It's definitely higher than 5km/s, but I would not go up to 9.5km/s. My napkin math was - booster provides 2km/s and the LEO is 7.2km/s, so if the ship arrives

It's definitely higher than 5km/s, but I would not go up to 9.5km/s. My napkin math was - booster provides 2km/s and the LEO is 7.2km/s, so if the ship arrives nearly empty LEO it must provide a minimum 5.2km/s. I did not account for gravity + friction losses which could be guesstimated to 2km/s. If we assume that ship handles all of them (which is not true booster does some) we come up to 5 + 2 = 7.2km/s. The equation you have uses block 1 prop + dry mass numbers. Block 1 does not have significant payload capability and the last one just flow on OFT 6. As such let's use Block 2 numbers, first one should fly early next year. Dry mass target 100t, payload 100t, prop mass 1,500t. So (3.72 km/s) * ln(1700 / 200) = 7.96 km /s. This is with using min advertised payload of 100t and Elon's forward looking 100t number for dry mass. Way above 5km/s, but reaching 9.5km/s with 100t of payload will be challenging. I've pulled stats from https://en.wikipedia.org/wiki/SpaceX_Starship https://en.wikipedia.org/wiki/SpaceX_Starship .