Did you know that the GPS must take into account special and general relativity?
If engineers didn`t adjust for the motion of the satellite relative to the
receiver on Earth the receiver’s clock would gain 7 microseconds each
day due to special relativity. Reverse adjustments to compensate for the weaker
gravity at the high altitude of the satellite (general relativity) prevent the
loss of 45 microseconds per day. Who cares about 38 microseconds? You do. The
GPS receiver calculates your position using d = vt. The radio signals travel
at the speed of light, causing a timing error of 38 microseconds to translate
to a distance error of more than 11 km! Without careful attention to the effects
of both special and general relativity, the GPS simply would not work.
The Perimeter Institute`s
latest resource for physics teachers deals with this everyday application of
relativity. This resource consists of a six-minute video and
a generous selection of worksheets and activities
designed to make this resource useful in a variety of places in the curriculum;
Worksheet 1 has a variety of ways that you can use the video with a grade-9 geography or astronomy class. You won`t be teaching them about relativity, but you will be letting them know that they might want to take a physics course in a couple of years.
Worksheet 2 is a hands-on activity in which students emulate the work of the GPS system using the Pythagorean theorem, d = ct and large-scale maps. This is a nice fit for grade-9 astronomy, grade-11 kinematics or grade-12 Earth & Space science.
Worksheet 3 is a set of problems looking at the kinetic and potential energy of a satellite. If you don`t have relativity in your curriculum you could fit it in with these topics in grade-12 physics.
Worksheet 4 is a set of problems dealing with special relativity. It is a great addition to a unit on special relativity because it is an everyday application and it shows that relativity is still important even at so-called non-relativistic speeds.
Worksheet 5 is an exploration of accelerating
frames of reference using whirling trays and
tossed bottles of water. It is a way of sneaking general relativity
into grade- 12 physics. Concept questions following these activities allow the
students to do what Einstein did in 1908: predict that a gravitational field
will slow time. Who knew that general relativity could be made so simple? You
can use this resource as a stepping stone to a four-class lesson on general
relativity.
Get your FREE copy now!
You can order this free resource from PI`s website: http://www.perimeterinstitute.ca/Perimeter_Inspirations/General/Perimeter_Inspirations/
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Thanks to Tim Langford for his editorial skills. Thanks to Philip Freeman of B.C. for lots of insight into making general relativity accessible to high school students.