Based on my calculations (which are very probably incorrect. ) a 400 Mu planet (like a home world) with no orbitals would require 277 Battle Cruisers to be conquered:

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277 ships, atk: 4986 def: 13296 vs planet, atk: 2800 def 14400.
58 ships destroyed.  218 ships remaining.
218 ships, atk: 3936 def: 10496 vs planet, atk: 2800 def 9414.
58 ships destroyed.  160 ships remaining.
160 ships, atk: 2885 def: 7696 vs planet, atk: 2800 def 5478.
58 ships destroyed.  101 ships remaining.
101 ships, atk: 1835 def: 4896 vs planet, atk: 2800 def 2592.
58 ships destroyed.  43 ships remaining.
43 ships, atk: 785 def: 2096 vs planet, atk: 2800 def 756.
Defender destroyed!
43 attack ships remaining.