Transcript Universal Gravitation

Newton’s Law of Universal
Gravitation
Law of Universal Gravitation
• P 577-584
Law of Universal Gravitation
• Every particle is attracted to every other
particle
• The force of gravity between any two objects
is proportional to the product of the masses
and inversely proportional to the square of
the distance between their centres
Fg = G m1m2
r2
Universal Gravitational Constant
G = 6.67x10-11 N*m2/kg2
Problem
Explain how Fg=mg is related to
Fg = G m1m2
r2
Express g in terms of the variables and
constants in Newton’s Law of Universal
Gravitation
Connecting Kepler’s 3rd Law
• Write Newton’s law of universal gravitation
using the mass of the Sun (ms) and the mass
of a planet (mp)
Fg = G msmp
r2
Connecting Kepler’s 3rd Law
• Since the force of gravity must provide a
centripetal force for the planets, set the
equation equal to the required centripetal
force.
Fg = G msmp = mp v2
r2
r
Simplified: Gms = v2
r
Connecting Kepler’s 3rd Law
• Kepler’s 3rd Law includes the period, T
• Velocity in terms of period is:
v= 2∏r / T
• Substitute into the previous:
Gms = (2∏r / T )2
r
Connecting Kepler’s 3rd Law
• Multiply each side by r/4∏2
Gms / r (r/4∏2) = (2∏r / T )2 (r/4∏2)
Gms/ 4∏2 = r3 / T2
K = Gms/ 4∏2
The Kepler Mission
• News Release
Practice Questions
• P 580 #1-6