To address this question, it is important to first give an idea of why one would wish to send a
spacecraft mission to the vicinity of a fixed point of the rotating earth-sun system.
Here are a couple of reasons:
Then why orbit a fixed point instead of maintaining the spacecraft position at the point
itself? There are several reasons with varying degrees of subtlety. Here is one example:
Intense radiation from the sun interferes with data transmission if the spacecraft sits directly between the earth and sun.
Orbiting fixed point L1 (shown below) at a convenient radius solves the data transmission interference problem.