Lab Problems

Tour Home

1. Start with the Mission to Mars.

  • First, read the Background information and then use that information to figure out the proper semimajor axis (a) and eccentricity (e) for the spacecraft orbit.
  • Then work out Mars' position at launch (the angle theta) and enter all these quantities into the applet.
  • Hit "Launch" and see if your mission is successful.

    Note: you can also do this by trial-and-error, just by typing in different values and launching a bunch of probes until one makes it to Mars. This is a very inefficient and costly way of exploring Mars, and not at all the way NASA does it! You should first calculate the orbit, and then launch your probe. If you're careful, you should be able to hit it on the first shot!

2. With a successful Mars mission under your belt, now it's time to explore the outer planets.

  • Load up the Grand Tour applet, and now you need to calculate a and e for each leg of the orbit (Earth to Jupiter, Jupiter to Saturn, etc).
  • Next, you need to find the starting angle for each planet. Careful here: remember this is now the angular position of each planet when the probe initially launches from Earth.

    And this time I dare you to do it by trial and error!

3. Now, examine the time and energy required for your Grand Tour.

  • Once you have the mission running, note how long it takes to make it all the way to Neptune. Also note how much energy it takes for this mission.
  • Now run the Voyager 2 mission by clicking the "Voyager" checkbox, and note the time taken and energy used.
  • Voyager was able to complete the mission faster because it used more energy -- energy which typically came from the use of gravity assist boosts during the flybys of each planet. Your mission involved the minimum energy orbit, and so took much longer to unfold.