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Because as you get farther away from Earth's center, the gravitational force between you and Earth weakens.

To understand the gravitational force experienced by an object (such as a space craft) due to another object (such as the earth), we may look to Newton's Universal Law of Gravitation.

F = G*(m1 * m2) / r2

Where:

F = Force of Gravity between object 1 and object 2

G = Universal Gravitational Constant (was found with a lot of experiments)

m1 = The mass of object 1

m2 = The mass of object 2

r2 = The squared distance between object 1 and 2 (spacecraft to centre of earth - centre is used as an average, in actual fact you'd have to get in to differential equations to correctly account for the non-uniform distribution and changing of mass of Earth)

If you actually work it out, you'll find that the force due to gravity you'll experience on the top of a mountain versus sea-level will be marginally less. Like, irrelevantly.

What? You want me to explain more? Sigh. Okay.

mass of earth (m1) is approx. 5.9742 × 1024 Kg

mass of a person (m2), let's assume it to be 80 Kg

G = 6.674×10−11 N m2 Kg−2

r1 = radius of earth (sea level) 6378.1 Km

r2 = radius of earth + height of Mt Everest 6378.1+8.85 = 6387Km

F1 (gravitation force experienced @ sea level) = [6.674×10−11 N m2 Kg−2 * 5.9742 × 1024 Kg * 80 Kg] / (6378100m)2

F2 (gravitation force experienced @ top of Everest) = [6.674×10−11 N m2 Kg−2 * 5.9742 × 1024 Kg * 80 Kg] / (6387000m)2

delta(F1,F2) = (1/(63870002)) - (1/(63781002)) [factored out the common stuff]

delta(F1,F2) = 4.079377*10-13 - 4.068*10-13

delta(F1,F2) = 1.1377 × 10-15

For contrast, the number of cells in the human body is considered to be of the order of 10 trillion cells (1012).

So, the difference is the same difference as taking 100 (102) human bodies, counting all the cells (sea level) and then adding one more cell (top of everest).

That's "engineering" speak for, there's no realistic difference.

Now, if you start computing the actual net gravitational force you experience, you'd need to dive in to far more interesting math. You'd need to consider other planetary bodies, other mountains, the mountain your own and so on. That'd nevertheless be remarkably pointless as everything's moving and the net force can be very very closely approximated with Newton's Law of Gravitation, without getting in to math that makes physics professors salivate and people with jobs weep.

This then leaves the question of why things in space float? Thing is, they don't at all. They only seem to. The force of gravity between earth and that spaceship I mentioned is going to be VERY similar to the force experienced between the two at sea level. The key is that as the spaceship is in free fall towards the planet, it also moves (VERY fast) tangent to the planet's surface. It works out that the tangent ("straight") distance traveled by the spaceship is largely cancelled out by how far it falls towards the planet. Not a great explanation, but I'm right.

Phew, I think I can rest easy, for now.

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Why does Mercury and Mars have less gravity than Earth?

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Is there more or less gravity on Mercury than Earth?

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