Click on a number to view the explanation of the corresponding item.

Basic Control Buttons

There are four basic control buttons. They are, from left to right:

Rewind. Resets the simulation to the starting point with the previously chosen system parameters. After clicking Rewind, click Play to restart the motion.

/ Play/Pause. Clicking starts the motion.

After Play has been clicked, the button will change into the Pause button .

Click it if you want to take a 'snapshot' of the motion at a given instant. To resume the motion, click Play once more.

Step. Lets you step through the motion in equal time steps.





Reset. Resets the applet to its default setting.

Adjustments in the system parameters can only be made after first clicking REWIND or RESET.



Trace

This toggle button displays or hides the path taken by the planet.



Area Sweep

This toggle button displays/hides sectors of equal area shaded dark or light in the planet's orbit as shown in the image below.





Vectors

The Vectors toggle button displays/hides the panel shown below on which you can select the vectors you want to have displayed.



The following vectors can be displayed:

• velocity of planet relative to stars - Velocity of the planet relative to the inertial frame of the fixed stars background. The Lab frame is represented with a fixed stars background at rest. The arrow representing the velocity is in magenta.
• velocity ' of planet relative to sun - Velocity of the planet relative to the inertial frame in which the sun is at rest. It is represented by a blue arrow.
• velocity of sun relative to stars - Velocity of the sun relative to the inertial frame of the fixed stars background. It is represented by a yellow arrow.

  When the motion is paused, you can click on the yellow sun-velocity vector and drag it. By positioning it properly, as in the image below,

  

  you can verify that the three velocity vectors , ', and satisfy the Galilean velocity addition theorem: = ' + .

• acceleration of planet relative to stars and sun - The planet's acceleration relative to the sun is also the planet's acceleration relative to the fixed stars because the sun is moving with constant velocity relative to the fixed stars. This acceleration vector is represented by an orange arrow.



Vector Labels

The applet allows you to display three different velocity vectors and one acceleration vector. The symbols for these vectors can be either displayed or hidden by means of the Labels toggle button.



Data

The Data toggle button displays/hides the data shown in the following image.



• E /m: energy of the sun-planet system, divided by the mass of the planet
• L /m: angular momentum of the planet relative to the sun, divided by the mass of the planet
• dA/dt: areal speed of the planet relative to the sun
• ω: angular speed of the planet relative to the sun
• t: time, with t = 0 at the beginning of the motion
• r: distance from the sun to the planet
• v: speed of the planet relative to the fixed stars
• v': speed of the planet relative to the sun
• a: magnitude of the planet's acceleration

All quantities in this list are expressed in units in which the length unit is the astronomical unit (AU), which is the average radius of the earth's orbit, and in which the time unit is the year (Year), which is the time required for the earth to go once around the sun.



Graph of Angular Speed vs. Time



The Graph toggle button displays/hides a graph of the planet's angular speed relative to the sun.

By clicking anywhere in the area of the graph, the graph can be dragged to any convenient location on the screen. When holding down the Control key while dragging in the area of the graph (horizontally or vertically), different parts of the graph can be brought into view while the graph stays in the same area of the screen.



Sliders



There are three sliders in all. They are described below, in the order from left to right.

You can adjust a slider setting either by dragging the slider tab or by entering an exact value in the slider input dialog.

To enter an exact value, click on the Input Dialog button of the slider to open the dialog. The dialog for the Sun Velocity slider is illustrated below. The range in which values can be entered, from -10 AU/Year to 10 AU/Year in this case, is indicated above the data entry field.



Clicking on a slider to the left or right of the slider tab allows fine adjustment of the slider setting.

• Eccentricity. This slider sets the amount of "flatness" (eccentricity) of the ellipse.
  
  The eccentricity of an ellipse can vary between 0, for a circle, to 1, which is the limiting case in which an ellipse degenerates into a parabola. However, the slider allows the eccentricity to be varied only in the range from 0 to 0.800, in steps of 0.001.
  
  
• Semi-Major Axis. This slider lets you set the semi-major axis of the ellipse, which is half of the longest diameter of the ellipse, to a value between 1.0 AU and 5.0 AU, in steps of 0.1 AU. In the applet, the major axis of the ellipse is oriented horizontally.
  
  
• Sun's Velocity. This slider lets you set the velocity of the sun relative to the fixed stars, in the range from -10.00 AU/Year to 10.00 AU/Year, in steps of 0.01 AU/Year.  The velocity can be either to the right or to the left. Positive slider settings mean the velocity is to the right, negative settings to the left. This velocity can be displayed via the vector panel. (See Point 4, 'Vectors'.)
  
  The planet's motion relative to the sun and the planet's velocity ' relative to the sun are unaffected by different settings for the sun's velocity. However, the velocity of the planet relative to the fixed stars is affected. (See Point 4, 'Vectors'.)



Planet-Sun System



The sun is represented by a yellow disk and the planet by a green dot. By clicking in the area of the planet-sun system and dragging, you can move the system to any convenient location. This can be done at any time, even while the motion is in progress.