Locus and loci – paths things travel

Paths or trajectories moving things follow are a very important part of many things in life.  When you’re swimming, the path or trajectory your hand moves along each time you take a stroke affects how efficient your swimming style is, how fast you go and also how quickly you get tired.  Same thing if you’re running – the path that your foot takes through the air determines how far you run with each stride, how much energy you use and also how much clearance you have for small obstacles like a tree root in the ground.

On a much bigger scale, the path of a spacecraft must be planned exactly right in order to get the spacecraft to where it is meant to go.  A lot of spacecraft do a thing called a ‘gravity flyby’ where they fly near a planet and use the gravity from the planet to ‘slingshot’ the craft around it and increase their speed.  In this sort of situation, you want to get the path of the spacecraft just right – a slight miscalculation, and you might end up either getting a little too close to the planet and hitting it / burning up in its atmosphere, or missing it altogether.

A locus is the path travelled by a point or thing.  In the diagram above, the line shows the locus of the spacecraft.  Some people prefer to describe the locus as being the set of all points that something moves along, since a path is really just made up of a very large number of points.  Loci is the plural form of locus, so you’d use it when you’re talking about more than one path or set of points.

A lot of questions will ask you to describe what the locus of a thing is.  For instance, one question might ask you to describe the locus of a person on a Ferris wheel:

This one’s pretty easy – the locus is a circle. 

There are some classic types of loci for everyday situations that you should know. You also need to understand why they are that shape.