Is there a word that describes 'the study of measuring distances'?

Solution 1:

Distance measuring is done by ranging. It's a well-established word with millions of hits on Google. Even the well-known radar originally stood for "RAdio Detection And Ranging".

Survey(ing) is a much broader term. It also measures horizontal and vertical angles, elevations, GPS coordinates, etc. Surveying is determined not by the tool, but by the goal — making a space model of something big, but not too big. A house or a land plot are subjects of surveying, but not a continent, which is the subject of another subdiscipline of geodesy, named astronomical geodesy. As for bacterias, they are measured by micrometry, if I remember correctly.

Metrology measures anything for the improvement of the tools and standards for the actual measuring. That includes distances, but also time, angles, temperature, current...

Geometry in the original sense was the same thing as survey today.

Solution 2:

A metrologist (not to be confused with meteorologist) is a specialist in "the science of weights and measures or of measurement" (Merriam-Webster). A metrologist works in the field of metrology. A dimensional metrologist specializes in measuring distances and sizes.

Is the word 'popular'? It's not a word you're going to encounter very often, but the Corpus of Contemporary American English (COCA) lists almost 70 instances of metrology in the literature since 1990.

Then again, note that 20 May is World Metrology Day, and celebrates the signing of the Metre Convention on that date in 1875.

Solution 3:

The archetypal person who specialised in measuring distances between locations was a surveyor, being a person who surveys, esp. one whose profession is the surveying of land; an engineer who determines the boundaries and elevations of land or structures.

These days the "measuring of linear distance" component of the profession is far less remarkable, thanks to GLS/GSM satellite location systems. No new word is likely to arise, since it's now trivial.

Solution 4:

Geometry - the study of measuring distances. It was invented by the ancient Egyptians and applied by land surveyors as a way of measuring land for tax purposes.