Transcript Universal Gravitation

Universal Gravitation
Chapter 12
The Falling Apple
• The idea that gravity extends through the
universe is attributed to Sir Issac Newton
• He knew that if an object undergoes a
change in direction or speed, a force is
responsible
• Newton had the insight to figure out that
the moon orbits Earth because it is falling
towards Earth, avoiding its straight-line
path
The Falling Apple
The Falling Moon
• The moon falls in the sense that it falls beneath
the straight line it would follow if no force acted
on it
• Newton imagined firing a cannonball from a
mountain top. If he fired the cannonball with a
small horizontal speed, it would follow a
parabolic path and hit Earth soon. If he fired
the same cannonball with greater horizontal
speed, it would go farther and have a less
curved path. If he fired the cannonball with
great enough horizontal speed, he reasoned
that the cannonball’s path would become a
circle and it would circle indefinitely (orbit)
The Orbital Cannon
Cannonball in Orbit
Launch Speed less than 8000 m/s
Projectile falls to Earth
Launch Speed less than 8000 m/s
Projectile falls to Earth
Launch Speed equal to 8000 m/s
Launch Speed greater than 8000 m/s
Projectile orbits Earth - Circular Path Projectile orbits Earth - Elliptical Path
Newton’s Law of Universal
Gravitation
• Law of Universal Gravitation – every
object attracts every other object with a
force that for any two objects is directly
proportional to the mass of each object,
the force also decreases as the square of
the distance between the centers of
mass of the objects increases
• The farther away the objects are from
each other, the less the force of attraction
between them
The Universal Gravitational
Constant, G
• When the proportionality constant, G, is
introduced, we can write the Law of
Universal Gravitation in the form of an
equation:
2
F = G(m1)(m2)/d
• G = 6.67 x 10-11 N∙m²/kg²
• We only sense gravitation for bodies the
size of a planet, smaller objects we can’t
sense, but the force is there!
Law of Universal
Gravitation
The Inverse-Square Law
• When a quantity varies as the inverse
square of its distance from its source, it
follows an inverse-square law
• The greater the distance from Earth’s
center, the less an object will weigh
• You may weigh 300N at sea level, but
only 299N at the top of Mount Everest
Inverse-Square Law
Universal Gravitation
• Earth is round due to gravitation, it has
“attracted” itself together to create a
spherical shape
• When planets deviate from their normal
orbits, they have been pulled due to the
attraction to other planets, this deviation
is called perturbation
• This is how we found Neptune, Uranus
was acting strangely, in a way that could
only be accounted for by another planet
perturbing its orbit
Perturbation
Assignment (due Tuesday 1/15)
• Read Chapter 12 (pg. 168-179)
• Do #15-35 (pg. 180-181)