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Planetary Orbit

Instruction Manual

Introduction

The simulation simulates planets orbiting a sun.
This simulation assumes that:

• All planetary orbits are perfectly circular and obeys Kepler's laws
• Only the orbital speed changes and the radius of the orbit is kept the same when the mass of the sun changes
• All planets are particles and have no mass or dimensions
• Planets can pass through each other

Interface

The interface in this simulation consist of two sides, the left hand side shows the simulation and the right hand side shows the control panel. The status bar on the browser displays the frame rate the simulation is performing, a frame rate of 60 is considered satisfactory.

Simulations functions	Diagram
Left click to create an anti-clockwise orbiting planet.
Right click to create a clockwise orbiting planet.

Control panel functions	Diagram 1	Diagram 2
Radius The distance between the mouse and the centre of the sun is displayed as shown in the diagram 1. Diagram 2 shows how the distance is measured.
Mass of the sun The mass of the sun is as shown in diagram 1. It can be edited as shown in diagram 2, click on it and press backspace to delete the variable. Press the number keys to change the variable. Hit enter to return the variable.
Data display The display data drop down menu, diagram 1, allows selected data of each planet to be shown, diagram 2, from the following:- Radius of orbit Orbit speed Centripetal acceleration
Time scale The time scale is as shown in diagram 1. It can be edited as shown in diagram 2, click on it and press backspace to delete the variable. Press the number keys to change the variable. Hit enter to return the variable.
Pause/play button The pause/play button will pause or unpause the simulation.
Reset button The reset button will reset the simulation to its initial state.
Change colour button The change colour button changes the colour scheme of the simulation from a selection of : Black White Blue

Background physics

One of Kepler's laws state that the time of obit squared is directly proportional to the average radius of the orbit cubed, ie . Sir Isaac Newton proved this law by using his equation of circular motion with the equation for gravitational force.

This simulation's algorithm is somewhat based on Kepler's law but it is mainly based on Newton's equation of circular motion to find the angular velocity. The angular velocity is then used to change the angular displacement of each planet.

So using the equation , the angular displacement of each planet is updated.

Scientific FAQ

• Why can't you change the mass of the planet?
  • The orbital speed does not depend on the mass of the planet, therefore it is not necessary to change the mass of the planet.


• Can this simulation be used to model the solar system?
  • Yes but only the inner solar system planets can be used in this simulation. This is because the scale of the whole of the solar system is so huge that it is impractical to model this.


• What should happen if the mass of the sun changes?
  • If the sun gains mass, it will have more gravitational force which will pulls the planets towards the sun. However as the planets are pulled towards the sun, the planets will convert its gravitational potential energy to kinetic energy and so gain velocity therefore will still be in orbit.
  • However if the sun loses mass, each planet will have less gravitational potential energy as a result of the sun having less gravitational force. Each planets' total energy will increase because of this so each planet may either increase the radius of its orbit or speed up.
  • If the mass of the sun suddenly becomes really small, each planet would travel in a straight line tangent to its orbit at that time.
  • The reason why this simulation is to assume the radius of each orbit is fixed is to simplify the simulation and fully focus on circular orbit.


• Are planetary orbits perfectly circular?
  • No and it doesn't need to be. Most are actually elliptical because planets have orbital speeds slightly different from what is required for a perfect circular orbit.

Technical FAQ

• Why can't I create a planet close to the sun?
  • This simulation won't let you create a planet with an orbit of radius less than 16x10⁹ m.


• How do I change the mass of the sun or the time scale?
  • Click on the number box and it should change colour. Press backspace to delete the digits and type in the desired value by typing in the number keys on the keyboard then press enter. If you have made a mistake, press the backspace button.


• How do you see the data for each planet?
  • The display data drop down menu can be opened by clicking on it. Select the data to be seen by clicking on the options of data.


• What's the maximum number of planets which can be created?
  • There is no limit to how many planets can be created however the simulation will slow down if too many are created.