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Can you visit Birka and Mariefred/Gripsholm Castle in one day?

I'll be in Stockholm for 3 to 4 days in July and am trying to combine day trip/sights.. is it feasible to take boat to Birka to see Viking ruins/city and then boat to Mariefred to see Gripsholm castle? Then I would take public transpo back to Stockholm from Mariefred.. Seems like it can be doable but I can't seem to find any info on how to do both online..
Thank you for any help!