In Interstellar, how did Cooper and TARS provide momentum while detaching from the main ship?

Question

Cooper refers to Newton's 3rd law while detaching. I didn't understand the physics behind this scene.

Answer 1

Tars is going to pilot the lander as they deplete its thrusters, pushing the Endurance clear of Gargantua's gravity. It'll then detach (as it's now dead weight). If it remains attached, it'll drag them back down again.

“Once we’ve gathered enough speed around Gargantua, we use Lander One and Ranger Two as rocket boosters to push us out of the black hole’s gravity,” he explained, as the lander reattached in the rear of the ring module, blocking her view of the Ranger and Cooper.

“The linkages between landers are destroyed,” Cooper said. “So we’ll control manually. When Lander One’s fuel is spent, Tars will detach—”

“—and get sucked into the black hole,” Tars finished.

Amelia thought they were joking at first. They did a lot of that, Tars and Cooper. Sometimes she wanted to change the humor settings on both of them. But it crept over her that this time there wasn’t any humor involved.

“Why does he have to detach?” she asked.

“We have to shed mass if we’re gonna escape that gravity,” Cooper explained.

“Newton’s third law,” Tars put in. “The only way humans have ever figured out of getting somewhere is to leave something behind.”

_{^{Interstellar: Official Novelisation}}

In fairness, you're not wrong. The part where they fire their thrusters is the bit that relates to Newton's Third Law (e.g. equal and opposite reactions) whereas the bit where they release the ships to lower their mass is actually Tsiolkovsky's rocket equation which relates more to Newton's Second Law (e.g. the conservation of momentum).

Then again, this is a film which claims that love is stronger than time and space, so I wouldn't complain too much about them jumbling up Newton.