Nicholas Copurnicus

Nicholas Copurnicus

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Wanderers (Planets)

InferiorNearer the Sun than the EarthMorning Star/Evening Star

SuperiorFarther from the Sun than the EarthLoops

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Movement of Mars

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Motion of the Sun Moon

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Ptolemy’s explanation

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Glory Years of Astronomy

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Motion of Mars by Copurnicus

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Galileo Galilei Outstanding scientist of his era Bought and built telescopes Observed Venus in gibbous phase moons around Jupiter millions of stars in the Milky Way spots on the Sun craters, highlands and seas on the Moon etc.

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Venus by Ptolemy

Venus by Copunicus

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Tycho Brahe

Invented wonderful observing tools

Twenty years of observations

Hired Kepler

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The Solar system by TychoChapter 3

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Kepler’s 1st LawEvery Planet

revolves around the Sun in an orbit that is an ellipse with the Sun at one focus

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Kepler’s 2nd Law

A line from the planet to the Sun will sweep out equal area in equal time

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P = a2 3

Yr AU

Kepler’s 3rd LawThe square of the period of a planet is equal to the cube of the semi-major axis

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Sir Isaac NewtonNewton was a genius whose work in mathematics, theoretical mechanics and optics completely revolutionized physics

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Gravity

F = G Mmr 2

Every object anywhere in the Universe attracts every other object in the Universe by a Force which is proportional to the product of their masses and inversely proportional to the distance separating them.

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GravityInverse Square LawThe equation for

the intensity of light has a similar form to the gravity equation so we can use light to demonstrate the Inverse Square Law.

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Laws of Motion

Newton’s 1st Law

A body at rest will remain at rest and a body in motion will remain in motion in a straight line until acted upon by a force.

Newton’s 1st Law

In the absence of a force the velocity (V) will not change

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Laws of Motion

Newton’s 2nd Law

The acceleration of a body is proportional to the force applied and inversely proportional to the mass of the body.

Newton’s 2nd Law

The change of velocity = acceler-ation (a) = Force / mass

F=ma a = F/m

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Laws of MotionNewton’s 3rd Law

m1v1 = m2v2

From this law we derive Thrust which makes possible Jet Engines and Rockets

For every action there is an equal and opposite reaction

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Orbital MechanicsKnowing that a bullet shot out of gun is pulled to the ground by gravity, Newton envisioned this experiment on the top of the highest mountain. From this experiment Newton related the motion of the Moon to the motion of a falling apple.

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Orbital MechanicsAn object is space has a velocity. During a given time the object would move from A to B. But in the same time the gravity from the sun causes it to fall toward the sun the distance from A to D. The resulting trajectory of the object is from A to C. If the object is a planet in orbit we note that the distance from C to the Sun is just the same as the distance A to the Sun.

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Kepler’s 3rd Law as Modified by Newton

Newton discovered while working from ‘first principles’ that Kepler’s 3rd Law needed to be modified. Leaving out constants…

(M1+M2) P = a2 3

Masses must be measured in Solar masses, period in Earth years and the distance between masses in Astronomical Units

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TidesMany books explain tides this way. Moon pulls on the water on the Moon side causing it to bulge up a little. The Moon pulls the center of the Earth away from the water on the far side causing it bulge up a little on that side.

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Barycenter

Tides (an alternate explanation)The Earth and the Moon revolve around the common center of mass for the system (Barycenter). The tide one Moon side is due to gravitational force but the tide on the other side is due to centrifugal force.

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The square of the period of a planet is equal to the cube of the semi-major axis is a statement of Kepler’s _____ Law

In-Class Quiz

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End Chapter 3