A favourite author are Emily Latham (are 'cos it's actually a collaboration) who has introduced me to a few new words.
Today I found ambit. A hostess seated someone she was trying to influence "close to her ambit". Area or range in which something acts or operates or has power or control. Orbit would definitely imply already having control but ambit doesn't necessarily.
I presume it is related to ambition???

I met "ambit" for the first time in Robert Harris' Enigma, as a word in a Times crossword puzzle:

"'Morning snack as far as it goes.' Five letters."
"Ambit."
"How do you get it so quickly?"
"It's not hard. You learn to know the way they think. Morning--that's A.M., obviously. Snack as far as it goes--bite with the e missing. As far as it goes--well, within ones ambit. One's limits.

pages 91-92.

I've always pictured it as meaning the distance one can walk, i.e. ambulate

mm, a useful word - what really surprised me on my way to double check the etymology was to find a full house of obscurantist listings though: Phrontistery, Luciferous Logolepsy and WWFTD!

The roots are indeed common as you assumed Zed.
ambition comes from: Middle English ambicioun, excessive desire for honor, power, or wealth, from Old French ambition, from Latin ambiti, ambitin-, from ambitus, past participle of ambre, to go around (for votes). ~ http://www.bartleby.com/61/35/A0243500.html

Looking at 'ambi*' gets you more directly to the Latinate origins but also suggests a Greek root (as in amphitheatre of course!):
http://www.bartleby.com/61/roots/IE15.html

A nice concatenation of footfalls in this family of words, isn't there?

All at once, out of the Murk, a dozen mirror'd Lanthorns have leapt alight together, as into their Glare now strolls a somewhat dishevel'd Norfolk Terrier, with a raffish Gleam in its eye - whilst from somewhere less illuminate comes a sprightly Overture upon Horn, Clarinet, and Cello, in time to which the Dog steps back and forth in his bright Ambit. - Thomas Pynchon, Mason & Dixon

and this, to the wandering eye:

HOLOFERNES: ...his humour is lofty, his discourse
peremtory, his tongue filed, his eye ambitious,
his gait majestical, and his general behavior vain,
ridiculous, and thrasonical. He is too picked, too
spruce, too affected, too odd, as it were, too
peregrinate, as I may call it.
SIR NATHANIEL: A most singular and choice epithet.
- Love's Labours Lost, Act 5, Scene 1

Oh, I dunno--I'm kind of ambivalent about it, myself.

A nice concatenation of footfalls in this family of words, isn't there?

Pussyfooting around the pun......