Subject:
Mathematics
Science

Topics: AlgebraCoordinate SystemsFractional exponentsFunctionsPatternsAstronomy
Common Core State Standard: F-IF.4, F-BF.1a, F-LE.2,
Concepts:

Mathematics:

· Fractional exponents

Science:

· Orbit

Knowledge and Skills:

Mathematics:

· Can solve equations involving fractional exponents
· Can plot a point in a two-dimensional coordinate system, given the coordinates, or determine the coordinates of a given point
· Can identify and describe patterns in a collection of related numerical data

Science:

· Can describe the characteristics of the orbits of planets in the solar system

Lesson:

Procedure: The investigation is best done by students working individually or in teams of 2.

Distribute the handout and ensure that students understand the question. Graphing calculators may be used if available.

### Planet Paths

Step 1. Do research to fill out the chart below:

 Planet Average distance from the sun, in millions of miles (d) Time duration of orbit, in years (t) Mercury Venus Earth 93.0 1.00 Mars Jupiter Saturn Neptune Uranus

Step 2. Graph the data from the chart, with average distance from the sun as the independent variable and time as the dependent variable. Describe the pattern you see.

__________________________________________________________________________________________________________________

Step 3. Try to find a value of k for each of these functions which creates a curve that matches the graph of planet paths. To do this:

a) Put in the data for one planet to get a value of k.

b) Use that value of k to plot the function.

c) See how closely your function matches the function of planet paths.

Function #1: t = kd

Function #2: t = kd²

Function #3: t = kd³

Function #4: t = kd½

Function #5 t = kd3/2

Which is the correct function? __________

What is the value of k? _______________