This is a fun one. Gravity pulls toward the center of the Earth. If you drilled a hole directly through the center and out the other side, and sat unmoving at the perfect center you would be weightless, since gravity pulls toward that point. We're assuming no heat here, since the heat would really kill you. If you stood on one side and jumped in, you would accelerate down toward the center being pulled by gravity. However, gravity would decrease as you get closer to the center since less and less mass would be pulling you in. At the center, you'd again be weightless but this does not mean you would stop moving, just that there would be no force making you go faster. You would shoot past the center and up partway to the other side. Essentially, you would spring back and forth hundreds of miles around the center of the Earth until wind resistance slowed you down at the dead center.

If there were also no wind resistance (say you pumped the air out of the tunnel and made a vacuum), you would spring back and forth around the center of the Earth forever. Lost wing resistance looks funny, but here's a video of a feather and a bowling ball being dropped in a vacuum. Guess which one lands first...?

When you are falling, it feels like you are in zero gravity. This is because the force of gravity is acting equally on all parts of your body at once, so no part of you is compressed, unlike if you are standing on the ground. The effect is the same as if you are in orbit around the Earth.

Yes, you would still be falling when you reached the surface on the other side. If you were in an enclosed container and falling so that you couldn't look out, you would have no way of even knowing that you had reached the other side.

To tackle this question, let’s review what we know about gravity. Earth’s mass pulls down on you with a certain gravitational force, which is equal to your mass multiplied by the acceleration. (That acceleration is 9.98 m/s² at the Earth’s surface.) This force decreases quickly as you move away from the surface, in an inverse square (1/r²) relationship.

If you have a pen and paper, you can sketch a graph with distance from the center of the earth as your x-axis (always a positive value) and force due to gravity on your y-axis (which is also always positive). Mark a spot to represent conditions on the Earth’s surface – somewhere in the middle of the x- and y-axes. Draw a curved from your point heading right that never quite touches the x-axis. This represents the decreasing force as you move away from the Earth’s center. Now, we need to consider another point – what is the force due to gravity at the very center of the Earth (where x=0)? If you could stand at the very center, you would still be attracted to the Earth’s mass, but it would be pulling you about equally in all direction. Thus, the force you feel would be zero – you would feel weightless at the Earth’s center! So, you can now mark a point on your graph at the origin (x=0, y=0).

To find out what it would feel like to travel to the center of the Earth, we have to connect these points. We know that the force due to gravity must be greater than zero. We also know that the relationship must be a continuous function – the line we draw on the graph can’t have any gaps or jumps, and it can’t overlap itself. The simplest case is a straight line between the points – does this trend make sense? As you travel beneath the Earth, you are attracted to the mass below you but also to the mass above and beside you. The forces directing you up and to the side would lessen the force you feel going downward, so the net force (y on your graph) should be decreasing. So, your steadily decreasing line makes sense if the mass of the Earth was equally spread out.

How does your graph compare to the green line on this graph from Wikipedia?
click here please
The dark blue line takes into account the differences in the Earth’s density.

So, what would this feel like? If you jumped into a shaft that went all the way through the Earth, you would fall toward the center of the Earth but the rate of acceleration would decrease as you got closer to the center. (You’d still keep moving faster as you moved closer to the center but wouldn’t get faster at the same rate.) As you passed the center of the Earth, you would feel a force slowing you down, pulling you back toward the center. Eventually, you would fall back toward the center and repeat the process of falling until you float weightless in the center of the Earth.

Interestingly, the experience might not be like you expect. Gravity works by pulling objects towards something with mass. Because of this, we feel we are pulled toward the center of the Earth. So you would fall towards the center of the Earth, but once you pass the center, you would then slow down and start "falling" in the opposite direction, back towards the center again. You'd never make it out to the surface on the other side of the Earth.

However, if you assumed there's no air resistance and so the transfer of energy is 100% efficient (and if the distance from the center of the Earth is exactly the same to your starting point as the opposite surface of the Earth), then you would speed up as you approach the center of the Earth (falling), and then shoot past the center, and then continually slow down as you're pulled back towards the center, but you'll eventually reach the surface on the other side and arrive with zero speed, because all energy would be conserved.