26 clues require a letter to be moved to enable them to be solved. These then spell out a message. Eight cells need relocating in a symmetrical pattern. Then some line drawing and some shading to illustrate the scholar’s thesis.
Some trick clues using obscure definitionss turned this into quite a solve. But eventually the message became apparent EPPURSI MUOVE GALILEO GALILEI or translated AND YET IT MOVES. The words AND YET IT are in a circular pattern at teh centre of the grid indicating what needs to move – i.e the earth being at the centre of the universe to an orbit around the central SUN – shading the centre yellow as every child loves to do on their artworks. It is filled with letters that can be rearranged to EARD (an obscure word for earth). The letters themsleves move outward by 2 cells from the central point of the grid. Leaving new words and allowing a new orbit to be shown. (see below)
Thanks Kolya – certainly familiar subject matter for me but maybe ease the difficulty of the clues a little next time?
Key * anagram
Across
1 Saint and peer going back to see chapters stopping over by heart of ancient Bactria (12)
E 1 Saint and per going back to see chapters stopping over by heart of ancient Bacteria (12)
st(saint) + Rev. per + to + cc (chapters) + I (heart of ancient) = STREPTOCOCCI
10 Pester aunt and her honey (7)
P 10 Ester aunt and her phoney (7)
(aunt + her)* = URETHAN
11 Wader’s in dark river without sun cap (5)
P 11 Wader‘s in dark river without spun ca (5)
Acheron (dark river) – Rev. ca = HERON
12 Silver seller’s rouge covers two little eruptions principally (6)
U 12 Silver seller‘s rogue covers two little eruptions principally (6)
cur (rogue) around tle (two little eruptions principally) = CUTLER
13 Maybe Sciver-Brunt and Pop Idol host treading water? (6)
Nat (may Sciver-Brunt) + Ant (Pop idol host) = NATANT
15 Tiger, say, switching over to active tinctures (5)
Woods (Tiger say) swapping a(active) for o(over) = WOADS
17 Campers rant, emitting gasps about heating vessels (5)
R 17 Campers ant, emitting grasps about heating vessels (5)
Rev. Hidden camperS ANT Emitting = ETNAS
19 Anoint the next one carrying money (5)
sear (next answer) around m (money) = SMEAR
21 Second organ brand (4)
s (second) + ear(organ) = SEAR
23 Schooner rows backwards, leader to starboard (5)
S 23 Schooners row backwards, leader to starboard (5)
stern(row) moving s starboard (right) = TERNS
24 Feeble heads of state slander Islam and remark when Austria’s lost (5)
I 24 Feeble heads of state islander slam and remark when Austria’s lost (5)
sis (heads of state islander slam) + say – a(Austria) = SISSY
26 Do business in Kentish Town (4)
DD DEAL
28 Once in Cusco, smash members of ruling party hoarding Aztec oil essentially (5)
ins(members of ruling party) around t I (azTec oIl essentially) = INTIS (smash meaning money)
31 Cloudy over home salon (5)
M 31 Cloudy over hoe salmon (5)
c(cloundy) + o (over) + hoe = COHOE
32 Andorra’s attaché defends retro silk dress (5)
Rev. hidden andorRAS ATtache = TASAR
34 Mistakenly poke nose into tender, entertaining licentiate (6)
nurse (tender) around l (licentiate) = NURSLE
35 Ranunculaceae forum shunned by Capt. Stokes (6)
U 35 Ranunculaceae form shunned by Caput. Stokes (6)
create (form) – c(caput) + S(Stokes) = REATES
36 Ringo’s into rock music that defines Mod (5)
O 36 Ring’s into rock music that defines Mood (5)
lap(ring) in aa (rock) = ALAPA
37 Little pests are caught before starting to revive Ivan’s ague (7)
V 37 Little pests are caught before starting to revive Ian’s vague (7)
ac (are caught) + a(before) + r (start to revive + (ian)* =ACARINA
38 In the form of projection, neat silicate seals iffy door, stopping leaks (12)
E 38 In the form of projection, neat silicate seals iffy door, stopping lakes (12)
ll (lakes) around ox(neat) + mica(silicate) around (door)* = LOXODROMICAL
Down
1 Following prosperity, one arranged loan (12)
success(prosperity) + I(one) + (loan)* = SUCCESSIONAL
2 Infer Tories will be deserting Right (4)
construe(infer) – cons(tories) = TRUE
3 Spending time round tung tree to improve reception (6)
G 3 Spending time ground tun tree to improve reception (6)
(tun tree – t)* = RETUNE
4 Signs of petty vexation set about husband on a Sunday (5)
A 4 Signs of petty vexation seat about husband on Sunday (5)
pew(seat) about h(husband) + s (Sunday) = PHEWS
5 Deck fan protecting lover (5)
L 5 Deck flan protecting over (5)
tart(flan) about o(over) = TAROT
6 Ok to enthral houri with special paper circles? (5)
I 6 Oik to enthral hour with special paper circles? (5)
cad(oid) around h(hour) + s (special) = CHADS
7 One needling councillor about old Ayr spit (6)
L 7 One needing councillor about old Ayr split (6)
cr (councillor) about rave (old Ayr(Scottish) split) = CRAVER
8 Larne dance’s fee for postponing arrival 8)
E 8 Learn dance’s fee for postponing arrival 8)
con(learn) + tango (dance) = CONTANGO
9 Distribution of time between overs becoming bad press (12)
O 9 Distribution of time between verso becoming bad press (12)
interval (time between) swapping (press)* for v(verso) = INTERSPERSAL
14 Discover refined beverage (5)
classic (refined) – cover = LASSI
16 Prepare to bin dry flower (4)
attire (prepare) – tt(dry) = AIRE
18 Grout left in cold bruised part of lobe? (8)
G 18 Rout left in cold bruised part of globe? (8)
(rout linc)* = TRINCULO
20 Home alone, quaffing Frederick’s gins (5)
A 20 Home lone, quaffing Frederick’s gains (5)
hidden hoME LONe = MELON
22 Slums too by the sound of it (4)
L 22 Sums tool by the sound of it (4)
Homonym of adze(tool) = ADDS
25 Pilot forgoes bass guitar for Texan resin (6)
I 25 Pilot forgoes basis guitar for Texan resin (6)
story (plot) – y (basis) + ax (guitar for Texan) = STORAX
27 Excluding natural killer, added plot and chink of light (6)
L 27 Excluding natural killer, addled pot and chink of light (6)
(pot chink – nk)* = PHOTIC
29 Leaves sierra: hated anonymous deal (5)
E 29 Leaves sierra: heated anonymous dal (5)
s(sierra) + (a (anonymous) + dal)* = SALAD
30 Iran turned up to capture manly US agent (5)
I 30 Ran turned up to capture mainly US agent (5)
Rev. ran + cop (capture) – p = NARCO
31 Clapton, Bruce and Baker are unorthodox in small measure (5)
(are)* in cm (small measure) = CREAM
33 Driver, once smitten, finally deserts army (4)
Senna (driver once) – n (smitten finally) = SENA

Why do you want easy clues in a barred thematic? Clue diificulty is part of the attraction, surely.
@Dunbar I’m not asking for easy clues juat not quite so many obscure definitions aa I felt this one had. To me the barred thematic fun is the end game. If the clues are too tough people never get to it.