Dear Mecha,
 
  The Greek word for "carcase" in Matthew 24:28 is "ptoma" which is word # 4430 in Strong's Concordance Greek Dictionary of the New Testament.  The definition given for ptoma is "lifeless body (corpse, carrion): dead body, carcase, corpse."  So the dead body can't be the body of Christ that is the carcase in that verse.
 
  However, a similar verse, Luke 17:37 also says, "And they answered and said unto him, Where Lord?: And he said unto them, Wherever the body is, thither will the eagles be gathered together."  In this verse the Greek word for "body" is "soma" which is word #4983, and it's meaning is "the body (as a sound whole), used in a wide application, lit. or fig.: bodily, body, slave." So this verse could mean the collective body of people assembled where the eagles are gathered together.
 
  Ezekiel 39:17-22 also shows the Lord speaking to a son of man and tells him to request every feathered fowl and beast of the field to assemble themselves together to eat the great sacrifice of flesh and to drink the blood of men, and the Lord also sets his glory among the heathen at that time and the house of Israel shall know the Lord.
 
  In Rev. 19:17-18, an angel is requesting all the fowls of heaven to gather themselves together for the supper of the Great God to eat the flesh of captains might men and of horses and the flesh of all men, both free and bond, both small and great.  This happens when the Lord Jesus returns from heaven with his army of saints which is the body of Christ.  It will be the carcases of dead men that these birds will be feasting on.
 
  It sounds like the events of Matthew 24:28, Ezekiel 39:17-22, and in Rev. 19:17-18 take place at the second coming of the Lord to the earth with all his saints in heaven.
 
  Also he Greek word for "eagles" in Matthew 24:28  and in Luke 17:37 is "aetos" which is #105 in Strong's Concordance Greek Dictionary, and it means, "eagle."
 
  God bless,
 Donna