The Science of Interstellar

The Endurance heads toward Gargantua with a certain amount of energy, which like its angular momentum remains constant along its trajectory. This energy consists of three parts: the Endurance’s gravitational energy, which gets more and more negative as the Endurance plunges toward Gargantua; its centrifugal energy (its energy of circumferential motion around Gargantua), which increases as the Endurance plunges because the circumferential motion is speeding up; and its radial kinetic energy (its energy of motion toward Gargantua).

The surface in Figure 27.3 is the Endurance’s gravitational energy plus its centrifugal energy plotted vertically, and location in Gargantua’s equatorial plane plotted horizontally. Wherever the surface dips downward, the Endurance’s gravitational plus centrifugal energy decreases, so its radial kinetic energy must increase (since the total energy is unchanged); its radial motion must speed up. This is precisely what happens in our intuitive, volcano analogy.

Outside the moat of Figure 27.3, the surface’s height is controlled by the Endurance’s negative gravitational energy (see the “gravitational energy” label on the figure). By comparison, there the positive centrifugal energy is unimportant. On the outer edge of the volcano, by contrast, the height is controlled by the rising centrifugal energy, which has come to dominate over the gravitational energy. On the inside of the volcano, near Gargantua’s horizon, the gravitational energy has grown hugely negative and overwhelms the centrifugal energy, so the surface plunges downward (Figure 27.5). The critical orbit is on the volcano’s rim.

^{Fig. 27.5. The Endurance’s critical orbit on the rim of the volcano, with centrifugal energy and force dominating outside the rim and gravitational energy and force dominating inside. [Image of the Endurance is from Interstellar.]}

The Critical Orbit: Balance of Centrifugal and Gravitational Forces

Upon reaching the volcano’s rim, the Endurance, ideally, would travel around and around it, at constant speed. Because it moves neither inward nor outward, the inward pull of gravity on the rim must precisely be counterbalanced by the outward centrifugal force that arises from the ship’s fast circumferential motion.

This indeed is the case, as shown in Figure 27.6—an analog of the force balance plot for Miller’s planet (Figure 17.2). At the Endurance’s critical orbit, the red curve (the inward gravitational pull on the Endurance) and the blue curve (the outward centrifugal force) cross, so the two forces are in balance.

^{Fig. 27.6. The gravitational and centrifugal forces acting on the Endurance, and how they change with changing distance from Gargantua.}

However, the balance is unstable, as our volcano-rim analogy suggests.[50] If the Endurance is randomly pushed inward just a bit, then gravity overwhelms the centrifugal force (the red curve rises above the blue curve), so the Endurance is pulled on inward toward Gargantua’s horizon. If the Endurance is pushed outward just a bit, then the centrifugal force wins the battle with gravity (the blue curve is above the red curve), so the Endurance is pushed on outward, escaping Gargantua’s tight grip.

By contrast (as we saw in Chapter 17), on the orbit of Miller’s planet, the balance between the gravitational and centrifugal forces is stable.

Disaster on the Rim: Ejection of TARS and Cooper

In my science interpretation of the movie, the volcano’s rim is very narrow, so the critical orbit on the rim is exceedingly unstable. Tiny errors in navigation will send the Endurance careening down toward Gargantua (down into the volcano) or away from Gargantua (down toward the moat).

Errors are inevitable, so the Endurance’s course must be corrected, continually, by a well-designed feedback system, like an automobile’s cruise control but much better.

In my interpretation, the feedback system is not quite good enough and the Endurance winds up dangerously far down the inside lip of the volcano. The Endurance must use all the thrust at its disposal to climb back up to the critical orbit.

But this is too subtle and technical for action-packed scenes and a hugely diverse audience, so Christopher Nolan chose a simpler, more in-your-face approach. No mention of instability. No mention of feedback. The Endurance simply plunges too close to Gargantua, and Cooper responds with all the thrust he can muster to climb back out and escape Gargantua’s grip.