The Importance of Units

Artist’s conception of the Martian Climate Orbiter.

In December 1998, NASA launched the 125-million dollar Mars Climate Orbiter, intended as the red planet’s first weather satellite. After a 416-million mi journey, the spacecraft was supposed to go into Mars’ orbit on September 23, 1999. Instead, it entered Mars’ atmosphere about 100 km (62 mi) lower than planned and was destroyed by heat. The mission controllers said the loss of the spacecraft was due to the failure to convert English measurement units into metric units in the navigation software.

Engineers at Lockheed Martin Corporation who built the spacecraft specified its thrust in pounds, which is an English unit. Scientists at NASA’s Jet Propulsion Laboratory, on the other hand, had assumed that thrust data they received were expressed in metric units, as newtons. Normally, pound is the unit for mass. Expressed as a unit for force, however, 1 lb is the force due to gravitational attraction on an object of that mass. To carry out the conversion between pound and newton, we start with 1 lb = 0.4536 kg and from Newton’s second law of motion,

force    = mass ˣ acceleration

= 0.4536 kg ˣ 9.81 m/s²

= 4.45 kg m/s²

= 4.45 N

because 1 newton (N) = 1 kg m/s². Therefore, instead of converting one pound of force to 4.45 N, the scientists treated it as 1 N. The considerably smaller engine thrust expressed in newtons resulted in a lower orbit and the ultimate destruction of the spacecraft. Commenting on the failure of the Mars mission, one scientist said: “This is going to be the cautionary tale that will be embedded into introduction to the metric system in elementary school, high school, and college science courses till the end of time.”