gravitation and the clockwork universe. apollo 11 lunar lander how can satellites orbit celestial...
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Nicolas Copernicus (1473 – 1543)
Copernicus worked out the details of the heliocentric model of the universe.
Occam’s razor
Too simple to be wrong
Tycho Brahe
Greatest naked eye observer
Trusted the geocentric view
His observations confirmed the heliocentric theory
Measured the positions of the stars and planets accurately.
Tycho argued that nearby stars should shift their position as the Earth revolved around the Sun.
Tycho Brahe looked for stellar parallax
An Ellipse
Focus
Foci
Major axis
Minor axis
Eccentricity
e = 1 => line
e = 0 => circle
e2 = 1-(b/a)2
Kepler’s Three Laws
The orbit of a planet is an ellipse with the Sun at one foci
A line joining a planet and the Sun sweeps out equal areas in equal times
The harmonic law P2 = a3 (a is the semi-major axis)
The Harmonic Law
The square of the sidereal period of a planet is directly proportional to the cube of the semi-major axis of the orbit.
Objects Accelerate as they Fall
Speed increases at a constant rate.
Falling bodies move with constant acceleration..
Experimented by rolling balls down various inclines.
a = dv/dt
Sir Isaac Newton (1642 – 1727)
Newton laid the foundation for differential and integral calculus. His work on optics and gravitation make him one of the greatest scientists the world has known.
Law of Gravity
F = Force
G = Gravitational constant of the universe
6.67 x 10-11 N•m2/kg2
m = mass of objects
r = distance between objects
Action at a Distance
Sun’s Gravitational Force on Earth
G = 6.67 x 10-11 N•m2/kg2
MEarth = 5.98 x 1024 kg
Msun = 1.99 x 1030 kg
rES = 1.50 x 1011
Skating - The laws of Motion
Neglect air resistance
Neglect friction
•At rest on a level surface:–If you just wait, you stay stationary–If you’re pushed, you start moving in that direction
Moving on a level surface:–If you just wait, you coast steadily in straight line–If you’re pushed, you change direction or speed
Physics Concept
• Inertia
– A body at rest tends to remain at rest– A body in motion tends to remain in motion
Physical Quantities• Position – an object’s location
• Force – a push or a pull• Acceleration – its change in velocity with time
• Velocity – change in position with time
• Mass – measure of its inertia
• Speed = distance/time
Mass and Inertia• Mass is the measure of an object’s inertia.
• Mass is how much matter is contained within the object.
• The kilogram (kg) is the basic unit of measure for mass.
• Inertia is the object’s resistance to a change in it’s motion.
Newton’s Second Law
The force exerted on an object is equal to the product of that object’s mass times its acceleration. The acceleration is in the same direction as the force.
force mass acceleration
F = ma
Check Your Understanding• Suppose that I throw a ball upward into the air. After
the ball leaves my hand, is there any force pushing the ball upward?
• Out in deep space, far from any celestial object, would an astronaut weigh anything? Would the astronaut have mass?
• If you weight on the moon is one-sixth of what it is on Earth, what is the moon’s acceleration due to gravity?
w = mg
The further a satellite is from the Earth the weaker the Earth’s pull, therefore it should travel slower so gravity can pull it back.
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