# Why is the Endurance still in "orbit"?

According to the flight plan in Interstellar the Endurance never entered orbit around Miller's planet, which is further evidenced by the time dilation not experienced by Romilly. So how is it that after a significant delay of 23 years, 4 months, 8 days the main characters still managed to fly the Ranger back up to space to find the Endurance? Does there exist a "synchronous" orbit at different radii from the same center of gravity? Otherwise an insane amount of fuel would be needed to actively adjust the orbit of the Endurance around Gargantua synchronized with Miller's planet and yet far enough to avoid significant time dilation for 23 years!

Original line around 1:04:29:

Cooper: "Here's Gargantua. Here's Miller's planet. Instead of taking the Endurance into orbit around Miller's planet, which would conserve fuel, but we would lose a lot of time. What if we take a wider orbit around Gargantua, parallel with Miller's planet outside of this time shift, to here? Then we take the Ranger down, we get Miller, we get her samples. We come back, we analyze, we debrief. We're in, we're out. We lose a little fuel, but we save a whole lot of time."

Assuming a circular orbit, for each angular velocity, there exist a unique radius for that orbit. (Actually two, but they are in opposite directions.) The calculation is rudimentary in Newtonian mechanics equating centripetal force with gravitational force, giving r^3 = GM / w^2 where w is angular velocity with linear velocity v = rw. If you alter forward velocity to match angular velocity, you enter a completely different orbit at a different angular velocity, unless you actively expend fuel to compensate. Therefore the Endurance would not be in-sync with Miller's planet around Gargantua without spending fuel. And even though ordinary satellites do have to actively manage their orbit, they are merely compensating for friction to maintain the same orbit.

Hence to clarify my question: Is this a plot hole, or does there exist an elliptical orbit that admits an absolutely wider distance from another planet's orbit which also has roughly identical angular velocities about the C.G.? Perhaps after relativistic effects are factored in? (By "absolutely" I mean no crossover at all, otherwise time dilation.)

Disclaimer
My answer only assumes circular orbits for the ease of explanation. Everything I've said applies to elliptical orbits; but I chose to omit their existence for the purpose of keeping things simple.

# TL;DR

• The Endurance could have orbited Gargantua at any orbital height. Although the relative distance between the Endurance and planet Miller would fluctuate, it would always be possible to know where the Endurance should be (relative to planet Miller, at a given point in time) and fly there, assuming there is enough fuel of course.
• Due to time dilation, it is theoretically possible for the Endurance to create a synchronous orbit with the perceived orbit of planet Miller (i.e. as perceived when looking at planet Miller from the Endurance, not as experienced when standing on planet Miller's surface).
• Although this special scenario is not explicitly mentioned in the script, it makes a lot of sense to do this as it comes with many benefits, including both communication availability and ease of returning to the ship.

What if we take a wider orbit around Gargantua, parallel with Miller's planet outside of this time shift, to here?

From this part of the quote you added, I read that the ship never orbited around planet Miller, but rather around Gargantua (the black hole itself).

As an analogy:

• The Sun (Gargantua) has several planets orbiting it
• Earth (planet Miller) orbits the Sun
• Mars (the Endurance) also orbits the Sun, but it's orbit is wider (larger radius) than Earth's.

Because they have different orbital heights, Mars and Earth experience a year (one orbit around the sun) differently. This means that Mars and Earth continually change position relative to each other (due do different orbital speeds), but they catch up to each other after a given cyclus.

As an analogy: the hour hand and the minute hand on a clock go around at different speeds, but they still match up with each other every time the minute hand "laps" the hour hand.

This means that the travel distance can vary wildly (depending on their current relative distance), but you can always calculate where the other object is supposed to be (because orbital periods never change so long as the orbit itself never changes).
Assuming the Ranger has enough fuel to travel to the Endurance at any point in time (meaning that they do not need to wait for the Endurance to be close enough to planet Miller), then it makes sense that they could take the Ranger up to the Endurance whenever they wanted.

So the direct answer to your question is that while the Endurance did not orbit around Miller's planet, it did orbit around Gargantua; which means that it would still have been reachable many years later (but requires more travelling compared to when the Endurance would have orbited planet Miller).

There is another interesting point, which has mainly come forward from the comment discussion in the other answer. First, let me explain how orbits work in a normal situation. I'm resuming the Earth/Mars example.

Earth orbits the Sun. Mars orbits the Sun at a higher orbital height than Earth. Because Mars has an increased orbital height, this has some consequences:

• The speed of a satellite is influenced by the orbital height. For a higher orbital height (Mars), the satellite will move slower (compared to Earth).
• Because Mars orbits at a higher orbital height, it has to travel a longer distance to make a trip around the sun. This is somewhat obvious, as the circumference of a circle increases as its radius increases (and orbital height = radius of the orbit).

Relative to Earth and its orbit, Mars travels slower along an orbit that has a larger circumference. This is a double whammy: two independent reasons why Mars takes longer to orbit the Sun, compared to Earth.

Now, the interesting part is the logical consequence:

Two satellites that orbit the same planet at different orbital heights, can never orbit the planet at the same orbital period.
The closest satellite (Earth) will always orbit much faster than the furthest satellite (Mars).

This is a normal situation. I consider it normal, because it does not contain a special scenario where Earth and Mars are experiencing a different flow of time (to a point where it is meaningfully measurable).

However, when we consider planet Miller and the Endurance, we do need to take this into account!

Let's say that, forgetting time dilation, if the Endurance looks at planet Miller orbiting Gargantua, it sees planet Miller complete an orbit in 100 seconds. Anyone standing on the surface of planet Miller could also measure 100 seconds for a single orbit.

However, if we now impose time dilation on planet Miller (e.g. time moves at 50%); then the observer on planet Miller's surface will still measure 100 seconds, but an observer on the endurance would measure 200 seconds.

Conclusion:
If planet Miller's time passes time at X% of "normal time", then an outside observer will observe planet Miller's orbital period to pass at X% of its undilated (expected) orbital period.

"Normal time" is the observer's frame of reference, which in this case is the Endurance.

The slower time progresses on planet Miller, the slower that planet Miller will appear to orbit around Gargantua. Since we know that time passed really slowly on planet Miller, that means that it is orbiting Gargantua at a really slow pace (as observed from the Endurance).

Without time dilation, because the Endurance takes a wider orbit than planet Miller, planet Miller should orbit around Gargantua faster than the Endurance. This is unavoidable, assuming unpowered orbits.

However, because planet Miller experiences time at an incredibly slow pace, it also orbits around Gargantua at an excessively slow pace.

This means that it is possible for the Endurance to pick an orbital height which gives them the same orbital period as the perceived orbital period of planet Miller (as experienced by an outside observer, not an inhabitant of planet Miller).

What if we take a wider orbit around Gargantua, parallel with Miller's planet outside of this time shift, to here?

Although Cooper never explicitly specifies it, it makes sense that the Endurance chose the specific orbit that synchronizes its orbital period to planet Miller's orbital period, for the purpose of keeping communications open (not blocked by other bodies) and having a fixed travel destination from planet Miller back to the Endurance (ignoring planetary rotation, which is not an obstacle if you already travel using orbits)

Because of the different time dilation, a unique opportunity presented itself to synchronize orbits while maintaining different orbital heights.

• Well stated! The only real error in the film that I can see is really subtle, in that time dilation isn't a discreet thing that one can be 'outside of'. A wider orbit of Garganuta would experience less time dilation, but it wouldn't be 'outside of a time shift'. In fact, you could probably state that time dilation continuously exists everywhere in the universe to some greater or lesser extent. Commented Aug 11, 2017 at 23:32
• @MadTigger: True, but that eventually boils down to the "no universal frame of reference" argument. Maybe my answer should've referred to the difference in dilation (planet Miller vs Endurance), rather than one experiencing time dilation and another seemingly not experiencing it, but maybe that would've overcomplicated the answer (they could have also omitted it from the movie for the same reason: too complex for the intended audience and not quintessential to the plot). Commented Oct 19, 2017 at 16:29

Orbit is a relative term meaning circling around an object. The orbit does not require that it be only n distance away. The international space station orbits the earth just as much as the moon does. The earth orbits the sun just as much as the outer asteroid ring of plutonian objects do.

As they said, the Endurance is taking a wider orbit. All you need to do for that is calculate the forward velocity vs the gravitational downward pull, to create a stable orbit at any given distance. All a stable orbit is, is a carefully planned free fall wth a decay rate of decades.

As far as the ranger finding the endurance, they calculated everything ahead of time. Orbit calculations would be valid for centuries unless an external force changes things.

• "The international space station orbits the earth just as much as the moon does" yes, but not at the same angular velocity. Assuming a circular orbit, for each angular velocity, there exist a unique radius for that orbit. If you alter forward velocity to match angular velocity, you enter a completely different and asynchronous orbit. Commented May 21, 2017 at 4:39
• But then you are assuming that the orbit was synchronous, when the mass of the planet was so significant that the surface was moving at a much different speed. Nothing suggest that the Endurance was flying a synchronous orbit. They could have found it by following a beacon or other technological means.
– anon
Commented May 21, 2017 at 5:23
• Endurance never entered orbit around Miller's planet. Endurance entered orbit around the black hole Gargantua, at a wider radius than Miller's planet. Just like Mars and Jupiter would not remain aligned right on top of Earth and the Sun, Endurance would not be anywhere near Miller's planet for the Ranger to return to. A screen capture is added to illustrate the orbit used in the movie. Commented May 21, 2017 at 6:06
• Maybe I miss read your question, but that seems simpler. They match the speed needed. Since they are only interested in a quarter or half or even a single rotation, any difference in speed or angle is minor and could be handled by a radio beacon.
– anon
Commented May 21, 2017 at 6:46
• Them ignoring or more likely glossing over the finer technical details does not make a plot hole. They choose artistic timing over technical accuracy in this scene. They still had the general idea correct and it's one of the few changes made for plot reasons.
– anon
Commented May 21, 2017 at 6:49