What even is an orbit?

Interesting question. Let’s see what Google has to say about this.

Hmm. That make sense to you? It didn’t to me. If an object is following a “gravitationally curved trajectory” and is under the influence of gravity, why doesn’t it just fall down? Why does it follow this trajectory that somehow keeps it in space? Well, that’s the kicker. It does fall down. In fact, it’s falling down all the time.

Let’s say that you are trying to orbit the Earth at a height of 100 kilometres above its surface. Now, if you were to somehow just appear there, you would start falling down towards the surface at approximately 9.77 metres per second, per second.  This is just slightly slower than how fast you would fall near the ground, meaning that gravity is almost as strong up here as it was at ground level. Annoying, right? How do you stay up here then?

Well, unless you’re a flat earther, I think you will agree with me when I say that the Earth is round-ish. You will also agree with me when I say that Earth’s roundness means that if you were to start moving tangentially to its surface, the ground start to drop away from you as long as moved in a straight line. What if you, suspended in space 100 kilometres above the planet, were to start moving sideways really, really fast?

Using the equations of motion, you can calculate that you would fall about 4.88 metres in the first second after you magically appeared in space. Now, if you were to go onto the website http://earthcurvature.com/ and enter 7.88 kilometres into the field that you see there, it will tell you that on moving this far sideways, the ground will have dropped away from you about 4.87 m. So, if in one second you were to move sideways about that much, the Earth would have curved away from you exactly the same amount as you would have fallen towards the Earth, meaning that your altitude above the surface of the Earth wouldn’t have changed.

Indeed, on using the formula for orbital velocity that you are going to or already have rote-learned in Class 11, we find that at 100 kilometres above the surface, you should be travelling at about 7.85 kilometres per second in order to remain in orbit – less than half a percent off from the value we calculated, which involved a lot of approximations and gross oversimplifications. Tell me that that isn’t beautiful.

Notice that this means that remaining in orbit doesn’t require acceleration. Since in space there is (mostly) nothing to slow you down, once you achieve orbit, you will stay there as long as your velocity remains unchanged. That is why the 420 tonne International Space Station can stay in orbit without requiring fuel – almost. Even 400 kilometres above the surface, there are still enough air particles hitting the ISS to slowly but surely slow it down. So, its orbit has to still occasionally be boosted to null out this effect.  

So, to recap, an object in orbit around a celestial body moves sideways so fast that as it falls towards the surface, it “misses” and keeps going around it forever (or until its velocity changes).

How does one get there?

As you know (I hope), rockets are vehicles that are used to send stuff to orbit. They usually consist of multiple sections called stages stacked vertically on top of one another. Each stage has its own fuel tanks and engines, and is designed to separate from the one below it in flight once the lower one’s fuel has been depleted. This approach has multiple benefits, including not having to carry the mass of empty fuel tanks, allowing use of engines optimized for different external pressures and thrust levels, and allowing more modularity when it comes to launching payloads of different masses. Although nearly all rockets have 2 or more such stages, concepts of single stage to orbit vehicles (called SSTOs) do exist, since that particular approach has the benefit of allowing much easier reuse of launch vehicles.

Saying that rockets are the only way to get to orbit is slightly misleading, but at present very much true. Other than the Space Shuttle, there has been no mainline launch vehicle since the inception of the various space programs that has not been a traditional rocket. There are concepts of spaceplanes like the Skylon program which would takeoff like an aircraft, fly up to hypersonic velocities on air breathing engines (which are incredibly efficient compared to rockets), and then switch over to rocket engines for the final leg into orbit. However, building engines and aircraft that can fly at these hypersonic velocities is extremely challenging, and so for now, rockets remain our sole gateway to space. Maybe very far forward in the future, things like space elevators and kinetic launchers will be feasible, but for now, they’re just science fiction.

As you can probably tell, getting into orbit is pretty darn hard. You have to carry your payload hundreds of kilometres above the Earth’s surface, accelerate it to over 5 times the speed of the fastest bullet, and do this in rapidly changing conditions – from 1 atmosphere of pressure to zero, and from normal ambient temperature to negative or positive hundreds of degrees Celsius – all while knowing exactly where you’re going because there is no scope for navigational error. This is why rockets, despite working off some of the most basic principles of physics, are still the most advanced and complex machines ever built by humans. So, rockets have to follow very specific trajectories during launch to reach orbit safely and efficiently. One such depiction of a safe and efficient rocket launch is shown below, courtesy of xkcd.

Kidding, of course. There are no care bears in the upper atmosphere 😉

In all seriousness though, the trajectory followed by a rocket during launch is pre-programmed and flown by a computer, so the astronauts on board are more the passengers than the pilots. The only time astronauts had any real control over the spacecraft was with the space shuttle, and even then it was only during re-entry or emergency situations where they actually exercised it. Computers are simply much more suited to this kind of job thanks to their accuracy and, more importantly, consistency. When it comes to space, every last bit of efficiency and reliability counts.

The first phase of the flight is the vertical ascent. The rocket remains more or less perfectly vertical off the launch pad for the first several seconds of flight. This is because at low speeds and accelerations, turning would result in the rocket “sliding” sideways, going out of line with its velocity vector (which can be thought of simply as the direction of travel), resulting in unwanted aerodynamic loads. The amount of time spent in this phase depends on the rocket’s performance – those with a higher thrust to weight ratio can start turning quicker than those with a lower thrust to weight ratio. As a general rule, the turn should start as soon as sufficient acceleration and velocity is obtained.

A Falcon 9 in the vertical ascent phase

Next, the rocket starts what is known as the “gravity turn,” a maneuver in which it pitches over slightly and then continues to point at its velocity vector, letting gravity curve it into its natural trajectory. Although most modern rockets do not follow an exact gravity turn, they fly trajectories at least approximating one as it is the most energetically efficient path in an ideal scenario. The goal is to reach orbital velocity right as the spacecraft hits its target altitude. Remember that all of the energy expended in moving the rocket upwards is energy that is being lost to gravity. The only thing that really counts is energy being put into moving sideways.

A plot of a mathematically ideal gravity turn

You might ask, if gaining horizontal velocity is all that matters, why not start turning as soon as possible? Well, there a lot of things that can go wrong from flying too shallow of an ascent. The best trajectory to follow into orbit is a delicate balance between going too high and wasting fuel and going too low and losing energy to drag or even worse, losing the entire vehicle due to atmospheric heating. Generally speaking, it is safer to go high since that’s mostly only inefficient, whereas going low can result in what is sweetly referred to as “rapid unscheduled disassembly.”

By the time the vehicle reaches the Karman line (the altitude of 100 kilometres above Earth generally accepted as the edge of space) it is usually on its vacuum optimized upper stage. During this final phase of the launch, the vehicle is almost completely horizontal, letting its upward momentum carry it to the top of its trajectory where ideally it will attain orbital velocity and enter orbit. Once it attains that magical number of roughly 7-8 kilometres per second of velocity (at low altitudes), it will officially be in orbit and continue to circle the Earth until it uses its engines to slow down or until atmospheric drag decays its orbit to a point where it burns up.

Low Earth orbit (blue), geostationary transfer orbit (grey) and geostationary orbit (orange)

In the case of payloads that need to be launched to higher Earth orbits and beyond, the upper stage continues to accelerate, flinging its payload into a highly elliptical orbit or even on a hyperbolic escape trajectory. The payload then uses its own propulsion to circularize and fine tune its orbit while the upper stage of the launch vehicle normally expends the last dregs of fuel in its tanks to drop its perigee (the lowest point of its orbit around Earth) into the Earth’s atmosphere, where it will burn up and not contribute to the ever growing problem of space junk.

In summary, a rocket launch involves reaching a balance between altitude and speed such that you lose the minimum possible amount of energy to both gravity and the atmosphere while making sure to not exceed aerodynamic and thermal limits.

Assignments on orbits and getting to orbit

  1. Say you are in a circular orbit around the Earth. What effect will firing your engines perpendicular to your direction of travel and parallel to the surface have on the height of your orbit? Explain.
  2. Would a standard gravity turn still be the most optimal path to orbit if Earth did not have an atmosphere? Why?
  3. The method that was used to calculate orbital velocity in this module involved a lot of assumptions and simplifications. At higher altitudes, it becomes useless for several reasons. State these reasons and explain how an accurate value can be similarly obtained.
  4. Besides all of the reasons noted above, what are some other factors that might make rockets not follow a perfect gravity turn? Explain using specific examples of real-world rockets wherever possible.

In order to submit your responses to these questions, kindly follow these instructions.

Further reading