inching. moving slowly/small degree of progress.
As in “Elon is inching his way towards Mars”.
“Metering closer to his goal” sounds … totally off. So how do I avoid using arguably antiquated measurements (which has contributed towards the loss of one space mission) without sounding totally crazy? Are there equivalent expressions using metric units, or do we need a work-around, or ...?
After having consulted a number of resources [1] [2] [3], I have concluded that there is currently no synonym of inching that is based on a metric word.
It takes time for such expressions to develop, and I'd be surprised if a phrase like "centimeter forward" ever evolved. But what do I know?
Anyway, until (and probably even after) that happens, using inching is perfectly fine. It doesn't matter whether you are somewhere where the metric system is used or not. You're not going to cause any space disasters merely by using a word.
If you really wanted to use a metric word you could say something like "advancing a centimeter at a time", but that seems rather inelegant to me. I'd stick with inching.
Like Max said, it's a figure of speech. For example, I might tell my friend not to put all his eggs in one basket. Hardly anyone transports eggs in baskets anymore, and certainly, my friend doesn't.That, however, doesn't prevent me from using that particular figure of speech as an effective way to emphasise a practical point to him.
How do I avoid using archaic measurements?
You could avoid referring to units of measurement at all. I have looked at the synonyms of inching, but in my opinion their negative connotations make most of them inferior to inching. (Provided, of course, that you do wish to avoid such negative connotations.)
I did find, however, one possible candidate:
To move slowly or with small movements in a specified direction.
This matches with the definition of inching from the same source:
To move very slowly or by a small amount in a specified direction or manner.
Elon is edging his way towards Mars.
Please note that even this word may have an unsuitable slang connotation, though perhaps rare. In either case, I do find inching a better choice.
The metric equivalent is "inching".
Words move on from their original meaning, and "to inch" means "to move slowly", regardless of what units you actually use to measure distances. Likewise, people quite happily "dial" on a telephone that has no dial and, after somebody dials your number, your phone "rings", even though it has no bell.
The arbitrary units of old had centuries to be the basis for words and phrases. While the modern (US) inch is from the 20th century. Inches of variable lengths have been since at least the 1300s in current spelling. Wikipedia claims even a first occurrence from 700 AD.
inch (n.1)
"linear measure, one-twelfth of a foot," late Old English ynce, Middle English unche (current spelling c. 1300) - Etymonline
The verb is from a lot later:
inch (v.)
1590s, "move little by little" (intrans.), from inch (n.1). Meaning "drive or force by small degrees" (trans.) is from 1660s. - Etymonline
This shows that both words are actually pre-imperial. Imperial units have been only established in the nineteenth century. Thus, I would challenge the categorization as imperial unit verb in the first place.
There are a few metrical words, like the verb to meter, which has already been appropriated by the usage in parking meters for example. Given the length of words for the smaller metrical units it's unlikely inching will be replaced anytime soon.
Since the definition of the verb from dictionaries does't even refer to inches (anymore?) I would consider the verb non-imperial already. It is older than the imperial system which just happens to have a successor to the old British inch the verb is based on.
inch VERB [NO OBJECT] 1 Move along slowly and carefully. - ODO
Conclusion
Using inching is perfectly okay and there is no math associated with it that will let your spaceships crash.
You could use a word not connected to units of measurement, e.g., creep.
From Dictionary.com:
creep: to move or advance slowly or gradually: The automobile crept up the hill. Time just seems to creep along on these hot summer days.
Your example:
“Elon is creeping his way towards Mars”.
Although not a verb, nor a single word, you might consider an adverbial phrase such as millimeter by millimeter.
Trying nor to scare away her dinner, the cat moved towards the mouse millimeter by millimeter.
Inched works better, but you requested an alternative.
Incrementing is also a possible choice, though I would use it without "his way".
Definition:
To increase by steps or by a step, especially by one.
Example:
Elon is incrementing towards Mars.
It is not terribly popular, though, and it would probably come off as overly technical.
