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: eccentricity of the sun-planet system
• a: semi-major axis of the planet's elliptical orbit around the sun
• dA/dt: areal velocity of the planet relative to the sun
• w: angular velocity 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

Note. The symbol a occurs twice in this list, once for the semi-major axis, once for the magnitude of the acceleration. It will be clear from the context, which quantity the symbol denotes.

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.

• Energy/Mass. This slider sets the ratio E/m of the planet-sun system's mechanical energy E and the planet's mass m in the range from -19.73 AU²/Year² to -6.28 AU²/Year², in steps of 0.01 AU²/Year².
  E is the sum of the planet's kinetic energy in the reference frame in which the sun is at rest and the potential energy -GM/r of the planet-sun system.
  
  
• Angular Momentum/Mass. This slider lets you set the ratio L/m of the magnitude L of the planet's angular momentum relative to the sun and the mass m of the planet.
  
  The values of E/m and L/m determine the eccentricity and the semi-major axis of the planet's orbit, in other words, the shape of the orbit.
  
  
• 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.