Is gravity higher or lower on a mountaintop?

Question

On the top of Mount Everest versus bottom of the Mariana Trench, which would you feel the strongest gravity? I would think the Mountaintop would feel weaker because you are farther from the Earth's center but then again you would have more mass underneath you.

Answer 1

I see your concern, and how you think this might be a contradiction. The other answerers are giving the correct answer, but they are overlooking half of your question.



Remember that the simplest form of Newton's law of gravitation ONLY applies to what are known as POINT MASSES. That is to say, objects that are SO SMALL geometrically, compared to how far apart they are spaced.



It is a problem of CALCULUS to officially determine anything else.



And indeed, there are people who have proven that in the case of external points of SPHERICALLY SYMMETRIC bodies, you can officially "get away with" treating the bodies as if they are point masses. There is a calculus proof to this, that is a common problem in a college sophomore level class of multivariable Calculus.





Earth certainly isn't a point mass.



And neither is Earth, a spherically symmetric body. Earth is approximately spherically symmetric, and for most purposes, you can get away with such an approximation.



The material that makes up MT. Everest, certainly isn't spherically symmetric with the rest of Earth

And neither is the material that makes up the ocean. In fact, at the bottom of the Marianas Trench, the ocean mass immediately above, would actually be pulling up on you.





None of this really is that significant. And I can make a density argument as to why.



The Earth's greatest density is in its CORE layers. And this density is much less in the mantle and crust.



In terms of water's density being defined as 1 gram/cm^3, here are the relative densities of each layer.

Inner core: 13 gram/cm^3 (0 to 19% of Earth's radius, 2% of Earth's total mass)

Outer core: 11 gram/cm^3 (19% to 55% of Earth's radius, 30% of Earth's total mass)

Mantle: 5 gram/cm^3 (55% to 98% of Earth's radius, 51% of Earth's total mass)

Crust: 2.5 gram/cm^3 (final 98% to 100% of Earth's radius)

Ocean water: 1.03 gram/cm^3

https://upload.wikimedia.org/wikipedia/commons/8/89/RadialDensityPREM.jpg



Mountains are primarily made out of crust-like material. Therefore, the local factors will be much less significant than the bulk factors. 82% of Earth's total mass is in the interior layers, and is much denser than Mt Everest.



So my assessment is definitely that there is less gravity at mountain tops, and more gravity at deep ocean depths. Local factors are assumed negligible.

Answer 2

Gravity is lower the farther away you get from the center of the object. The force of gravity is defined as



F= G*(M₁*M₂)/r^2



Where F is the force of gravity, G is the gravitational constant, M is the mass of the object, r is the distance between the centers of mass.



This means that the farther the two object's centers of mass are from each other the less the force of gravity is.

Answer 3

Yes.



It's at a higher altitude but at a lower field strength...ar, ar, ar.



On ME, roughly 25,000 ft, the g = 9.786 N/kg, which is a bit less than the nominal 9.81 N/kg for the sea level average.



In the MT, roughly 36,000 ft (11,250 m below sea level), g = g0(1 - 2 (r/R)^2 + (r/R)^3) = 9.81*(1 - 2*(11.3/6380)^2 + (11.3/6380)^3) = 9.8099, not much change. And you can see why, r = 11 km below sea level is not very deep into the R = 6380 km radius of Earth; so not much mass is removed. [See source.]



But you are right...g is weaker in both directions and for the reasons you mention. If you bored down to the center of Earth, a depth of r = 6380 km, the gravity field strength g = 0. Can you see why?

Answer 4

large ocean depths are no longer at greater gravity or decrease gravity, a minimum of no longer heavily. Water tension isn't gravity. Rocks on the backside of the sea nonetheless adventure 9.8 N/kg of gravity as do rocks on land. And definite gravity does decelerate the passage of time, as an observer in a nil-g-ecosystem inertial reference physique could word. no longer by any important volume does it ensue for Earth, inspite of the actuality that verbal substitute satellites are calibrated for generic relativistic outcomes...basically in case.

Answer 5

lower = the strength of this field at any given point is proportional to the planetary body's mass and inversely proportional to the square of the distance from the center of the body.



http://en.wikipedia.org/wiki/Gravity#Earth.27s_gravity



edit 16 hours later = i see this question attracted people with much more credentials then myself and a bug much farther up their "you know what " then i do. hahaha