How tall is the universe?
The top of the observable Universe it currently about 46 billion light years up. But the Earth is spherical, so which way is up changes depending where you are, and could be in any direction.
Because the Universe is expanding (in the sense of metric expansion), and because the observable Universe grows with time (because light has time to travel further), AND because the observable Universe is always centered on the observer you're interested in (in this case you, riding your spaceship), you will never be able to reach its edge.
And I feel compelled to link this image summarizing the contents of the Universe, by "height". Note that the scale is logarithmic, which is explained at the bottom of the image.
The way you've described it, you would call the universe infinitely tall. The observable universe isn't infinite in extent. Not be any means. The distance from here to the edge of the observable universe is about 46.6 billion light years right now. However, the reason I say it's infinite by your definition is that it is expanding fast enough that if you kept rising upwards forever, you would never hit the edge.
Let me be a bit more technical. There very well could be a physical edge. It isn't within our observable limits, but that doesn't mean there isn't an edge that can be bumped into. However, the rate that edge is receding from us (because it is outside our observable limits) makes it so that no matter how fast you move in its direction, the expansion of the universe would always make it move away from you faster. So in any practical sense, the universe is infinite in extent because we can travel forever and not hit a boundary of some kind. It may not actually be infinite in extent, but any boundary will always be farther away than we can travel to.
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Kalis about 1 year
Let's suppose that I am on a spaceship in low-earth orbit, if I rise my spaceship higher and higher and hover it upwards forever, will there ever come a point where I just can't get up any further or is the universe infinitely tall?
Hritik Narayan over 8 yearsYou can't have "tallness" for a universe. The observable universe is like a sphere, filled with galaxies and other celestial stuff in all directions.
Kalis over 8 yearsIf it's like a sphere (much like Earth) then we can use this example; let's suppose that I am at the core of the Earth, if I keep drilling upwards..I'll reach the surface but then if I keep going upwards by using a rocket, there will come a point where I will exit Earth. We can apply the same scenario on the universe (although not sure about the exit)
Hritik Narayan over 8 yearsThen this question is the same as one which asks for the size of the universe. The observable universe has an approximate diameter of 93 billion light years centered at the Earth. This however, is not the entire universe. We can't observe anything beyond this general region because of cosmological expansion.