gravitation
Example 1
Galileo discovered 4 moons of Jupiter. Io, which he measured to be 4.2 units from the center of Jupiter, has a period of 1.8 days. He measured the radius of Ganymede’s orbit as 10.7 units. Find the period of Ganymede.
Newton’s Law of Universal Gravitation
Gravity is a force that can act over distance
Aside from Newton’s three laws of motion, he also came up with the law of universal gravitation
The force of gravity is directly proportional to the product of the two masses and inversely proportional to the distance between the centers
Newton’s Law of Universal Gravitation
Fg = G(m1m2) / r2
Fg = gravitational force measured in Newtons
m = the masses measured in kilograms
r = the distance between centers measured in meters
Newton’s Law of Universal Gravitation
G = the constant of proportionality
The value of G never changes
G = 6.67 x 10-11 Nm2/kg2
Newton’s Law of Universal Gravitation
This in an inverse square law meaning that as the distance doubles the force is 1/4 as strong
If the distance triples the force is 1/9 as strong
Newton did not discover the value of G during his lifetime
He reasoned that it must be very small since we are not aware of the attraction to the objects around us
Newton’s Law of Universal Gravitation
The value of G was not discovered until Henry Cavendish (1731 - 1810) conducted his “weighing” the Earth experiment
He set up a balance, and then rolled 6 tons of lead under one side
After rebalancing the lever he knew the size of the force the 6 tons of lead exerted
Newton’s Law of Universal Gravitation
This gave him every variable but G
He then could calculate the value of G
With G now known the mass of the Earth could be determined
Earth’s mass is 5.98 x 1024 kg
Earth’s average radius is 6.37 x 106 m
Newton’s Law of Universal Gravitation
Example 2
The mass of the Hubble Space Telescope is 11,600 kg. Determine the weight of the telescope when it is on Earth and orbiting 598 km above the surface
Recommended