No, oortcloud is correct. Dennis Young said: "For slowing down, gravity drag in the Martian atmosphere will work, but if the craft is traveling at the speeds discussed, would likely take weeks or months to slow down. The other way would be to whip around Mars and use the laser to slow it down every time it comes out from the planet's shadow. This, too, would take time."No, you're not wrong. Mars' "escape velocity", is less than half of that of our earth. To escape earth's gravity, (from low earth orbit), requires accelerating to about 25,000 mph. Accordingly, (rough estimate), Mars' escape velocity, should be on the order of perhaps 11,000 mph.
"Capture velocity", (also distance dependent from the target), would be roughly the same, but you would still have a protracted period where the craft would decelerate slowly to orbital velocity. (Obviously, retro rockets would need to be used, the same as our lunar missions, to hasten braking)..
He probably meant atmospheric drag, since the statement as it reads is essentially meaningless, but in any event, as he posed the suggestion, a ship traveling at the speeds being discussed would barely notice Martian gravity, and even a brush with the atmosphere would create a spectacular and very final torch of the ship (not to mention pancaking the crew). As for "whipping around Mars," you would have to slow down to orbital velocity in the first place to be able to get around Mars, so that point is moot as well. It's not like banking an aircraft into a tight turn. So you (Captain Cranky) are correct at least in that rocket deceleration would be necessary before any other braking methods could be used.