10182

# Flying to the Moon

If you follows the suggestion of Francis Godwin in 1638 and harnesses some swans to a chair and directs them toward the Moon, you might or might not reach it. If the swans always travel toward the current position of the Moon, at constant speed, then the swans will fail to reach it unless their speed is at least as great as that of the Moon. In this Demonstration, the basic unit is 1 lunar distance and the swans start at the surface of the Earth, whose radius is 0.0167. The Moon is assumed to travel in a circle, with an orbital period (with respect to the fixed stars, not the Sun) of 27.3 days. In the event of failure, the swans continue to orbit around the dashed red path.

### DETAILS

The differential equation for the motion of the swans is easily set up in vector form as , where is the speed of the swans and is the position of the Moon. This equation states that the swans' velocity vector has constant length and is always directed toward the Moon. Note that the gravitational attraction of the Moon and Earth are ignored. If the swans' speed is not greater than that of the Moon, then the swans approach a circular path, shown as a dashed red curve (see second and third snapshots). This example is discussed in more detail in [1].
Reference
[1] A. Simoson, "Pursuit Curves for the Man in the Moone," College Mathematics Journal, 38(5), 2007 pp. 330–338.

### PERMANENT CITATION

 Share: Embed Interactive Demonstration New! Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details » Download Demonstration as CDF » Download Author Code »(preview ») Files require Wolfram CDF Player or Mathematica.

#### Related Topics

 RELATED RESOURCES
 The #1 tool for creating Demonstrations and anything technical. Explore anything with the first computational knowledge engine. The web's most extensive mathematics resource. An app for every course—right in the palm of your hand. Read our views on math,science, and technology. The format that makes Demonstrations (and any information) easy to share and interact with. Programs & resources for educators, schools & students. Join the initiative for modernizing math education. Walk through homework problems one step at a time, with hints to help along the way. Unlimited random practice problems and answers with built-in Step-by-step solutions. Practice online or make a printable study sheet. Knowledge-based programming for everyone.