Jelly, 28 26 25 24 23 bytes

-1 byte thanks to carusocomputing (replace the word thimble with abcdefg)

9ØaḣŒ!s²ḣµs9K€;€”.K;⁷µ€

TryItOnline!

How?

Makes a list of all 362880 permutations of the first seven nine letters of the English alphabet abcdefghi, which all have the properties of Martian words and are all distinct, and formats them into an essay using the first 729 words.

9ØaḣŒ!s²ḣµs9K€;€”.K;⁷µ€ - Main link: no arguments
9                       - 9 as x
         µ              - monadic chain separation
 Øa                     - yield lowercase alphabet
   ḣ                    - head to x ("abcdefghi")
    Œ!                  - all permutations (362880 distinct Martian words)
       ²                - square x = 81 
      s                 - split into chunks of length 81 (the paragraphs)
        ḣ               - head to x (get the first 9 paragraphs only)
                     µ€ - monadic chain for €ach (for each chunk:)
          s9            -     split into chunks of length 9 (the sentences)
            K€          -     join with spaces for €each (between words in each sentence)
              ;€        -     concatenate €ach with
                ”.      -         '.' (add a full stop* after each sentence)
                  K     -     join with spaces (add a space between the sentences)
                   ;    -     concatenate with
                    ⁷   -         a line feed
                        - implicit print

* period

Ruby, 86 83 82 79 bytes

(8019..8747).map{|x|$><<x.to_s(3).tr('012','abf')+(x%9>7?".\n":x%3>1?". ":" ")}

The trick: print all numbers between 102000000 and 102222222 in base 3

Python 3, 121 119 bytes

from itertools import*
i=729
while i:i-=1;print(*list(permutations('thimble'))[i],sep='',end='.'*(i%9<1)+' \n'[i%81<1])

repl.it

How?

Counts down from i=729 and gets a list of the letters of the ith permutation of 'thimble' as the next distinct Martian word (list(permutations('thimble'))[i]).

Avoids ''.join(...) by use of a *expression to unpack the list while changing the default separator for print from a space to the empty string (sep='').

Uses the end argument of print to optionally add spaces, full stops and line feeds as required using modular arithmetic. A full stop goes after every ninth word ('.'*(i%9<1)) and a line feed goes after every eighty-first word, otherwise a space does, achieved by indexing into a two character string (' \n'[i%81<1]).

Mathematica, 113 bytes

StringRiffle[(p=Partition)["ark"["bus","car"][[#]]&/@Differences@Array[ThueMorse,730],3]~p~3,n=".\n",". "," "]<>n

Unnamed function that produces a string as output; that string is a Martian essay where each sentence has three words and each paragraph has three sentences. (Its deterministic output is below.)

The core of the algorithm uses the cool mathematical fact that the differences of the Thue–Morse sequence form an infinite sequence of the three symbols –1, 0, and 1 that has no contiguous digit repetitions. Differences@Array[ThueMorse,730] generates that sequence, to length 729.

Then "ark"["bus","car"][[#]]&/@ is applied to this sequence; this converts each 1 to "bus" (the first argument), each –1 to "car" (the last argument), and each 0 to "ark" (the function head). (p=Partition)[...,3]~p~3 divides this sequence of words into nested lists, each consisting of three lists of three words each. Finally, StringRiffle[...,n=".\n",". "," "] concatenates all the words together, with different separators depending on the list levels; and <>n appends the final period and newline.

The output sure doesn't look repetition-free....

ark car bus. car ark bus. ark car ark.
bus car bus. ark car bus. car ark bus.
car bus ark. car ark bus. ark car bus.
car ark bus. ark car ark. bus car bus.
ark car ark. bus ark car. bus car ark.
bus car bus. ark car bus. car ark bus.
ark car ark. bus car bus. ark car bus.
car ark bus. car bus ark. car ark bus.
ark car bus. car ark bus. car bus ark.
car bus car. ark bus ark. car ark bus.
car bus ark. car ark bus. ark car bus.
car ark bus. ark car ark. bus car bus.
ark car bus. car ark bus. car bus ark.
car ark bus. ark car bus. car ark bus.
ark car ark. bus car bus. ark car ark.
bus ark car. bus car ark. bus car bus.
ark car bus. car ark bus. ark car ark.
bus car bus. ark car ark. bus ark car.
bus car ark. bus ark car. ark bus car.
bus ark car. bus car ark. bus car bus.
ark car ark. bus ark car. bus car ark.
bus car bus. ark car bus. car ark bus.
ark car ark. bus car bus. ark car bus.
car ark bus. car bus ark. car ark bus.
ark car bus. car ark bus. ark car ark.
bus car bus. ark car ark. bus ark car.
bus car ark. bus car bus. ark car bus.
car ark bus. ark car ark. bus car bus.
ark car bus. car ark bus. car bus ark.
car ark bus. ark car bus. car ark bus.
car bus ark. car bus car. ark bus ark.
car ark bus. car bus ark. car ark bus.
ark car bus. car ark bus. ark car ark.
bus car bus. ark car bus. car ark bus.
car bus ark. car ark bus. ark car bus.
car ark bus. car bus ark. car bus car.
ark bus ark. car ark bus. car bus ark.
car bus car. ark bus car. bus ark car.
ark bus ark. car bus car. ark bus ark.
car ark bus. car bus ark. car ark bus.
ark car bus. car ark bus. car bus ark.
car bus car. ark bus ark. car ark bus.
car bus ark. car ark bus. ark car bus.
car ark bus. ark car ark. bus car bus.
ark car bus. car ark bus. car bus ark.
car ark bus. ark car bus. car ark bus.
ark car ark. bus car bus. ark car ark.
bus ark car. bus car ark. bus car bus.
ark car bus. car ark bus. ark car ark.
bus car bus. ark car bus. car ark bus.
car bus ark. car ark bus. ark car bus.
car ark bus. car bus ark. car bus car.
ark bus ark. car ark bus. car bus ark.
car ark bus. ark car bus. car ark bus.
ark car ark. bus car bus. ark car bus.
car ark bus. car bus ark. car ark bus.
ark car bus. car ark bus. ark car ark.
bus car bus. ark car ark. bus ark car.
bus car ark. bus car bus. ark car bus.
car ark bus. ark car ark. bus car bus.
ark car ark. bus ark car. bus car ark.
bus ark car. ark bus car. bus ark car.
bus car ark. bus car bus. ark car ark.
bus ark car. bus car ark. bus car bus.
ark car bus. car ark bus. ark car ark.
bus car bus. ark car bus. car ark bus.
car bus ark. car ark bus. ark car bus.
car ark bus. ark car ark. bus car bus.
ark car ark. bus ark car. bus car ark.
bus car bus. ark car bus. car ark bus.
ark car ark. bus car bus. ark car ark.
bus ark car. bus car ark. bus ark car.
ark bus car. bus ark car. bus car ark.
bus car bus. ark car ark. bus ark car.
bus car ark. bus ark car. ark bus car.
bus ark car. ark bus ark. car bus car.
ark bus car. bus ark car. bus car ark.
bus ark car. ark bus car. bus ark car.
bus car ark. bus car bus. ark car ark.
bus ark car. bus car ark. bus car bus.
ark car bus. car ark bus. ark car ark.

Mathematica, 100 bytes

StringRiffle[(p=Partition)[Permutations@Characters@"thimble"~Take~729,9]~p~9,n=".\n",". "," ",""]<>n

A direct port of Jonathan Allen's Jelly algorithm.

05AB1E, 25 24 22 bytes

A7£œ9ôvyJðý"."«})9ô9£»

Try it online!

A7£                     # Push first 7 letters of the alphabet.
   œ                    # All 5040 permutations of "abcdefg".
    9ô                  # Split into pieces of 9 (Sentences).
       vy       }       # For each piece...
         Jðý"."«        # Join by spaces and finish with a period.
                 )9ô    # Split into pieces of 9 (paragraphs).
                    9£  # Take only the first 9 paragraphs.
                      » # Join by newlines and implicitly print.

Turns out the 810 word version is shorter than the 729 word version.

Output:

abcdefg abcdegf abcdfeg abcdfge abcdgef abcdgfe abcedfg abcedgf abcefdg. abcefgd abcegdf abcegfd abcfdeg abcfdge abcfedg abcfegd abcfgde abcfged. abcgdef abcgdfe abcgedf abcgefd abcgfde abcgfed abdcefg abdcegf abdcfeg. abdcfge abdcgef abdcgfe abdecfg abdecgf abdefcg abdefgc abdegcf abdegfc. abdfceg abdfcge abdfecg abdfegc abdfgce abdfgec abdgcef abdgcfe abdgecf. abdgefc abdgfce abdgfec abecdfg abecdgf abecfdg abecfgd abecgdf abecgfd. abedcfg abedcgf abedfcg abedfgc abedgcf abedgfc abefcdg abefcgd abefdcg. abefdgc abefgcd abefgdc abegcdf abegcfd abegdcf abegdfc abegfcd abegfdc. abfcdeg abfcdge abfcedg abfcegd abfcgde abfcged abfdceg abfdcge abfdecg.
abfdegc abfdgce abfdgec abfecdg abfecgd abfedcg abfedgc abfegcd abfegdc. abfgcde abfgced abfgdce abfgdec abfgecd abfgedc abgcdef abgcdfe abgcedf. abgcefd abgcfde abgcfed abgdcef abgdcfe abgdecf abgdefc abgdfce abgdfec. abgecdf abgecfd abgedcf abgedfc abgefcd abgefdc abgfcde abgfced abgfdce. abgfdec abgfecd abgfedc acbdefg acbdegf acbdfeg acbdfge acbdgef acbdgfe. acbedfg acbedgf acbefdg acbefgd acbegdf acbegfd acbfdeg acbfdge acbfedg. acbfegd acbfgde acbfged acbgdef acbgdfe acbgedf acbgefd acbgfde acbgfed. acdbefg acdbegf acdbfeg acdbfge acdbgef acdbgfe acdebfg acdebgf acdefbg. acdefgb acdegbf acdegfb acdfbeg acdfbge acdfebg acdfegb acdfgbe acdfgeb.
acdgbef acdgbfe acdgebf acdgefb acdgfbe acdgfeb acebdfg acebdgf acebfdg. acebfgd acebgdf acebgfd acedbfg acedbgf acedfbg acedfgb acedgbf acedgfb. acefbdg acefbgd acefdbg acefdgb acefgbd acefgdb acegbdf acegbfd acegdbf. acegdfb acegfbd acegfdb acfbdeg acfbdge acfbedg acfbegd acfbgde acfbged. acfdbeg acfdbge acfdebg acfdegb acfdgbe acfdgeb acfebdg acfebgd acfedbg. acfedgb acfegbd acfegdb acfgbde acfgbed acfgdbe acfgdeb acfgebd acfgedb. acgbdef acgbdfe acgbedf acgbefd acgbfde acgbfed acgdbef acgdbfe acgdebf. acgdefb acgdfbe acgdfeb acgebdf acgebfd acgedbf acgedfb acgefbd acgefdb. acgfbde acgfbed acgfdbe acgfdeb acgfebd acgfedb adbcefg adbcegf adbcfeg.
adbcfge adbcgef adbcgfe adbecfg adbecgf adbefcg adbefgc adbegcf adbegfc. adbfceg adbfcge adbfecg adbfegc adbfgce adbfgec adbgcef adbgcfe adbgecf. adbgefc adbgfce adbgfec adcbefg adcbegf adcbfeg adcbfge adcbgef adcbgfe. adcebfg adcebgf adcefbg adcefgb adcegbf adcegfb adcfbeg adcfbge adcfebg. adcfegb adcfgbe adcfgeb adcgbef adcgbfe adcgebf adcgefb adcgfbe adcgfeb. adebcfg adebcgf adebfcg adebfgc adebgcf adebgfc adecbfg adecbgf adecfbg. adecfgb adecgbf adecgfb adefbcg adefbgc adefcbg adefcgb adefgbc adefgcb. adegbcf adegbfc adegcbf adegcfb adegfbc adegfcb adfbceg adfbcge adfbecg. adfbegc adfbgce adfbgec adfcbeg adfcbge adfcebg adfcegb adfcgbe adfcgeb.
adfebcg adfebgc adfecbg adfecgb adfegbc adfegcb adfgbce adfgbec adfgcbe. adfgceb adfgebc adfgecb adgbcef adgbcfe adgbecf adgbefc adgbfce adgbfec. adgcbef adgcbfe adgcebf adgcefb adgcfbe adgcfeb adgebcf adgebfc adgecbf. adgecfb adgefbc adgefcb adgfbce adgfbec adgfcbe adgfceb adgfebc adgfecb. aebcdfg aebcdgf aebcfdg aebcfgd aebcgdf aebcgfd aebdcfg aebdcgf aebdfcg. aebdfgc aebdgcf aebdgfc aebfcdg aebfcgd aebfdcg aebfdgc aebfgcd aebfgdc. aebgcdf aebgcfd aebgdcf aebgdfc aebgfcd aebgfdc aecbdfg aecbdgf aecbfdg. aecbfgd aecbgdf aecbgfd aecdbfg aecdbgf aecdfbg aecdfgb aecdgbf aecdgfb. aecfbdg aecfbgd aecfdbg aecfdgb aecfgbd aecfgdb aecgbdf aecgbfd aecgdbf.
aecgdfb aecgfbd aecgfdb aedbcfg aedbcgf aedbfcg aedbfgc aedbgcf aedbgfc. aedcbfg aedcbgf aedcfbg aedcfgb aedcgbf aedcgfb aedfbcg aedfbgc aedfcbg. aedfcgb aedfgbc aedfgcb aedgbcf aedgbfc aedgcbf aedgcfb aedgfbc aedgfcb. aefbcdg aefbcgd aefbdcg aefbdgc aefbgcd aefbgdc aefcbdg aefcbgd aefcdbg. aefcdgb aefcgbd aefcgdb aefdbcg aefdbgc aefdcbg aefdcgb aefdgbc aefdgcb. aefgbcd aefgbdc aefgcbd aefgcdb aefgdbc aefgdcb aegbcdf aegbcfd aegbdcf. aegbdfc aegbfcd aegbfdc aegcbdf aegcbfd aegcdbf aegcdfb aegcfbd aegcfdb. aegdbcf aegdbfc aegdcbf aegdcfb aegdfbc aegdfcb aegfbcd aegfbdc aegfcbd. aegfcdb aegfdbc aegfdcb afbcdeg afbcdge afbcedg afbcegd afbcgde afbcged.
afbdceg afbdcge afbdecg afbdegc afbdgce afbdgec afbecdg afbecgd afbedcg. afbedgc afbegcd afbegdc afbgcde afbgced afbgdce afbgdec afbgecd afbgedc. afcbdeg afcbdge afcbedg afcbegd afcbgde afcbged afcdbeg afcdbge afcdebg. afcdegb afcdgbe afcdgeb afcebdg afcebgd afcedbg afcedgb afcegbd afcegdb. afcgbde afcgbed afcgdbe afcgdeb afcgebd afcgedb afdbceg afdbcge afdbecg. afdbegc afdbgce afdbgec afdcbeg afdcbge afdcebg afdcegb afdcgbe afdcgeb. afdebcg afdebgc afdecbg afdecgb afdegbc afdegcb afdgbce afdgbec afdgcbe. afdgceb afdgebc afdgecb afebcdg afebcgd afebdcg afebdgc afebgcd afebgdc. afecbdg afecbgd afecdbg afecdgb afecgbd afecgdb afedbcg afedbgc afedcbg.
afedcgb afedgbc afedgcb afegbcd afegbdc afegcbd afegcdb afegdbc afegdcb. afgbcde afgbced afgbdce afgbdec afgbecd afgbedc afgcbde afgcbed afgcdbe. afgcdeb afgcebd afgcedb afgdbce afgdbec afgdcbe afgdceb afgdebc afgdecb. afgebcd afgebdc afgecbd afgecdb afgedbc afgedcb agbcdef agbcdfe agbcedf. agbcefd agbcfde agbcfed agbdcef agbdcfe agbdecf agbdefc agbdfce agbdfec. agbecdf agbecfd agbedcf agbedfc agbefcd agbefdc agbfcde agbfced agbfdce. agbfdec agbfecd agbfedc agcbdef agcbdfe agcbedf agcbefd agcbfde agcbfed. agcdbef agcdbfe agcdebf agcdefb agcdfbe agcdfeb agcebdf agcebfd agcedbf. agcedfb agcefbd agcefdb agcfbde agcfbed agcfdbe agcfdeb agcfebd agcfedb.
agdbcef agdbcfe agdbecf agdbefc agdbfce agdbfec agdcbef agdcbfe agdcebf. agdcefb agdcfbe agdcfeb agdebcf agdebfc agdecbf agdecfb agdefbc agdefcb. agdfbce agdfbec agdfcbe agdfceb agdfebc agdfecb agebcdf agebcfd agebdcf. agebdfc agebfcd agebfdc agecbdf agecbfd agecdbf agecdfb agecfbd agecfdb. agedbcf agedbfc agedcbf agedcfb agedfbc agedfcb agefbcd agefbdc agefcbd. agefcdb agefdbc agefdcb agfbcde agfbced agfbdce agfbdec agfbecd agfbedc. agfcbde agfcbed agfcdbe agfcdeb agfcebd agfcedb agfdbce agfdbec agfdcbe. agfdceb agfdebc agfdecb agfebcd agfebdc agfecbd agfecdb agfedbc agfedcb. bacdefg bacdegf bacdfeg bacdfge bacdgef bacdgfe bacedfg bacedgf bacefdg.

JavaScript (ES6), 130 bytes

This essay contains 774 Martian words, from a dictionary of 308 distinct words, made of all Martian letters.

_=>[...Array(2322)].map((_,i)=>['aeimnou','bcdgkpt','fhlrsvz'][i%3][(z=z*71%1e9)%7]+(++i%3?'':i%9?' ':i%27?'. ':`.
`),z=1).join``

Letters are picked in a pseudo-random manner, using the following formula:

(71^n mod 1000000000) mod 7

Where 71 is the smallest value for which no contiguous word repetition appear with this modulo.

let f =

_=>[...Array(2322)].map((_,i)=>['aeimnou','bcdgkpt','fhlrsvz'][i%3][(z=z*71%1e9)%7]+(++i%3?'':i%9?' ':i%27?'. ':`.
`),z=1).join``

console.log(f());