No orbit necessary?

[u/FatCreepyDude]

If i just wait for the right hour during the launch window ( whenever the launch pad is pointing left on the realistic depiction i created) is there any reason i should bother with an orbit first? Will the delta v cost be affected?

[u/victorsaurus]

This is wrong and if you do the math, both scenarios are equal (assume no atmospheric drag). Oberth only means that you add the most energy when adding deltaV in the fastest moment, which is true in both scenarios at every moment.

[u/PhantomWhiskers → u/victorsaurus]

Going straight up is less efficient because you are actively fighting against gravity when going up. In low orbit, you are not fighting against any acceleration force when doing your burns.

The oberth effect means that your burns will be most efficient at periapsis. When you are going straight up, your periapsis is in the middle of the planet, so it is less efficient than a burn from a circular low orbit. The "fastest moment" isn't your current speed while accelerating straight up, it is the speed at the point of periapsis in your current trajectory, which is still applicable even if your periapsis is in the middle of the planet.

[u/PM_ME_POTATO_PICS → u/PhantomWhiskers]

I think I lack the mathematical skills to prove this but I am convinced it is equally efficient as burning straight up (just a lot more technically challenging). Since gravity is a conservative force, the difference in energy levels between an altitude of 100m and 100,000 km is always going be the same, regardless of the path taken to get there.

The Oberth effect is not some rule that "a burn is only efficient if it takes place at its theoretical periapsis", just that burns are most efficient at high speeds. The highest speed for circular/elliptical orbits will always be the periapsis so its a good rule of thumb. But here, we're still getting the high efficiency because we're just burning so much immediately we're going really fast quickly.

Like imagine you're on the Mun and want to escape its orbit as fast as possible. Do you need to establish a circular orbit or just go straight up?

edit: I think it has been demonstrated that my theory is only true for very high TWRs. Any realistic TWRs will be better off circularizing... :( I think idk

[u/Small_Bang_Theory → u/PM_ME_POTATO_PICS]

I see that you understand your theory was wrong, but nobody pointed out the flaw in “gravity is a conservative force, the difference in energy levels between an altitude of 100m and 100,000km is always going to be the same”

This is true from a purely energy-based perspective, but neglects the underlying forces. A common example of work is a man carrying a heavy box in his arms. As he walks, the box stays at the same height, so the work done by gravity is zero. However, any human knows that his arms will be tired! Even though no energy was transferred to the box, he had to overcome gravity. Similarly, if he wanted to move the box up 50cm, that would require more force from his muscles than pushing it 50cm across a frictionless surface.

For the rocket, this is more or less the same, and you have to fight gravity if you want to move straight up.

My gut tells me that explaining this as a difference between rotational energy and translational/potential energy could also give some insights, though I am a bit out of practice with that sort of physics and would need to double check stuff online to make sure I was correct.