the loss of the Mars Climate Orbiter, a spacecraft that smashed into the planet instead of reaching a safe orbit, a NASA investigation concluded Wednesday. The Mars Climate Orbiter, a key craft in the space agency’s exploration of the red planet, vanished after a rocket firing September 23 that was supposed to put the spacecraft on orbit around Mars. An investigation board concluded that NASA engineers failed to convert English measures of rocket thrusts to newton, a metric system measuring rocket force. One English pound of force equals 4.45 newtons. A small difference between the two values caused the spacecraft to approach Mars at too low an altitude and the craft is thought to have smashed into the planet’s atmosphere and was destroyed. The spacecraft was to be a key part of the exploration of the planet. From its station about the red planet, the Mars Climate Orbiter was to relay signals from the Mars Polar Lander, which is scheduled to touch down on Mars next month. “The root cause of the loss of the spacecraft was a failed translation of English units into metric units and a segment of ground-based, navigation-related mission software,” said Arthus Stephenson, chairman of the investigation board. This story illustrates the importance of being aware that different systems of units exist. Furthermore, we must be able to convert between systems of units! 6
1.6 Choice of Units There are no wrong units to use, but a clever choice of units can make a problem look simpler. The vast range of problems makes it impossible to use a single set of units for everything without making some problems look much more complicated than they should. We can’t easily compare the mass of the sun and the mass of an electron, for instance. This is why astrophysicists and atomic physicists use different systems of units. We won’t ask you to choose between different unit systems. For your present purposes the SI system is perfectly sufficient. In some cases you may come across quantities expressed in units other than the standard SI units. You will then need to convert these quantities into the correct SI units. This is explained in the next section. 1.7 How to Change Units— the “Multiply by 1” Technique Firstly you obviously need some relationship between the two units that you wish to convert between. Let us demonstrate with a simple example. We will consider the case of converting millimetres ( mm ) to metres ( m )— the SI unit of length. We know that there are 1000 mm in 1 m which we can write as 1000 mm = 1 m. Now multiplying both sides by 1 1000 mm we get 1 1000 mm 1000 mm = 1 1000 mm 1 m, which simply gives us 1 = 1 m 1000 mm . This is the conversion ratio from millimetres to metres. You can derive any conversion ratio in this way from a known relationship between two units. Let’s use the conversion ratio we have just derived in an example: Question : Express 3800 mm in metres.
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