What is the difference between 遠い and はるか?

Question

I am looking for a way to express the concept of (physical) distance. Searching jisho.org yields two possible results:

• [遥]{はる}か (Na-adjective, Adverb, Noun): far; far away; distant; remote; far off​
• [遠]{とお}い (I-adjective): far; distant​

Both are marked as a "common word", so I believe that "London is far away from here" could be translated as either:

• ロンドンはここよりはるかです。
• ロンドンはここより遠いです。

However, many of the WWWJDIC examples for はるか seem to be for metaphorical distance:

• 彼の出費は収入をはるかに上回っている。
  His expenses exceed his income by far.
• 計算機があれば計算ははるかに楽だ。
  Calculation is miles easier if you have a calculator.
• 光は音よりはるかに早く伝わる。
  Light travels much faster than sound.
• 鉄は金より遥かに役に立つ。
  Iron is much more useful than gold.
• 新しいデザインの方が古いデザインよりもはるかによい。
  The new designs are much better than the old ones.
• 我々ははるか前方に他の船を見た。
  We saw another ship far ahead.
• 彼は誰よりもはるかに良く出来る学生だ。
  He is by far the best student.
• 彼女は、一昨年よりもはるかに暮らし向きがよい。
  She's far better off than she was the year before last.
• 飛行機の速度はヘリコプターのそれよりはるかに速い。
  The speed of an airplane is much greater than that of a helicopter.
• 数そうのヨットがはるか沖合を並んで航行していた。
  Several yachts were sailing side by side far out at sea.

...whereas the examples for 遠い are generally more literal:

• 駅まで歩くには遠すぎますから、バスに乗りましょう。
  It's too far to walk to the station, so let's take a bus.
• たとえあなたが遠くへ行ってしまっても、電話で連絡をとりあいましょう。
  Even if you go far away, let's keep in touch with each other over the phone.
• スコットが元気になるのもそう遠くないでしょう。
  It will not be long before Scott gets well.
• 北海道はたいへん遠いですね。
  Hokkaido is very far, isn't it?
• 私の車はここから遠くないところに止めてある。
  My car is parked not far from here.
• 遠い灯台のかすかな光を見た。
  We saw the gleam of a distant lighthouse.
• どのくらい遠い？
  How far?
• 彼がその家を買わないと決めたのは、第一に高すぎることと第二に会社からあまりにも遠かったからだった。
  He decided not to buy the house, because in the first place it was too expensive, and in the second place it was too far from his office.
• 子供が親から遠く離れていたら、彼らの安全や幸福に関して親がしてやれることはない。
  When parents are far away from their children, there is nothing they can do about their safety or welfare.
• 彼は私よりも砲丸を遠くまで投げた。
  He put the shot farther than I did.

I'm not sure if this is because はるか is more "flexible" than 遠い, or if the examples for はるか just happen to include more varied usage by coincidence.

My question is therefore twofold:

• Are my suggested translations for "London is far away from here" correct?
• Are 遠い and はるか equivalent, or do they have different connotations / usage patterns?

Answer 1

You're correct to assume that 遥か and 遠い have different connotations and usage patterns; in fact, there's very little overlap between them.

遠い is your standard, general-use word for "far". It's straightforward and neutral, and can be used in most of the ways you'd imagine - stating factual distances, comparing them, identifying something as being a long way away, and even some limited metaphorical uses such as 彼には遠く及ばない "I am far inferior to him" and 遠い未来 "the far future".

遥か, on the other hand, is anything but neutral. It's inherently emphatic, and its most common usage isn't even about literal distance at all - it's used adverbially in the form 遥かに, intensifying comparative adjectives (or verbs that imply a comparison). In this sense it's far more flexible than 遠い, having more in common with something like ずっと - it's equivalent to the English "far" in "far smaller", "far exceeding", "far more beautiful" etc.

Even when it is talking about physical distance, 遥か is only used to emphasise that they're extremely large distances, and it rarely appears as a descriptor on its own. Instead it serves to intensify other words relating to distance, such as 遥か遠く, 遥か向こうに or 遥か彼方に (all meaning something like "far off in the distance").

In the rare cases when 遥か is used as an adjective in its own right, it tends to sound somewhat poetic, and it still refers more to "distance" as in the property of being "distant" rather than as a measurement. For instance, you might hear the poetic-sounding 遥かな街 "a far-off city", but you would almost never hear something like AよりBの方が遥かな街です, because 遥か is a property rather than a measurement, so it doesn't lend itself to comparison - just like you wouldn't usually say "A is more far-off than B" or "A is more in the distance than B" in English. (AよりBの方が遥かに遠いです, on the other hand, is of course perfectly natural.)

Finally, there are a couple of particular quirks in 遥か's grammatical usage. While 遥かな is one possible attributive form, the somewhat archaic alternate form 遥かなる appears with similar frequency - the archaic flavour of this form makes for even more poetic-sounding expressions. But whichever the form chosen, adjectival 遥か is almost always used attributively (before a noun) rather than predicatively (followed by だ or です). So 遥かな街です and 遥かなる街です are both possible, but something like その街は遥かです would be very unusual.