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Tycho Brahe (1546-1630) best observer of his day

Made most accurate measurements of his time

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Tycho’s Observatory at Uraniborg

• He developed new instruments and new techniques for

conducting observations.

• Kepler used his observations to derive his laws of planetary

orbits.

• It was the precision of Brahe's observations that enabled

Kepler to determine that the orbits of the planet’s are ellipses

with the Sun at one focus.

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Johannes Kepler (1571-1630)

Developed three laws of planetary motion.

Was able to describe how the planets moved.

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First law: The orbits of the planets are ellipses.

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Eccentricity (e) is a number between 0 and 1 that tells you how elliptical an orbit is.

Some sample eccentricities:

Earth’s orbit: e = 0.017 (only slightly off-circular)Pluto’s orbit: e = 0.248 (more elliptical)Halley’s comet: 0.967 (very elliptical)

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Kepler’s second law:

Planets sweep out equal areas in equal times

-means planets orbit at varying speeds, faster closer to sun, slower further from sun (Kepler didn’t know why)

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Kepler’s Third Law: Kepler found a simple relationship between a planet’s

orbital period (P) and its average distance from the Sun (A)

P2Planet = A3

Planet

P = period of planet’s revolution in years

A = average distance of planet from sun in A.U.

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• note: Uranus, Neptune & Pluto werediscovered much later(during 1800-1900s)with advent of morepowerful telescopes

• presence predicted

Solar System

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Isaac Newton (1642 – 1727)

developed laws for physical matter

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Law of INERTIA

person moving at a constant speed

car stops but person keeps moving

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Newton’s Second Law: When forces act on a body, they changethe (speed & direction) motion of the body: acceleration, deceleration

Velocity – rate of motion (speed: 35 mph; 5 m/s) with direction

Acceleration – rate of change of motion (could be speed or direction!)

F = m * a

Gravity causes an acceleration!

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Newton’s Third Law

• For every action (force) there is an equal and opposite reaction (force)

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Newton’s Laws explain that something must be acting on the planets to keep them in orbit

According to the law of inertia planets should fly off in a straight line

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What determines how strongthe force of gravity is ?

Mass of object (being acted on)

Mass of object (acting on)

Distance between them!

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Newton’s Law of Universal GravitationTwo bodies attract each other with a force that is proportional to the mass of each body and inversely proportional to the square of the distance between them.

Where the gravitational constant G = 6.67 · 10-11 N m2/kg2 and r is the distance between the objects with masses m1

and m2.

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Newton’s law of gravitation for the Solar System

Mr

m

M is the mass of the Sun

m is the mass of a planet (i.e., Earth)

r is the distance between them

Example: What if you discovereda planet TWICE as far from theSun as the Earth – how would itsgravitational pull compare to Earth’s?

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• What does it mean for an object to be in orbit?

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Is there gravity beyond the Earth’s surface?

“weightless” : not beyond influence of gravity

• treat astronaut as any other orbiting body• Earth’s pull is what keeps astronaut in orbit• feels ‘weightless’ because she and spacecraft are experiencing

gravity together