Kepler’s LawKepler’s Law

Kepler’s Three LawsKepler’s Three Laws

Orbit of each planet is an ellipse & Orbit of each planet is an ellipse & Sun is at one focusSun is at one focus

Equal areas in equal intervals of Equal areas in equal intervals of timetime

TT²² = a = a³³

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Kepler’s First LawKepler’s First Law

The orbit of the planets are The orbit of the planets are ellipsesellipses, with , with the sun at one focus of the ellipse.the sun at one focus of the ellipse.

Aphelion & PerihelionAphelion & Perihelion

Aphelion is the point on the orbit Aphelion is the point on the orbit farthest from the sunfarthest from the sun

Perihelion is the point on the orbit Perihelion is the point on the orbit closest to the sunclosest to the sun

KEPLER’S FIRSTLAW

Ellipses and Ellipses and EccentricityEccentricity

The amount of flattening of the ellipse is The amount of flattening of the ellipse is termed the eccentricity.termed the eccentricity.

Circle = 0Circle = 0

Straight Line = 1Straight Line = 1

EllipsesEllipses

The The sunsun is not at the center of the ellipse. is not at the center of the ellipse.

There is nothing at the other focus.There is nothing at the other focus.

FocusFocus

Focus – one of two special points on Focus – one of two special points on the major axis of an ellipsethe major axis of an ellipse

Foci – plural of focusFoci – plural of focus A+B is alwaysA+B is always

the same on the same on any point on any point on the ellipsethe ellipse

KEPLER’S FIRSTLAW

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Kepler’s Kepler’s Second LawSecond Law

The line joining the planet to the Sun sweeps The line joining the planet to the Sun sweeps out equal out equal areas in equal times as the planet areas in equal times as the planet travels around the ellipse.travels around the ellipse.

Good ExampleGood Example

Perihelion = Point closest to Sun (fastest)Perihelion = Point closest to Sun (fastest)

Aphelion = Point farthest from Sun (Slowest)Aphelion = Point farthest from Sun (Slowest)

In Another Words…In Another Words…

The area from one time to another The area from one time to another time is equal to another area with time is equal to another area with the same time intervalthe same time interval

All of the areas (in yellow and peach) All of the areas (in yellow and peach) have equal intervals have equal intervals of timeof time

KEPLER’S SECOND

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Acceleration of PlanetsAcceleration of Planets

Planet moves faster when closer to the Planet moves faster when closer to the sunsunForce acting on the planet increases as Force acting on the planet increases as

distance decreases and planet accelerates in distance decreases and planet accelerates in its orbitits orbit

Planet moves slowerPlanet moves slowerwhen farther when farther from the sunfrom the sun

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KEPLER’S SECOND

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Astronomical DistancesAstronomical Distances

An Astronomical Unit (AU) is the average An Astronomical Unit (AU) is the average distance between Earth and the Sun.distance between Earth and the Sun.

Used when measuring distances to other solar Used when measuring distances to other solar system objects.system objects.

A A Light year Light year is the distance it takes light to is the distance it takes light to travel in 1 year.travel in 1 year.

Used to measure distances to other stars and Used to measure distances to other stars and galaxies.galaxies.

Kepler’s Kepler’s Third LawThird Law

The closer the object is to the Sun the The closer the object is to the Sun the faster its period of revolution.faster its period of revolution.

Example: Example:

Earth & Mars OrbitEarth & Mars Orbit

TT² ² ∝∝ a a³³

T = orbital period in yearsT = orbital period in years a = semi-major axis in astronomical a = semi-major axis in astronomical

unit (AU)unit (AU) Can calculate how long it takes Can calculate how long it takes

(period) for planets to orbit if semi-(period) for planets to orbit if semi-major axis is knownmajor axis is known

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Astronomical UnitAstronomical Unit

Astronomical unit – AU Astronomical unit – AU AU is the mean distance between AU is the mean distance between

Earth and the SunEarth and the Sun 1 AU 1 AU ≈ 1.5 x 10≈ 1.5 x 1088 km ≈ 9.3 x 10 km ≈ 9.3 x 1077 miles miles

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Examples of 3Examples of 3rdrd Law Law

Calculating the orbital period of 1AUCalculating the orbital period of 1AUTT²² = a = a³³TT² = (1)³ = 1² = (1)³ = 1T = 1 yearT = 1 year

Calculating the orbital period of 4AUCalculating the orbital period of 4AUTT²² = a = a³³TT² = (4)³ = 64² = (4)³ = 64T = 8 yearsT = 8 years

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