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Optional Practical: Orbit simulation (Algodoo)


Introduction

When a body is in a circular orbit round another one the centripetal force required for the circular motion is provided by the gravitational attraction, by equating these terms we can find a value for the speed,v of the orbit.

fraction numerator G M m over denominator r squared end fraction equals fraction numerator m v squared over denominator r end fraction v equals square root of fraction numerator G M over denominator r end fraction end root

Setting up the simulation

In reality the value of G is 6.67 x 10-11 Nm2kg-2 this means that orbits around low mass objects would be very slow, In Algodoo you can vary the gravitational constant to speed things up a bit.

  • Open a new scene and show the grid

  • Draw a circle, double click it and from materials give it a mass of 1000 kg and an attraction of 0.04 Nm2kg-2 (this is G).
  • Place a second smaller circle 10 m to the right of the first one and give it a mass of 0.005 kg
  • Calculate the speed necessary to put the smaller mass in orbit set the velocity using the "velocities" options.

  • Double click the orbiter (pause first) and display the information. You can make this stay in view by dragging the window to one side.

  • Observe the values for KE, PE and total energy as the body orbits.

Investigation

  • Observe what happens if you change the velocity of the orbiter.
  • Observe the effect of adding a small amount of air resistance (note the changes in energy)

  • Try adjusting the "attraction". Observe the changes in energy, try to keep the orbiter in orbit.
  • Set the large mass to 500 kg and calculate the radius and speed for a circular orbit. Try this out to see if you are right.
  • Make a mini solar system with several "planets".
  • See if you can put a moon in orbit around a planet.
  • Try putting a 500 kg mass in orbit round another 500 kg mass.
  • Cover the surface of a planet with water and observe the tidal effect as a moon orbits.
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