The sort of vocabulary that you would expect the simple folk of the Dark Ages to be using are mostly still of Germanic origin; they are the building blocks of the language, the basics of verb and noun forms, and words for basic abstract concepts.
In later years, the Catholic Church's supremacy meant that the language of inquiry, knowledge, and spirituality was Latin.
For many centuries, scientists would publish all their work in Latin.
It is no surprise that Latin has filled the gaps in English and provided adjectives such as lunar where English had none.
This is compounded by the imposition of Norman French in the Middle Ages.
Since the language of government changed from English, many of our words for government and justice derive from Latin via Norman French.
Our words for meats also come from Norman French, e.g. beef, veal, venison, mutton in place of English cow, calf, deer, sheep .
Later still, British scholars would turn to Latin and Greek to coin new words to describe new technologies and modern concepts, as we still do today.
There's an interesting discussion of the influence of Latin on English on wikipedia here: http://en.wikipedia.org/wiki/Latin_influence_in_English
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Let's not forget that Latin was the language of science and philosophy and nearly all higher learning for hundreds of years.
For example, Copernicus wrote his seminal treatise about the heliocentric theory, De revolutionibus orbium coelestium , in Latin.
It's not surprising that many of the technical names for natural phenomena and educated words in general would be derived from Latin.
We see remnants of this today in medicine: the parts of the body are named from the Latin.
Your orthopedist will tell you you've torn your medial collateral ligament in your knee.
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The English language is a hotchpotch of many languages, a melting pot from most European language roots, with a good deal of other elements thrown in for added spice.
As a result, we often have a vast array of words to choose from for any given topic of conversation.
The more elemental and eternal the concept, the longer we will have talked about it and thus the further back through our history words will have been borrowed in order to discuss the concepts.
Generally, you will find that the simple forms of words are likely to hark back to older influences; basic words are often from Old English, or Saxon influence.
Whilst more technical terms may not have been so common in the vernacular speech, so may retain scientific form, coming from Latin or Greek.
The essential rule to remember is that English etymology is a many splendored thing; variety is the spice of life, after all.
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Some [simplistic] reasons: The Latin-based adjective is more elegant for contextual reasons, e.g. sideways vs. lateral
It is impossible to form an adjective otherwise, e.g. sun :: solar
And better a word than a phrase, e.g. lunar vs. of the moon
The non-Latin adjective may mean something else entirely, e.g. handy vs. manual
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To emphasize Robusto's point (3).
Sir Issac Newton published his Philosophie Naturalis Principia Mathematica not in English but in Latin in 1687.
This was the last major work written in Latin published in England.
However,the level of Latin at Cambridge and Oxford was and remained quite high.
Perhaps no more than that of Gottingen or Tubingen in Germany.
But "OxBridge" exerted more influence on the Kingdom of England than Gottingen/Tubingen et al exerted on the many German States.
To the English writer back then (and even till the present)
Latin roots seem more fitting for abstract words.
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All of these answers are Useful and True.
I want only to supplement them with two observations:
There's a strong 'native' tendency in English to use the bare noun attributively rather than to derive a frank adjective: from your examples, moon beam , side dish ,
hand axe Where we do have adjectives built with ordinary suffixes, they have often evolved specific senses which do not sort comfortably with a simple "of or pertaining to X":
again from your list, moony , sideways , handy
So there's a lot more what-you-might-call "lexical space" to put Latinate adjectives into, and often a specific lexical need for them.
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As a non-native English speaker, I always wondered why, for example, you say  moon , but then you say  lunar  (same goes for  side  and  lateral ,  hand  and  manual  and so forth): in some cases, the noun is not the base of the adjective, which derives from the Latin root instead.  What is the reason for this phenomenon?
Adjectives with Latin etymology when noun has non-Latin etymology
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<etymology><nouns><adjectives><history><latin>
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The reason for this phenomenon is probably that the sort of vocabulary that you would expect the simple folk of the Dark Ages to use was mostly still Germanic in origin. Meanwhile, the Catholic Church's later supremacy meant that the language of inquiry and knowledge was Latin. In fact, for centuries, scientists published all their work in Latin. Therefore, Latin will have filled the gaps in English to provide adjectives where English had none. A lot of English vocabulary is of Germanic origin, later supplanted by Latin through Church  influence. Latin was language of scientific texts and fills the gaps in English, as well as English being influenced by Norman French. However, British scholars later returned to Latin and Greek for new concepts and technologies. So English is a hotchpotch of many languages and simple words may come from older sources. There is also a tendency to preference Latinate words also for its greater elegance "lateral" instead of "side"
The reason for this phenomenon is probably that the sort of vocabulary that you would expect the simple folk of the Dark Ages to use was mostly still Germanic in origin. Meanwhile, the Catholic Church's later supremacy meant that the language of inquiry and knowledge was Latin. In fact, for centuries, scientists published all their work in Latin. Therefore, Latin will have filled the gaps in English to provide adjectives where English had none. The English language is a mixture of many different languages, and a major influence was the Germanic language of ordinary people in the Middle Ages contrasted with the French and Latin of the church and state. Latin was also used as the language of science and education, so those looking to coin new words would use Latin words or roots. For this reason, technical terms are still often derived from Latin rather than Germanic roots.
 Latin was the language of science and philosophy and nearly all higher learning for hundreds of years. However, it should be considered that the English language is a hotchpotch of many languages, a melting pot from most European language roots along with many other elements. Depending on the context, a Latin-based adjective may more elegant for contextual reasons, e.g.  sideways  vs.  lateral; and a non-Latin adjective may mean something else entirely, e.g.  handy  vs.  manual. Latin adjectives may be used in the way that they are primarily because Latin was the language of science and philosophy for hundreds of years and is often more elegant and easier to use in certain situations. Furthermore, the adjective relating to an English noun may already have a different meaning to the one that the writer wishes to express, in which case, the Latin term is more appropriate. As it happens, English is a mixture of a number of European languages.
Lot of vocab is of Germanic origin, later supplanted by Latin through Church  influence. Latin was language of scientific texts and fills the gaps in English, as well as English being influenced by Norman French. British scholars later returned to Latin and Greek for new concepts and technologies. We reference words of Saxon influence. preference for Latinate words.
The English language is a mixture of many different languages, and a major influence was the Germanic language of ordinary people in the Middle Ages contrasted with the French and Latin of the church and state. Latin was also used as the language of science and education, so those looking to coin new words would use Latin words or roots. For this reason, technical terms are still often derived from Latin rather than Germanic roots.
Science and philosophy was written and published in Latin for hundreds of years. English has many influences from a range of European languages. Latin language is often more elegant and easier to use in some situations. The derived adjective from an English noun might already serve another purpose.