data transfer ESATA to USB3

Solution
USB and eSATA use very different protocols to exchange data between devices. So NO, there is no simple adapter to convert one to the other. Interconnection would require hardware to translate one system to the other and backwards. Normally that is done by a mobo in a computer that has the required port management chips and software to convey data between the two.

You say your new external drive "has the new keyed USB3 connector". I presume you mean the cable that came with it has that type of MALE connector on the end that plugs into your laptop. However, your laptop does not have a matching USB3 FEMALE socket. It does have an eSATA socket. I would bet that the laptop also has a USB2 socket. Now, look again at the cable with the...
USB and eSATA use very different protocols to exchange data between devices. So NO, there is no simple adapter to convert one to the other. Interconnection would require hardware to translate one system to the other and backwards. Normally that is done by a mobo in a computer that has the required port management chips and software to convey data between the two.

You say your new external drive "has the new keyed USB3 connector". I presume you mean the cable that came with it has that type of MALE connector on the end that plugs into your laptop. However, your laptop does not have a matching USB3 FEMALE socket. It does have an eSATA socket. I would bet that the laptop also has a USB2 socket. Now, look again at the cable with the external drive. I'm guessing it is also plugged into a USB3 socket on the drive unit, not something permanently connected. Those sockets are designed for backwards compatibility. Disconnect the cable at the drive, and I expect the socket will also accept a standard USB2 cable in the socket. You can use that cable to connect to your laptop's USB2 connector. The resulting communication will not be as fast as eSATA, but it will do the job.
 
Solution
Thank you for your very detailed and articulate answer to my problem.
I now understand that there are different protocols between the esata and USB3 and its not "just a simple transfer of data" as I incorrectly believed.
 
Thank you for your very detailed and articulate answer to my problem.
I now understand that there are different protocols between the esata and USB3 and its not "just a simple transfer of data" as I incorrectly believed.