Kepler’s Laws of Planetary Motion Reading

REGENTS EARTH SCIENCE Kepler's Laws of Planetary Motion

Name Date

Period

Aim: How can we describe the motion of planets from Kepler's Laws?

Kepler's Laws of Planetary Motion:

1. Kepler's 1st Law: Planets move along ellipses (or oval like orbits), with the Sun at one focus.

2. Kepler's 2nd Law: The line from the Sun to the planet covers equal areas in equal times.

3. Kepler's 3rd Law: The square of the planet's orbital period is proportional to the third power ("cube") of the average distance from the Sun. The mathematical formula is P2 = a3. (THIS LAW WILL NOT BE ON THE

REGENTS)

Activity 1: Read the passage below and answer the following questions: Kepler's 1st Law: Elliptical Orbits

You may think that most objects in space that orbit something else move in circles, but that isn't the case. Although some objects follow circular orbits, most orbits are shaped more like "stretched out" circles or ovals. Mathematicians and astronomers call this oval shape an ellipse.

All of the planets in our Solar System, many satellites, and most moons move along elliptical orbits. An ellipse can be very long and thin, or it can be quite round- almost like a circle. Scientists use a special term, "eccentricity", to describe how round or how "stretched out" an ellipse is. If the eccentricity of an ellipse is close to one (like 0.8 or 0.9), the ellipse is long and skinny. The highest the eccentricity can be is 1, which is a straight line. If the eccentricity is close to zero, the ellipse is more like a circle. The lowest of eccentricity is 0, which is a circle.

The Sun isn't quite at the center of a planet's elliptical orbit. An ellipse has a point a little bit away from the center called the "focus." There are two foci in the elliptical orbit. The Sun is at the focus of the ellipse, while the other focus is at imaginary position in the space. Because the Sun is at the focus, not the center, of the ellipse, the planet moves closer to and further away from the Sun every orbit. The close point in each orbit is called perihelion. The far away point is called aphelion.

1) Use the information in the paragraph above, label the perihelion and aphelion positions in the following:

F2

F1

2) What is the distance between the two foci?

cm (nearest tenth 0.0)

3) What is the length of the major axis?

cm (nearest tenth 0.0)

4) Calculate the eccentricity of the ellipse to the nearest thousandth place (0.000). (See formula on ESRT pg 1) Show your work.

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Activity 2: Read the passage below and answer the following questions: Kepler's 2nd Law: The Speeds of Planets Kepler's second law he again discovered by trial and error. Kepler realized the line connecting the planet and the Sun sweeps out equal area in equal time. Look at the diagram below.

What Kepler found is that it takes the same amount of time for the planet to go from A to B as it does to go from C to D. But the distance from C to D is much larger than that from A to B. It has to be so that the shaded regions have the same area. So the planet must be moving faster between C and D than it is between A and B. This means that when planets are near the Sun in their orbit, they have a higher orbital velocity (speed in orbit) than when they are further away. The greater orbital velocity of planets near the Sun is due to the greater gravitational attraction between the planets and the Sun.

5) Why is orbital velocity greater at the perihelion position?

6) Use the T- chart below to compare and contrast the aphelion and perihelion position of an ellipse in relation

to:

a) position in relation to the Sun

b) gravitational attraction

c) orbital velocity

Aphelion

Perihelion

a) Furthest from the Sun

a)

b)

b)

c)

c)

Activity 3: Write a paragraph to summarize Newton's Law of Universal Gravitation.

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