Now technically, the retrorockets do slow the spacecraft down slightly, but that is not the reason they are fired. A retro-directed rocket burn has the effect of lowering your perigee altitude. Burn the retrorockets long enough and hard enough, and your perigee altitude will get so low that you will intersect the atmosphere. This is called a deorbit burn. Ironically, by the time you hit the atmosphere, you’ve fallen enough that you’re going faster than when you were up in a circular orbit. (Typical circular low Earth orbital speed is 17,500 miles per hour.)
In addition, the parachutes are not opened when the spacecraft first hits the atmosphere. Doing so would burn the parachutes to a crisp. Instead, the spacecraft is oriented so that its heatshield is pointing “straight into the wind”, so to speak. It is the drag on the spacecraft caused by the air slamming into and screaming past its heatshield that causes most of the braking on the way down. Only when the spacecraft has slowed enough that it’s going subsonic (less than about 750 miles per hour) is it safe to let out the parachutes.
The second quote was this:
If touchdown on land isn’t affected by a tangled parachute, I’ll be a chimpanzee’s uncle!
No. It wouldn’t. Without a parachute, an average sized space capsule (say, the Apollo Command Module, for example) would hit the deck at about 300 miles per hour. At that speed, water basically behaves like concrete. It was the 200 mile-per-hour impact of the Space Shuttle Challenger’s crew cabin with the Atlantic ocean that killed its occupants.
Although the Cosmonaut whose parachute got tangled up after re-entry would have turned into a bloody pancake whether he’d smacked down in Siberia or the Pacific ocean, it happened to be a touchdown on land that actually killed him.
While you add some interesting detail that clarifies the answer, nothing Cecil said is technically wrong. They use a retrorocket burn to deorbit, and after they are in the atmosphere they use parachutes. Cecil just left out the technical parts about how the dorbit burn works, about the heat shielding and drag, etc.
I’m glad you didn’t title your thread “Cecil was Wrong!”
Also, to pick even further nits, the Apollo reentry modules were designed with some “lifting body” properties so that once they got to denser parts of the atmosphere, the airflow around the capsule would help some to the braking (the bulk being provided, still, by sheer blunt heat-conversion) and to keep the vehicle in a proper attitude.
To pick even further nits, the Soviet-designed capsules have additional retrorockets (touchdown rockets, actually) that fire just before touchdown to soften the landing. See http://www.rocketry.com/mwade/spaceflt.htm for everything you will ever need to know about Soviet