Kepler’s Breakthrough

• Kepler used Brahe’s data to develop three laws that could be used to describe planetary motion.

• All of the laws are based upon an understanding of the ellipse.

After Tycho BraheAfter Tycho Brahe’’s death, s death, Johannes Kepler (pictured here Johannes Kepler (pictured here with Tycho in the background) with Tycho in the background) used Tychoused Tycho’’s observations to s observations to deduce the three laws of deduce the three laws of planetary motion.planetary motion.

KEPLERKEPLER’’S THREE LAWS OF PLANETARY MOTIONS THREE LAWS OF PLANETARY MOTION

LAW #1. The orbit of a planet around the Sun is an ellipse with the LAW #1. The orbit of a planet around the Sun is an ellipse with the Sun at one focus.Sun at one focus.

The amount of elongation in a planetThe amount of elongation in a planet’’s orbit is defined as its s orbit is defined as its orbital eccentricity.orbital eccentricity. An orbital eccentricity of 0 is a perfect An orbital eccentricity of 0 is a perfect circle while an eccentricity close to 1.0 is nearly a straight line. circle while an eccentricity close to 1.0 is nearly a straight line.

In an elliptical orbit, the distance from a planet to the Sun In an elliptical orbit, the distance from a planet to the Sun varies. The point in a planetvaries. The point in a planet’’s orbit closest to the Sun is s orbit closest to the Sun is called called perihelion, perihelion, and the point farthest from the Sun is and the point farthest from the Sun is called called aphelion.aphelion.

KEPLERKEPLER’’S THREE LAWS OF PLANETARY MOTIONS THREE LAWS OF PLANETARY MOTION

LAW #2: A line joining the planet and the Sun sweeps out LAW #2: A line joining the planet and the Sun sweeps out equal areas in equal intervals of time.equal areas in equal intervals of time.

Planet moves faster Planet moves faster in its orbit when in its orbit when closer to the Sun.closer to the Sun.

Planet moves slower Planet moves slower in its orbit when in its orbit when farther away from farther away from the Sun.the Sun.

KEPLERKEPLER’’S THREE LAWS OF PLANETARY MOTIONS THREE LAWS OF PLANETARY MOTION

LAW #3: The square of a planetLAW #3: The square of a planet’’s sidereal period around the Sun is s sidereal period around the Sun is directly proportional to the cube of its semi-major axis.directly proportional to the cube of its semi-major axis.

This law relates the amount of time for the planet to complete one orbit around the Sun to the planet’s average distance from the Sun.

If we measure the orbital periods (P) in years and distances (a) in astronomical units, then the law mathematically can be written as P2 = a3.

Newton’s Physics—Motion and Gravity

• Newton’s Three Laws of Motion– A body remains at rest or moves in a straight line at a

constant speed unless acted upon by an net outside force.

– The acceleration of an object is proportional to the force acting on it and dependent upon its mass.

– Whenever one body exerts a force on a second body, the second body exerts and equal and opposite force on the first body.

• Newton’s Universal Law of Gravitation– Fgravity = G x m1m2

d2

Newton’s Physics—Angular Momentum

• Angular momentum depends upon three things1. Speed of rotation or revolution2. Mass3. How spread out the mass is

• Angular momentum is related to the amount of energy stored in an object due to its rotation and revolution

• Angular momentum is also related to the sideways or tangential velocity of an orbiting object

• Angular momentum is conserved--as the spread of mass decreases, the rotation rate must increase.

• This is important to the understanding of the formation of stars and the solar system.

Not to scale

Sun and Earth experience equal and opposite forces of gravity

However, due to tangential velocity as a result of angular momentum gained during formation of the solar system, the Earth moves away at the same time it is pulled toward the Sun.

As a result, centripetal force (which means center-seeking force) due to gravity, accelerates or pulls Earth toward the Sun.

Sun contains 99.9% of mass in the solar system, tremendous inertia or resistance to acceleration.

Earth has less mass, less inertia, same gravitational force; thus, more easily accelerated

1

2

3

4

5

The Newtonian Physics of Earth Orbiting the Sun

Sun

E

Planetary configurationsPlanetary configurations are defined for the location of the planets as are defined for the location of the planets as they orbit the Sun from our point of view. they orbit the Sun from our point of view.

Orbital Periods for Planets

• Sidereal Period– The true orbital period of a planet with respect

to the background stars.

• Synodic Period– The period of time that elapses between two

successive identical configurations as seen from Earth (example: for Venus, greatest eastern elongation to greatest eastern elongation)

The cycle of these positions for a synodic period is The cycle of these positions for a synodic period is different from the actual orbital period of the planet different from the actual orbital period of the planet around the Sun (a sidereal period) because both the around the Sun (a sidereal period) because both the Earth and the planet orbit around the Sun.Earth and the planet orbit around the Sun.

©1996-2002 Scott R. AndersonLast update: 2002 October 22Please send questions, comments, suggestions, or corrections to srca@mindspring.com.

Determining the Distances to Astronomical Objects

Parallax• Parallax view: the variation in angle that occurs

when viewing a nearby object from different places.

• Importance of parallax: Danish astronomer Tycho Brahe reasoned that the distance of the object may be determined by measuring the amount of parallax. A smaller parallax angle meant the object was further away.

The apparent change in the location of an object due to the difference in location of the observer is called parallax.

Their views differ because of a change in position relative to the mountain

Because the parallax of the “star” was too small to measure, Tycho knew that it had to be among the other stars, thus disproving the ancient belief that the “heavens” were fixed and unchangeable.

http://www.astronomy.ohio-state.edu/~pogge/Ast162/Movies/parallax.gifhttp://instruct1.cit.cornell.edu/courses/astro101/java/parallax/parallax.html

Limitation to using parallax

• Eventually, the parallax shift will no longer be measurable.

• This is because the distance is too great for the effect to be observed.