Is it possible at all to go faster in an orbit around the earth?

[vjk2]

My understanding is that generally with space flight, when you accelerate in the direction of orbit, you don't go around the Earth any faster but instead ascend to a higher orbital plane, which arguably has a longer period of orbit.

Is there any manuver method that let's you move around the Earth faster?

 

[Simon Bridge]

You can apply radial thrust as well.

 

[BobG]

Accelerate in the opposite direction of motion. That reduces the size of the orbit and the satellite takes less time to orbit the Earth.

That's an almost intentionally confusing way to look at things, though.

You either add energy to the orbit, making it bigger and increasing the time it takes to complete an orbit ... or you subtract energy from the orbit, making it smaller and decreasing the amount of time it takes to complete an orbit.

Until transporters are invented allowing us to say, "Beam me up, Scotty!", kinetic energy is the only type of energy we can add or subtract - and that's what you're really doing: adding or subtracting kinetic energy.

When the energy is subtracted, and the orbit gets smaller, the potential energy is less. Some is gone because you subtracted energy from the orbit and some of it is converted to kinetic energy. So, while the speed of the spacecraft may have increased, it lost more potential energy than it gained in kinetic energy.

And just the reverse when you add energy to the orbit. Some of the kinetic energy is converted to potential energy, plus you've added energy. The speed winds up decreasing, but it gained more potential energy than it lost in kinetic energy.

 

[mfb]

You can apply radial thrust as well.

This. If thrust and fuel is not an issue, you can ignore orbital mechanics and just head to any position you like. In (current) space travel, thrust and fuel are relevant, so you have to look for cheap transitions between orbits. In that case, the quickest way to go around Earth is the lowest possible orbit, at a height of ~200km (everything below that quickly falls down to Earth due to friction).

 

[vjk2]

Oh, of course. Yes, you should be able to just ignore it all and use thrust to go fast. It would be tremendously expensive though.

 

[Simon Bridge]

The question, as stated, does allow that [radial thrust] as a serious answer.
Indeed, the preamble to the question appears to suggest that an orbit-radius change is not desired: OP knows about that but wants another way. The only other way is radial thrust (or finding a new law of physics).

But the question could be more closely defined than that - if the object, for example, is to end up at the same spot after going around the Earth exactly once by the fastest route then ... changing to an elliptical orbit? Everything will require a burn. As mentioned, manouvers are usually strongly constrained by energy availability.

Oh I suppose you could make your vessel dumbell shaped and spinning so that each end will spend part of the orbit faster and part slower... I don't think that's what is meant either somehow :D

I can only think of similarly "throwaway" answers :/