Questions of Gravity

You Weigh More On A Mountain, Due To Mountain Mass...

...than you would at the same geoid elevation without a mountain under you.

The ocean is very lumpy compared to an ellipsoid, it just does not affect boats very much.

Then again the ocean is very smooth compared to a geoid.

Paul in PA

You Weigh More On A Mountain, Due To Mountain Mass...

Thanks, Paul. Here's another one:

Do you weigh more as you approach a center of gravity? Theoretically, as you drilled toward the center of the earth, would you be pulled apart or squashed into a dense ball?

Dave

Assuming There Is A Hole Through The Center Of The Earth

If you jumped into said hole, as you approached the center of the earth you would be affected by the mass above you but you would also be decreasing the distance to the center of mass below you.

At the center of the earth the center of mass above and below you will be equal and you will weight nothing. However you will have considerable velocity and as you ping ponged up and down, you would barf your guts out and subsequently have considerably less mass.

Paul in PA

You Weigh More On A Mountain, Due To Mountain Mass...

I don't think the answer is that easy.
Is this a cotton mountain or solid granite?

A more realistic comparison would be sandstone and granite. 🙂
I used extremes to illustrate the point.

You Weigh More On A Mountain, Due To Mountain Mass...

So that is why it's so hard to get to the mountaintop.

You Weigh More On A Mountain, Due To Mountain Mass...

> Then again the ocean is very smooth compared to a geoid.

The geoid is based on the gravitational pull. It seems to me that the ocean would follow the geoid if it were calm and no waves were present. It could not get any more "smooth" than the geoid. And due to waves and the constant change in tides, it can never be that smooth. (or am I missing something?) I guess the "geopotential" at the surface of the ocean would be more consistent than along the surface of a land mass because of the changes in density of the land mass...but I have trouble with thinking of it as more smooth than the geoid (ie it would follow the geoid).

Assuming There Is A Hole Through The Center Of The Earth

:good: 😀

The old thing you learned in physics about the force of gravity being inversely proportional to distance squared only applies outside the body producing the gravity. Inside, Paul has it right that some of the mass is pulling you up as well as some pulling down.

Do you weigh more or less on top of a mountain? Less than at the base of the mountain but more than you would on a tower the same height as the mountain.

How is the gravity of the earth's surface measured? C&GS/NGS has used machines made for that purpose. The old ones were clumsy to transport to positions on the earth to make the measurements. They measured the time for an object to fall or the time for a pendulum to swing. The new one is flown as part of the GravD program.

How is equipotential determined? An equipotential is a set of points where the gravity is the same.

Why aren't the oceans as "lumpy" as a Geoid? They are just as lumpy, plus the effects of waves and currents. Since the variation of gravity is gentle versus location, you have to compare gravity or heights above the ellipsoid at positions many miles apart to find a difference.

Assuming There Is A Hole Through The Center Of The Earth

Thanks, Bill.

"... only applies outside the body producing the gravity."

There's probably a formula with a limit to figure gravity as a function of distance between surface and center of body. That would be an interesting graph.

Dave

Bill,

"An equipotential is a set of points where the gravity is the same."

But if gravity was more or less than the previous location's measurement, wouldn't the equipotential be above or below you, and how would you calculate the exact distance? What sort of grid is used to gather this data? And of course there needs to be a starting point, some Vertical Datum, to bench against.

Dave

You Weigh More On A Mountain, Due To Mountain Mass...

Tom,

One explanation I saw envisioned a trench cut from the ocean to wherever you are, and the level of the water would be the Geoid. So in spite of the sophistication of our measurement methods, we're still basically using the Roman water level. 😉

Dave

Gravity is affected by the density of the underlying mass, it isn't necessarily a matter of elevation. There are places on this planet where water flows uphill.

An Equipotential surface is defined as a surface who's points are normal to the direction of gravity. There are gravity stations all over the world and points in between are interpolated. This leads to tons of anomalies. Hopefully this new Grav-D thing will give us a more accurate model.

The Oceans are not an equipotential surface, they are affected by salinty levels and sub surface topography.

Ocean surface topography

says up to 2 m variation around the world. I seem to recall that the west coast is higher than the east coast...let's see. The Permanent Service for Mean Sea Level says that the Pacific is about 20 cm higher due to the water being less dense and "weather and ocean conditions."

> Ocean surface topography
>
> says up to 2 m variation around the world. I seem to recall that the west coast is higher than the east coast...let's see. The Permanent Service for Mean Sea Level says that the Pacific is about 20 cm higher due to the water being less dense and "weather and ocean conditions."

Hi Melita, Sea Surface Topography (SST)
The way I understand from Vanicek: SST is caused by sea dynamics and by prevailing meteorological phenomena(Montgomery 1937). Its magnitude is less than 2 m and when taken naturally, as the elevation of MSL above the geometrically defined geoid, it has generally a negative sign in polar regions and a positive sign in the
tropical belt.

> Ocean surface topography
>
> says up to 2 m variation around the world. I seem to recall that the west coast is higher than the east coast...let's see. The Permanent Service for Mean Sea Level says that the Pacific is about 20 cm higher due to the water being less dense and "weather and ocean conditions."

:good: :good:

Ralph,

"The Oceans are not an equipotential surface, they are affected by salinity levels and sub surface topography."

I never thought about salt. I suppose any chemical mixture would differ in density.

I've always thought of the ocean's surface as "smooth", as being only affected by tides and storms, but I guess I need to change that thinking. After all, if water had greater mass than rock, we'd never see surface water.

Dave

Thanks for the links, Melita!

My Bookmarks Folder is bursting! A couple of days reading, at least.

With a little application to study, I'll soon bestride Geodesy like a Colossus! 😀

Dave

Ralph,

Also, somewhere I was reading that MSL varies up the West Coast USA inversely to the East Coast USA.

Dave