Kepler’s Laws of Orbital Motion

Concepts of PhysicsMr. Kuffer

Orbital Theories: Ptolemy• Second Century A.D.• Reinforced geocentric view of the Universe (everything else revolved around the Earth)

Orbital Theories: Copernicus (1473-1543)• Polish astronomer who surmised that the Earth rotated about its own axis, and that it revolved around a stationary Sun.

FYI: Died about 20 yrs before galileo’s birth

Orbital Theories: Tycho Brahe (1546-1601)• Danish astronomer who spent years measuring the position of astronomical objects, including Mars• His goal: Understand the motion of the planets.• Did not possess mathematical skills needed to analyze his data.

Orbital Theories: Johannes Kepler (1571-1630)• Mathematician hired by Brahe to analyze planetary observations.• Worked for ten years, realizing that Mars’ orbit did not quite fit a circular orbit, or that of multiple circles.• Finally, he fit the data into an ellipse – and it worked!

Let’s Put This Into Perspective…

Nicolas Copernicus 1473 to 1543De Revolutionibus by Copernicus 1543Tycho Brahe 1546 to 1601Galileo Galilei 1564 to 1642Johannes Kepler 1571 to 1630Telescope invented by Johann Lipperhey 1608Isaac Newton 1642 to 1727

The Ellipse

Definitions:

• F1 and F2 are foci (pronounced “Foh-sigh”)

• Lines from both foci to the same point along the ellipse always add up to the same constant value (we will do a lab with this!)

The Ellipse, Washington, D.C.

Kepler’s First Law

All planets move in elliptical orbits with the Sun at one focus.

Important Vocabulary

Perihelion: Point of the orbit closest to the Sun.

Aphelion: Point of the orbit furthest from the Sun.

(Memory Trick: “Aphelion” = “Away”)

Kepler’s Second Law“The Law of Equal Areas”

A line drawn from the Sun to the planet sweeps out equal areas in equal time.

Kepler’s Second Law is the result ofthe Conservation of Angular Momentum

A familiar example of theConservation of Angular Momentum is an ice skater.

With her arms out, she turnsslowly. If she brings her armsin close to her body, she will speed up due to the Conservationof Angular Momentum.

Remember, the force of gravity is inversely proportional to the square of the distance betweenthe two objects.

Fg = G m1 m2 / r2

Intuitively,

As the planet gets closer to the Sun, the force of gravityincreases, accel increases, and the planet speeds up.

As the planet gets further from the Sun, the force ofgravity decreases, accel decreases, and the planet slows down.

“It’s not magic, it’s Physics!”

Kepler’s Third Law

Planets distant from the Sun have longer orbital periodsthan planets that are closer to the Sun.

R3 / T2 = Constant

Where T is the time (or period) for one orbit, and R is the average orbital radius.

The Kepler Space Probe

• NASA’s first mission capable of finding Earth-size and smaller planets around other stars.• Will survey our region of the Milky Way to detect planets in the “habitable zone,” which are distances from stars in which liquid water can exist on the surface. • Launched into space on March 6, 2009.

How will Kepler detect other Earth-like planets?

Kepler will use something called the “Transit Method”

Planetary transits can cause a 1/10,000th reduction in a star’s brightness

Once detected, the planet’s orbital size is calculated with Kepler’s ThirdLaw using the period of orbit and the mass of the star.

The size of the planet is calculated using the size of the star, along with how much the brightness of the star dropped during the transit.