It Is A Fake Isn't It ? 1897 Morgan Dollar .

If it is the wrong diameter, wrong weight, and wrong specific gravity, then I don't see how it can be legit. Where did you purchase it—was it a reputable source?

Density = mass pre unit volume
Specific Gravity = relative density, compared to that of water.
For most practical purposes, the numbers are close enough to be taken as the same.

Most collectors would not have accurate enough lab equipment to measure the water displacement volume, or the procedure is way too fiddly to bother with.

"How do you get a cat to take a tablet?
- crush it up and sprinkle the powder through it's fur."

A different alternative to relative density measurement:-
- Relative ping tone against a known genuine silver dollar.
Much simpler than a relative density test, and any collector can do a relative ping tone test easily.

A reputable source can also be a critical requirement, but sometimes that can be a problem.
Most collectors who need to sell are honest and reliable, and what they wish to sell is quite genuine. The problem is that buying on line needs some sort of reliable backup, in case the sale / purchase doesn't go as planned.

With very high valued coins, an independently provable provenance may be essential, irrespective of the reputation of the seller/auctioneer, or at least as a backup to the seller's well established good business reputation.

The coin has an easy tell that it is fake. The top arrow feather on reverse is straight. The straight arrow was only used on the 78 and 21 Morgan's. The coin has a 21 style reverse.