Question

• Use the “clear optional features” button to remove the 1st Law features.
• Open the Kepler's 2nd Law tab.
• Press the “start sweeping” button. Adjust the semimajor axis and animation rate so that the planet moves at a reasonable speed.
• Adjust the size of the sweep using the “adjust size” slider.
• Click and drag the sweep segment around. Note how the shape of the sweep segment changes, but the area does not.
• Add more sweeps. Erase all sweeps with the “erase sweeps” button.
• The “sweep continuously” check box will cause sweeps to be created continuously when sweeping. Test this option.

1. Erase all sweeps and create an ellipse with a = 1 AU and e = 0. Set the fractional sweep size to one-twelfth of the period. Drag the sweep segment around. Does its size or shape change?

2. Leave the semi-major axis at a = 1 AU and change the eccentricity to e = 0.5. Drag the sweep segment around and note that its size and shape change.

1. Where is the sweep segment the “skinniest”?
2. Where is it the “fattest”?
3. Where is the planet when it is sweeping out each of these segments? (What names do astronomers use for these positions?

3. What eccentricity in the simulator gives the greatest variation of sweep segment shape?

Answer 1

1) No, with e = 0, neither its size or shape changes

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2) The sweep segment is the skinniest when it is placed all the way to the right of the sun.

The sweep segment is fattest when all the way to the left.

The planet is closest to the sun when it is sweeping out the fattest segment (astronomers call it perihelion) and farthest from the sun when it is sweeping out the skinniest segment (astronomers call it aphelion)

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3) the greatest variation of sweep segment shape is given at eccentricity of about 0.6 - 0.7