# What kind of force is there in exact middle of earth? [closed]

Basically i have one question but this question leads to another.
firstly can we dig in earth that from one side we reach other side of earth ? i mean just going through it. Now let's say we can dig then i wanna know what force will be there in exactly middle of earth ?

i mean let's say i am here standing and facing gravitational force and maybe another man on other side of earth facing same force. so basically we both are opposite to each other and if there is nothing between us we will collide.
It sounds a lil confusing maybe i have drawn this image to explain what i am thinking.What force will be there in exact middle of earth ? something like space ? nothing ? or something like between 2 magnets pushing each other ?

Edit : As many people have responded beautifully i wanna know why everyone is considering all these Environmental conditions ? When we talk about a theory don't we take things ideally ? obviously we should consider other factors. But shouldn't we consider IDEAL situation ?

Secondly ! One thing i am confuse about is, ok as everyone said there will be ZERO force and we will be floating. So we will be floating ? from there no one can come back ? i mean HE can't go to my side and i can't go his side ?

• That is no question for space stack exchange. – Uwe Aug 28 '19 at 16:59
• @RaoHammasHussain: Gravity is always attractive, never repulsive. As per my answer, the shell theorem states that as you drop inside of your borehole the force of gravity reduces as though you were on the surface of a new planet with a decreased mass and radius, but the part above you won't pull you more than the part above you pushes (in fact it will be less, except at the exact center) – Michael Stachowsky Aug 28 '19 at 17:02
• Voting to close because drilling conceptual holes through the Earth is unrelated to space exploration. – Organic Marble Aug 28 '19 at 17:10
• @MagicOctopusUrn No, you aren't big enough to get a significant gravitational gradient. Each individual atom of your body is getting pulled uniformly in all directions, so they don't go anywhere. Note that even when you're standing on the surface, different bits of Earth are pulling you in different directions in a significant arc below you, and you are not ripped apart. – Russell Borogove Aug 28 '19 at 17:43
• @RaoHammasHussain Velocity and acceleration are two different things. When acceleration due to gravitational force goes to zero, your velocity remains extremely high. – Russell Borogove Aug 28 '19 at 17:44

In this answer, I'm going to assume the tunnel is a perfect vacuum and there's no intense heat or pressure. This is a thought experiment.

If you and John fall at the same time, you guys will meet approximately 20 minutes after you jump into the tunnel. Depending on how wide the tunnel is, you guys will most likely collide at a velocity of around 11 km/s. That's Apollo's command module re-entry speed! You will accelerate until you reach the center of the Earth, but once you reach the center, you will decelerate and deceleration will take another 20 minutes because now you have to undo all that velocity. So you will fall endlessly like a pendulum in a vacuum. Now if there's air resistance, then you will slow down until you stop and reach the center. Terminal velocity is around 195 km/h (differs depending on your drag coefficient (aerodynamics)) so it would take around 32 hours to reach the center (ignoring the gravity gradient).

Now assuming you teleport to the center of the Earth then you will float because the force of gravity is even all around you. But that's assuming you teleport and you're stationary. This is a great video by MinutePhysics and Vsauce that explains your very scenario.

So the answer to your question: If the tunnel was a vacuum, both of you would be falling endlessly. You would reach John's side, John would reach your side, and vice versa.

• Terminal velocity decreases as you go deeper, assuming constant air density, because the gravity decreases. Terminal velocity at center approaches 0, but you carry momentum from somewhat higher altitudes, so you'll connect at about 1 m/s combined velocity. How'd you get 11km/s -- are you assuming constant acceleration all the way down as well? I get 7900 m/s with the gravity gradient. – Russell Borogove Aug 28 '19 at 17:51
• 1 m/s or 1km/s? I don't think 1m/s is right – Star Man Aug 28 '19 at 17:54
• I got 11 km/s in a vacuum. – Star Man Aug 28 '19 at 17:55

Exactly at the center-of-mass of the Earth there is no net gravitational force. Gravity comes from mass, and all the mass of the Earth is evenly distributed around the center-of-mass (by definition), so all the forces cancel out. As you get deeper and deeper, the net gravitational force falls -- linearly if density is constant.

In practice, of course, you can't dig a hole that deep; much of the interior of the planet is flowing molten rock.

If you could magically make a stable, not-ridiculously-hot tunnel through the planet, and you and your antipodean friend each jumped into one end of the tunnel, you'd fall toward the center and meet there.

According to a crude simulation I've worked up, if standard sea level air pressure was magically maintained throughout the entire tunnel, you'd be moving at somewhere around 0.25-0.75 meters per second when you reached the center -- it depends on whether you spread out to catch as much air as possible, or straightened out in a headfirst dive to maximize your speed. In the median case you get to the center moving at 0.5 meters a second after a 48-hour fall! That's slow enough that you and your friend should be able to hug without injury when you meet. My simulation assumes constant density of planet all the way down, which is obviously not right, so you'd probably collide a little bit faster than that, but not greatly so.

If you pumped all the air out you'd be accelerating all the way down, but as you got closer to the center and more and more of the Earth's mass was "behind" you, your rate of acceleration would reduce; just as you got to the center the acceleration would tend toward zero, but of course your accumulated velocity would still be extremely high. It would take ~21 minutes to fall, and you'd reach the center at ~7900 meters/sec -- a figure which is suspiciously close to circular orbit velocity, by the way.

With no air and no obstruction in the tunnel, you'd shoot through the center, and the acceleration you experienced on the way down would be exactly reversed on the way up the other side. When you reached the opposite end of the tunnel, your velocity would be back to zero, and you'd start falling back to the center. Without any drag or friction involved, the end result would be that you'd bounce back and forth from one end of the tunnel to the other forever.

If you lowered yourself carefully down a 6400 kilometer cable to the center and let go, you'd be in free-fall at the center and wouldn't go anywhere.

Here's the Python code for my sim.

# initial altitude is earth's radius

# start motionless at T = 0
vel = 0.0 # m/s
t = 0.0

# time step, seconds; I get basically the same result with either 1 sec or 0.1 sec
tstep = 1.0

# air drag parameters; CD and sectional area are
# selected arbitrarily - they can vary enormously
# depending on the skydiver's pose.
rho = 1.225 # kg/m^3
cd = 0.4 #
area = 0.6 # m^2
mass = 80 # kg

# quick switch between the vacuum case and the air drag case
tunnel_has_air = True

while True:
# Gravity's the easy part; if we pretend
# Earth is constant density, then g is linearly
# proportional to altitude.
# This would break if altitude goes above Earth's surface,
# but it doesn't in this sim.

gravity_accel = 9.81 * alt / radius
vel -= gravity_accel * tstep

# Compute air drag
if tunnel_has_air:
drag = cd * area * 0.5 * rho * vel * vel # force
decel = drag / mass

# get the sign right
if vel > 0:
vel -= decel * tstep
else:
vel += decel * tstep

# Fall
alt += vel * tstep

# Update time
t += tstep

print "t %.1f altitude %.3f km velocity %.2f m/s" % (t,alt/1000.0, vel)

# When we get to within a decimeter of the center, we can stop
if alt < 0.1:
break

• Comments are not for extended discussion; this conversation has been moved to chat. – called2voyage Aug 28 '19 at 20:14
• "a figure which is suspiciously close to circular orbit velocity, by the way." In fact, the same constants, like G, earth's mass, earth's radius go into both situations (tunnel falling vs orbit) and the final equations use them in exactly the same algebraic forms. So, not suspiciously close, but mathematically identical... – DJohnM Aug 28 '19 at 22:52
• @DJohnM And StarMan's 11km/s figure, which is what you get if you assume constant gravity the whole way down, instead of decreasing, is exactly √2 times that, and is the same as Earth escape velocity. – Russell Borogove Aug 28 '19 at 23:21

In terms of gravity, there will be no force (ish). This is a consequence of the shell theorem, which states that inside a sphere of constant density the shell of the sphere exerts no gravitational force. Now, some caveats:

1. Earth is not a perfect sphere, but it's so close to one for our purposes that it doesn't matter
2. Earth is not constant density. Ignoring things like random rocks in the mantle, though, we might consider Earth to be made of thin shells of constant density, at least to a first order approximation.

So all this says that the force of gravity is zero ideally, negligible in practice. But as others have said, just about everything else will kill you :-P

Welcome to the site!

1. Nope. The deepest the human race has gotten is the now-defunct Kola Borehole, which didn't even make it through the crust. Though the crust is thinner at the ocean floor, that presents its own challenges.

2. Pressure and heat, mostly. You've got ~6*10^24 kilos of (mostly) iron above you at around 5000 degrees C and ~3e6 atmospheres. If you can stave off either of those, you've got some technology I've never heard of.

Regardless, it sounds like you're trying to develop a gravity train