Mathematics
Grade Levels: 6th Grade, 7th Grade, 8th Grade, 9th Grade,
Topics: AlgebraCoordinate SystemsExpressions and Equations
Common Core State Standard: F-IF.7e,
Knowledge and Skills:
• Can evaluate expressions by substituting values for variables
• Can simplify expressions using correct order of operations
• Can plot a point in a two-dimensional coordinate system, given the coordinates, or determine the coordinates of a given point
Lesson:
If the Space Shuttle were to make a maintenance trip out to a satellite in geosynchronous orbit, the Shuttle would need to enter into an elliptical orbit around the earth. That orbit could be described by this equation:
where a and b are numbers that determine the shape of the ellipse.
If all distances are measured in thousands of miles, then an actual orbit might be described by this equation:
1. Find the value of y for each value of x (to two decimal places):
2. Plot the ordered pairs from the table above and sketch the curve that
connects them.
3. In this orbit, the Earth would be at the position (-12.5,0), and the satellite
would be at the position (13.5,0). Plot these points on your graph. How far is
the earth from the satellite?
Answers:
1.
2.
3.
26,000 miles