Why "Гиппократ" but "ипподром"?

Question

Both these words have Greek origin, specifically:

Гиппократ (Hippocrates) comes from ίππος (horse) + κρατώ (I hold) = The one who holds the horses.

Ипподром (horse-race track) comes from ίππος (horse) + δρόμος (road/track).

The word for horse, in original (polytonic) Greek is written as

ἵππος

where over the ι there is an ascent and an aspirate:

The aspirate is the one that means an "h" has to be added in English to convey the original Greek sound (therefore "Hippocrates" in English.)

In Russian this (thick) "h" is turned into a "Г" (e.g. Hamburger - Гамбургер).

Why this is not the case with Ипподром?

Answer 1

The word "гипподром" is still used as a historical term for ancient stadiums for horse racing. The reason for dropping "г" was French influence where "h" is not pronounced (and the word hippodrome is not an exception). French was heavily used by Russian aristocracy and actually a lot of words were borrowed in French spelling. Even English names, like Ньютон were stressed the way they are stressed in French.

Here's a screenshot of N-gram for usage of both гипподром and ипподром (both in old and new spelling)

One can answer - why in that case Гиппократ, not Иппократ? Behold the terrifying truth, it actually was that way:

So actually Г-форм gained popularity gradually, throughout 19th century.

To me this looks like more or less random, the same Greek root gave us гиппопотам which, to my knowledge, never has been spelled without г-.