# Is the Oberth effect applicable to any speed change, or only to ejection of reaction mass?

Rocket engines provide the most efficient velocity change per mass fuel used when in periapsis because of the Oberth effect. But is this an effect of a spacecraft losing mass (exhausting it through its rocket engine) in a gravity well so that it then can go up out of it lighter, or is it more general? Would a spacecraft without reaction engine, for example one which instead uses a solar sail or beamed microwaves from Earth, still enjoy the Oberth effect? Even if its mass was the same when entering the gravity well, as when leaving it.

Would a spacecraft without reaction engine, for example one which instead uses a solar sail or beamed microwaves from Earth, still enjoy the Oberth effect? Even if its mass was the same when entering the gravity well, as when leaving it.

Mechanistically, there's actually no reason that these other means of propulsion would not be subject to the Oberth effect. In the two examples you gave, the propulsion is given by photons. These have an absurdly large specific impulse, and they are massless, but they follow similar rules. If the photons reflect off a mirror on the spacecraft while it makes a planetary flyby, then those photons could continue into space, but before they do so they will experience a slight redshift due to climbing the gravitational well - similar to how any other propellant would.

This is pedantic because the energy change is tiny compared to the total energy, but this is only because of the very high specific impulse. In more practical terms, it would be extremely difficult to get a high Oberth effect because low-thrust engines (and solar sails) spend very little of their thrusting phase at perigee where the Oberth effect is great.

Yet another alternative might be electromagnetic acceleration as a craft does a flyby of a planet. In this case we can't use the same logic because the force is transmitted between one body and another. However, the argument still works by virtue of the craft's higher speed at perigee. The energy that a stationary accelerator imparts is the impulse times velocity (from the mechanical power=force x velocity relationship).

• I can envision a high-g no-reaction-mass use of Oberth: You have a supercatapault on an airless body. You set your periapsis close enough to zero that your spacecraft can be grappled, it then boosts you. Being an airless body it isn't going to be all that big, though, so the benefit isn't that great. It also requires a very precise orbit. Jul 2, 2016 at 19:47

Would a spacecraft without reaction engine, for example one which instead uses a solar sail or beamed microwaves from Earth, still enjoy the Oberth effect?

Sure.

Suppose spacecraft A, powered by rockets, dives toward the Sun and fires all its thrusters at once near perihelion to get some desired delta-V. Next suppose spacecraft B, powered by solar sails, dives toward the Sun, reaches the same perihelion distance as spacecraft A, and turns its sails in just the right way near perihelion to get the same delta-V as spacecraft A.

Both spacecraft will be subject to the same Oberth effect because the Oberth effect is solely a consequence of change in velocity and the velocity at which that delta-V occurs. The underlying physics that results in that delta-V doesn't matter.

Both of these approaches have been proposed as mechanisms for escaping the solar system at high escape velocities. The idea of using solar sails to escape the solar system dates from the start of the space age (Tsu 1959). At a recent NASA Innovative Advanced Concepts symposium, Nosanov et al. analyzed using solar sails (with a final close approach to the Sun) as a means to escape the solar system, reaching the heliopause in 12 years or less and using existing materials. (Note that took Voyager 35 years to accomplish the same). I've only incorporated two references. There are many, many more.

T. C. Tsu, "Interplanetary travel by solar sail," Ars Journal 29.6 (1959): 422-427.

The change in apoapsis is caused purely by the change in velocity applied - whether that velocity change is caused by rocket propulsion, or by any of the other methods you've mentioned.

(EDIT: I should add this - you also mentioned the craft's rise out of the gravity well - its path along the orbit. This path is not affected by its mass, only by its velocity. Much like a pendulum's frequency depends only on the length of the pendulum, or two objects on Earth fall at the same speed, provided there are no aerodynamic effects.)

The Oberth effect can be explained this way. Every second you are falling in a gravitational field, it is altering your velocity--perhaps helping you, perhaps hurting you. If you do your burn when you're deeper in the gravity well, you're either increasing the time gravity will help you, or decreasing the time it will hurt you. For example:

• If you're moving away and you want to slow down, burn now. By slowing down, you spend more time near the planet with gravity pulling you back.
• If you're moving toward the planet and you want to speed up, wait until you're closer. If you burn now, you spend less time falling toward the planet getting accelerated by gravity.

...and so on. In each case, burning while deeper in the gravity well gets gravity to amplify your efforts. So you can see that it's not the fact that you're lightening your ship that makes it work for you (remember, the Oberth effect also works for slowing down your ship), so it should work for any type of drive.

The easiest way to understand the Oberth effect is simply to remember your Physics 101.

Work = Force x Distance.

If you are moving fast you will cover more distance during the burn and therefore do more work. Anything that applies a force over time will observe this "effect." Cheers!

• Oh, I wish that was so easy. The problem is "distance" depends on frame of reference, and the right one is quite difficult to determine at times, especially in a multiple-body problem. example
– SF.
Jul 1, 2016 at 8:56
• @SF. It is that easy. Pick whatever frame of reference you want. You probably want the one centered on the body you are orbiting though.
– Erik
Jul 1, 2016 at 9:34

The faster you're moving, the bigger the Oberth effect. You're moving fast during perigee, so changes in velocity done in the vicinity of perigee enjoy an Oberth benefit.

But solar sails have minute acceleration. Only a little change in velocity can be done while the sails are in the neighborhood of perigee. To do an impulsive burn at a 300 km altitude perigee, you'd need an acceleration that's a good fraction of 1 g, better yet -- several g's.

If acceleration is on the order of 1 mm/s^2, there will be little Oberth benefit unless many small burns are done over many perigees.

It's a function of the fact that at periapsis the ship has the highest velocity and the Oberth effect is about adding velocity when the velocity is already high in some frame of concern.

I believe it also applies to multistage rockets where the upper stage increase in kinetic energy may be substantially greater than the total chemical energy of the propellant of that stage.

It should then also apply to any continuous thrust engine no matter how it works where the mechanical power grows linear in V while the liberated power of the engines power source is constant. Energy is conserved as the integrated mechanical power always equates to the ships kinetic energy in any frame.