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Applications of Linear Systems

Word problems using two equations and two unknowns

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Shoot for the Moon

Credit: U.S. Post Office
Source: http://commons.wikimedia.org/wiki/File:First_Man_on_Moon_1969_Issue-10c.jpg
License: CC BY-NC 3.0

In 1969, American astronaut Neil Armstrong became the first man on the moon. Nearly 50 years later, NASA is planning to return to the moon. This time, astronauts will use the landing as the first step towards a mission to Mars. The new moon mission is composed of several stages. NASA launched the first stage of the mission, the Lunar Atmosphere and Dust Environment Explorer (LADEE), in September 2013.

Right on Target

To reach the moon, scientists needed to set up and solve a complex system of equations. One set of equations represented LADEE’s movement through space. The other tracked the movement of the moon as it circled the Earth. The solution to the system was the time and place where LADEE would meet the moon. They calculated that after LADEE left Earth, it would take the probe 30 days to reach the moon. LADEE will orbit the moon for another 30 days and then spend 100 days collecting data on the lunar atmosphere and dust particles. Researchers hope that information from LADEE will help them better understand the atmospheres and environments of other planets in our solar system.

Credit: NASA Ames Research Center
Source: http://commons.wikimedia.org/wiki/File:LADEE-Vibe-Z-Axis-4-TPrep_580x546.jpg
License: CC BY-NC 3.0

The LADEE mission was the product of a revolutionary space vehicle design program. In the past, NASA has designed each of its probes from scratch. The new system utilizes modules to construct the spacecraft. The same modules can be used for other missions and programs. This more efficient design process will help save time and money, allowing NASA to send more probes into space. LADEE itself is also incredibly energy efficient. It’s the size of a small car, but it only uses as much energy as five 60-watt light bulbs.

See for yourself: http://www.youtube.com/watch?v=E2GIvHn8omY

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Read about and watch the launch of LADEE at the links below.



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  1. [1]^ Credit: U.S. Post Office; Source: http://commons.wikimedia.org/wiki/File:First_Man_on_Moon_1969_Issue-10c.jpg; License: CC BY-NC 3.0
  2. [2]^ Credit: NASA Ames Research Center; Source: http://commons.wikimedia.org/wiki/File:LADEE-Vibe-Z-Axis-4-TPrep_580x546.jpg; License: CC BY-NC 3.0

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