Transcript Universal Gravitation

Universal Gravitation
Young Newton
o "I began to think of gravity extending to the Orb of the Moon, and
having found out how to estimate the force with which a globe
revolving within a sphere presses the surface of the sphere. From
Kepler's Rule of the periodical times of the Planets, I deduced that
the forces which keep the Planets in their Orbs must be
reciprocally as the squares of their distances from the centres
about which they revolve : and thereby compared the force
requisite to keep the Moon in her Orb with the force of gravity at
the surface of the Earth, and found them to answer pretty nearly".
I. Newton writing about the plague years of 1665-1666
Force of Gravity
• The acceleration of any
falling mass m is g.
– g = 9.81 m/s2
– Galileo 1638
ag
Kinematic view
• The force on the mass is
found from F = ma.
– Gravitational force F = mg
– Newton 1687
Fgrav  mg
Dynamic view
Always Falling
• The Moon accelerates toward
the earth like it’s falling.
• Newton’s laws apply to the
force on the Moon.
– Force depends on mass
– The Earth pulls the Moon
– The Moon pulls the Earth
• Newton used this to describe a
Law of Gravity.
orbital
velocity
FME
Earth
FEM  FME 
FEM
Moon
centripetal
acceleration
GM E mM
r2
Universal Gravity
• Newton realized that all
objects obey the same
universal law.
–
–
–
–
Other planets
Kepler’s laws
Apples
GMm
People
F
2
r
• The constant G is universal.
– G = 6.67 x 10-11 Nm2/kg2.
• What is the gravitational
force between two students
sitting in adjacent seats?
– Assume each mass 70 kg
– Assume separated by 1 m
(6.671011 Nm2 /kg2 )(70kg)(70kg)
F
(1 m)2
• F = 3.3 x 10-7 N.
Surface Gravity
• Gravitational acceleration on the Earth is g = 9.81 m/s2.
• This value is due to the universal gravitational force.
– Earth’s radius r = 6.37 x 106 m
– Earth’s mass M = 5.97 x 1024 kg
– g = F/m = GM/r2 = 9.81 m/s2.
• Surface gravity is different on other worlds.
– Moon 0.165g; Mars 0.376g
Normal Force
• The force of gravity acts
on all objects all the time.
– At rest: zero net force
– Newton’s first law
FN = Fgrav = mg
• The normal force pushes
back.
– Equal and opposite
– Newton’s third law
Fgrav = mg
Normal Force and Weight
• The normal force pushing
up against gravity is
measured as weight.
• Weight is a force, not a
mass.
– Kilograms – mass
– Pounds – force
• If g is less, weight is less.
Apparent Weight
• A person in an
accelerating elevator feels
a net force.
– Newton’s second law
– F = ma
• The normal force doesn’t
cancel gravity.
– FN = m (g – a)
– Weight feels different
Weightlessness
• If the elevator accelerated
downward at g, the normal
force would be 0.
• The person would feel
weightless.
• An object in free fall is
weightless, but not
massless.
Microgravity
research at NASA