CONTENT OBJECTIVE: 8K2.00 To understand the movement of celestial objects
INSTRUCTIONAL OBJECTIVES: The learner will:
2.01 state the basic concepts of celestial mechanics.
2.02 distinguish between perihelion and aphelion.
2.03 demonstrate how the universe is expanding.
2.04 demonstrate that gravity and centrifugal force are the two forces that hold the solar system together.
OUTLINE OF CONTENT:
II. Law of gravitation
III. Expanding Universe
TN COMPONENT OF SCIENCE: Habits of Mind
To enable students to demonstrate ways of thinking and acting inherent on the practice of science; and to exhibit an awareness of the historical and cultural contributions to the enterprise of science.
3.1 HISTORICAL AND CULTURAL PERSPECTIVE - The knowledge and processes of science have evolved over time as an approximation of truth within cultural contexts.
TN STANDARD(S): The learner will understand that:
3.1b Individual initiative and vision create changes in science
BENCHMARK: Scientists around the world have made significant contributions to the body of scientific knowledge.
3.1c The desire to understand the natural environment and to predict the course of natural events is universal.
BENCHMARK: People have developed theories to explain events.
large piece of paper, heavy cardboard, 2 thumbtacks, string, balloons (not red), red marker pen, black marker pen, tape measure, tennis ball, 4 feet of heavy string
Today we will discuss how our universe is expanding and the principle of celestial mechanics.
Johannes Kepler discovered the true orbits of the planets. He concluded, after much research, that a planet's path is not a circle, but an oval figure, an ellipse.
Teacher and student: If you are not familiar with ellipses, you can draw some for yourself. Pin a large piece of paper to some heavy cardboard. Stick two thumbtacks a short distance apart near the middle of the paper. Tie the ends of a string to make a loop. Place the loop over the tacks and pull the string tight with a pencil. Draw a line using the string loop to guide the pencil.
The points where the thumbtacks are located are the foci of the ellipse. An ellipse has two foci. See what happens to the shape of the ellipse when the distance between the two foci is changed.
(An ellipse looks like a circle but has the same shape as a cone if it were sliced through.)
The sun is always at one of the focus points of a planet's elliptical orbit. As a result, with the sun at one focus, the planet's distance from the sun constantly changes.
When the earth is closest to the sun, the distance between the earth and sun is 147,000,000 Km (91,300,000 mi). The earth at its nearest approach to the sun is said to be at perihelion. At aphelion the earth is at its farthest point from the sun. The distance is 152,000,000 km (94,500,000 mi).
(*A planet moves fastest when it is nearest the sun and slowest when farthest away.)
Every object attracts every other object in the universe by the force of gravitation. Newton's Law of Universal Gravitation explains how this force acts. According to this law, the gravitational force between two bodies depends on two factors: the mass of the bodies and the distance between them. The greater the mass, the greater the gravitational force between them. The greater the distance between them, the smaller the gravitational force between them. Astronomers use this law to predict the paths of orbiting bodies. (planets, moons, satellites)
A body at rest remains at rest and a body in motion remains in motion in a straight line at constant speed unless acted upon by another force. This property of a body is called inertia. Planets and other moving bodies keep moving because of inertia. Inertia also helps us to predict the path of orbiting bodies.
1. Students will demonstrate that gravity and centrifugal force are the sole forces that hold the solar system together. They will need a tennis ball and four feet of heavy string.
a. Tie one end of the string around the ball.
b. Hold the other end of the string and swing the ball around your head.
Results: The ball moves in a path around your head. As long as you hold the string, the ball continues to move around your head. Two forces are countering each other; therefore, the ball moves in this orbit. One is the centripetal force, the force caused by the string. The string is trying to pull the ball toward the center of its orbit. Centripetal force keeps the ball from flying away. The other is the centrifugal force. As the ball moves, its momentum makes it try to move away from the center of its orbit. Centrifugal force balances against the centripetal force. This tug-of-war keeps the planets orbiting around the sun in our solar system. Gravity serves as the centripetal force instead of a piece of string.
(For extended studies try different weights of objects attached to the string. Repeat the same swinging experiment. Is a different balance between the centripetal and centrifugal forces needed to keep these different objects spinning? How do you account for this difference?)
2. (Students will demonstrate how the universe expands.
Materials: balloons (not red), red marker pen, black marker pen, tape measure)
a. Copy the table shown.
b. Ask your partner to blow up a balloon just enough to make it taut and to hold it closed. Measure the diameter of the balloon.
c. Draw red dots about 2 cm apart all over the balloon to represent the galaxies.
d. With the black marker, circle one dot.
e. Choose 6 other dots, some close and some far away from the circled dot. Number the dots 1 through 6.
f. Measure the distances from the circled dot to the 6 other dots. Record the distances in column 2 of the table.
g. Ask your partner to blow into the balloon until the diameter is doubled. Hold the balloon's end closed.
h. Measure the distances from the circled dot to the 6 other dots again. Record these distances in column 3 of the table.
i. Subtract the numbers in column 2 from those in column 3. Record your answers in column 4.
j. Divide the numbers in column 3 by the numbers in column 2. Record your answers in column 5.
Distance After Expansion
Change In Distances
Factor By Which The Distances Changed
1. Blowing up the balloon represents the expansion of the universe. Explain how the changes in distances between galaxies depend on how far apart the galaxies were originally. (Compare columns 2 and 4 in your table.)
2. Does the factor by which the distances between galaxies changed also depend on how far apart the galaxies were originally? (Compare the numbers in columns 2 and 5 of your table.) Explain your answer. (response)
1. Turn to your neighbor and tell them Newton's Law of Universal Gravitation.
2. On a piece of paper write the difference between perihelion and aphelion.
aphelion - point on the earth's orbit farthest from the sun
centrifugal force - causes a body that is traveling around a center to fly outward
centripetal force - force pulling an object inward toward the center of a curving path
ellipse - kind of curve resembling a squashed circle
foci - two points inside an ellipse
perihelion - point on the earth's orbit nearest the sun
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