5: Discovering Kepler's Laws
- Page ID
- 162997
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Lab Overview
Lab Goals
The goal of this lab is to develop the scientific practices of identifying patterns/relationships between variables and making scientific claims based on evidence with clear reasoning. You will develop these lab skills while developing/reviewing your understanding of Kepler’s Laws for gravitational orbits. As a result of this lab, you should be able to:
- Restate Kepler’s Laws as claims and support those claims with evidence and reasoning.
- Identify additional patterns relating orbital shape to other orbital parameters (speed, semi-major axis, orbital orientation, etc).
Equipment and Setup
This lab requires the following equipment on each table.
- Computers with PhET Simulator
Submission Instructions
Submit a brief lab report that includes the following sections:
Methodology
Write a Methodology section that details the steps you took in the simulation to generate the data in your results section. Be sure to include information about what boxes were checked in each simulation. Include any description of how you adjusted parameters (position, velocity, etc) and measured values (if any). If your data was visual, describe what you look at in the visual when you made your changes.
Results
Include screenshots from the simulation. This might include orbits, graphs, or other data. If you have a collection of numerical data, make organized tables that are clearly labeled. All images should have a caption with numbers increasing throughout the paper. See example below:
Figure 1. [One sentence description]
Discussion
Write/type your answers to the Discussion Questions using the Claim-Evidence-Reasoning format. If it makes sense, you might group responses to multiple questions into a single claim.
Background Information
When orbits are circular, we can describe them based on their diameter or radius. The diameter is the length of a line that goes from one part of the circle, through the center, to the other end. A radius is the length of a line from the center to any point on the circle. The radius is half the diameter
Most orbits are more of an oval than a circle. These orbits can often be described by the major axis, which is the length of the long axis and their minor axis, which is the length of the short axis. Since we often describe circular or rotational motion based on radius, rather than diameter, we define a semi-major axis as the “long radius” and semi-minor axis as the “short radius” of an orbit. The mathematical name for this shape is an ellipse.
Lab Instructions
Simulation Setup
Open the Kepler Laws Simulation from the University of Colorado, Boulder PHET Interactive Simulations website:
Start with the First Law tile.
- Check the box for Foci
- Check the boxes for Axes and Semiaxes
Play around with the simulation for 3-5 minutes. Explore the different menus (on this tile) and different obits you can make. Then move on to the procedure on the next page.
Part 1 - Orbital Shape
Procedure
- Check the box for Always Circular to simplify the first exploration.Move the planet to different distances and search for a pattern between radius and speed for circular orbits. Uncheck the box for Always Circular to make the simulation more complex and more realistic.
- Try adjusting the velocity by changing the green vector. Search for patterns based on the discussion questions.
Discussion Questions
- For a circular orbit, what is the pattern between orbital radius and orbital speed?
- For an elliptical orbit:
- How can you make the orbit larger/smaller?
- How can you adjust the orientation of the major/minor axes in the orbit?
- What can you say about the location of the star as you make these changes? Use terminology about circles/ellipses.
- What (if anything) results in an incomplete (dashed line) orbit? What happens to the planet in such an orbit?
Part 2 - Orbital Wedge Areas
Move to the Second Law tile.
- Check the box for Apoapsis and Periapsis
- Check the boxes for Axes and Semiaxes
- Set Period Divisions to 6
- Check the boxes for Area Values and Time Values
Procedure
- Check the box for Always Circular to simplify the first exploration.
- Compare the area of each wedge. Are they the same? If not, is there a pattern for where they are bigger/smaller?
- Compare the period of each wedge. Are they the same? If not, is there a pattern for where they are longer/shorter?
- Compare the arc length of each wedge. Are they the same? If not, is there a pattern for where they are longer/shorter?
- Change the radius: How are the areas, periods, and arc lengths affected (or not affected) by a bigger/smaller radius?
- Uncheck the box for Always Circular to make the simulation more complex and more realistic. Drag the planet out (or change the velocity) to make the orbit an ellipse instead of a circle.
- Compare the area of each wedge. Are they the same? If not, is there a pattern for where they are bigger/smaller?
- Compare the period of each wedge. Are they the same? If not, is there a pattern for where they are longer/shorter?
- Compare the arc length of each wedge. Are they the same? If not, is there a pattern for where they are longer/shorter?
- Change the radius: How are the areas, periods, and arc lengths affected (or not affected) by a bigger/smaller radius?
Discussion Questions
The wedges are all created to show equal periods. Everything else is a reflection of this fact. Write CERs based on the following:
- Make a claim about wedge area and arc length for each period portions of a circular orbit.
- Make a claim about wedge area and arc length for each period portions of an elliptical orbit.
- For anything that has different values, identify a trend for when/where those values are greatest/least.
Part 3 - Semi-major Axis and Period
Move to the Third Law tile.
Procedure
- Adjust the orbit in and out. This should create a graph that shows how the period relates to the semi-major axis in an orbit. You can play the animation at a few points to understand what this graph represents.
- Examine the line/curve:
- Is there a positive or negative correlation between semi-major axis (a) and orbital period (T)?
- Is the relationship linear or nonlinear?
- If the orbit curves away from an axis, increase the power of that variable (eg, select a2 if the graph curves away from a or select T2 if the graph curves away from T). Repeat until you get a straight line. Record an equation that states your y (vertical) selection is equal to your x (horizontal) relation.
Discussion Questions
- Use the following sentence frame to make claims about the relationship between the semi-major axis and the orbital period. Only include your selection from each option in parentheses for the first and include your equation for the straight line graph in the second.
- There is a (positive/negative) (linear/nonlinear) relationship between the semimajor axis and the orbital period.
- In an orbit, the orbital period and semi-major axis are related by the equation …