Superlesson
Project 2-1

Superlesson
Project 2-2

Superlesson
Project 2-3

Advanced Algebra

Chapter 2, Linear Functions, Equations, and Inequalities

Planets have elliptical orbits, not perfectly circular ones. The distance of a planet to the sun is often expressed as an average of the closest and farthest a planet gets from the sun.

Part A, One-Variable Inequalities

1. Gather some information about the planet Jupiter and use it to answer the questions below. Note: You will need to scroll down to "Orbital Parameters."

a. What is the closest Jupiter gets to the sun (perihelion orbit)?

b. Write an inequality expressing this distance.

c. Graph your inequality from b on a number line.

d. What is farthest Jupiter gets from the sun (aphelion orbit)?

e. Write an inequality expressing this distance.

f. Graph your inequality from e on a number line.

g. Write a compound inequality that expresses the distance Jupiter can be from the sun.

h. Graph your inequality from g on a number line.

2. Pick another planet and look at its fact sheet.

a. Write a compound inequality that expresses the distance your planet can be from the sun.

b. Graph your inequality from a on a number line.

 

Part B, Inequalities and Absolute Value

3. Gather some information about the moon and use it to answer the questions below.

a. Suppose the measurement for the moon's surface gravity is only correct to within 5%. What is the maximum possible surface gravity on the moon?

b. What is the minimum possible surface gravity of the moon?

c. Write an absolute value inequality expressing the surface gravity (g).

 

4a. What is the equatorial radius of the moon?

b. What is the closest the moon gets to the Earth during the perigee orbit?

c. Suppose you don't know if the orbit of the moon is measured from the surface or from the center. What is the closest the surface of the moon could be to the Earth?

d. What is the farthest the surface of the moon could be from the Earth during the perigee orbit?

e. Write an absolute value inequality expressing the distance (d) from moon to the Earth at its closest approach.

 

Part C, Linear Inequalities with Two Variables

5. Go to NASA's Planetary Fact Sheet. For each planet, find out the perihelion orbit and the aphelion orbit.

a. Use those numbers to make a table.

b. Graph the data from your table.

c. Draw in a line showing where the orbits would be perfectly circular.

d. Do any planets have perfectly circular orbits?

e. Shade in the area where the perihelion orbit is shorter than the aphelion orbit.

f. Do any of the planets lie in the region you shaded in e? Explain.

Part D, Making Connections

6. Look at the Mars Fact Sheet to find the distance from Mars to the Sun.

a.Write a compound inequality expressing the distance from Mars to the Sun.

b. Look at the Earth Fact Sheet. Write a compound inequality expressing the distance from Earth to the Sun.

c. What is the farthest Earth is from Mars?

d. What is the closest Earth is to Mars?

7. If it costs NASA $1 billion to send a rocket to Mars when it is at its closest point, and $2.5 billion to send a rocket to Mars when it is at its farthest point, how many of each type of mission could it fund for $15 billion? Express your answer in a graph.