Coriolis problem - Point mass movement upon release from Earth

[A.T.]

Rotating planet assumes oblate ellipsoid shape, and freezes in
that shape. The planet stops rotating and the surface becomes
frictionless. Put a mass on the surface at a point between the
equator and a pole, heading straight east at the speed the surface
had at that point when the planet was rotating. The mass keeps
moving in the same direction, but gravity pulls it into a great ellipse
around the center of the planet, heading for the equator.

Wrong, for the reason explained in the post right above yours. Stopping the rotation of the planet doesn't matter if it is friction less and keeps the flatten shape. It's just a pointless obfuscation.

 

[Jeff Root]

Can you explain why the path of the mass curves around
the pole instead of continuing in the same direction?

-- Jeff, in Minneapolis

 

[A.T.]

Can you explain why the path of the mass curves around
the pole instead of continuing in the same direction?

-- Jeff, in Minneapolis

See post #66.

 

[Jeff Root]

That's what I asked you to explain. What is this mysterious
component of Newtonian gravity that is "parallel to the local
surface"? Where does it come from?

-- Jeff, in Minneapolis

 

[jbriggs444]

That's what I asked you to explain. What is this mysterious
component of Newtonian gravity that is "parallel to the local
surface"? Where does it come from?

It comes from the fact that the surface is tilted. It is not perpendicular to a line drawn to the gravitational center of the Earth.

Because the surface is tilted, a force directed toward the center of the Earth has a component parallel to the surface.

Note that the small discrepancy between the "gravitational center of the Earth" and the "geometric center of the Earth" is unimportant here. The tilt of the surface is the important bit.

 

[russ_watters]

Now that's funny! I know, they see flat, so therefore its flat. I think they are serious too. They had one observation on the salton see of a guy holding a mirror (tipping up and down) and then a person on the opposing shore at 19miles away who saw the reflection and caught it on camera. refraction didn't seem like it could account for 150+ft of something being hidden by calculated curve... so , maybe it was one of the "flat spots" on the earth. ;)

The allowable distance between two objects of a certain height is twice the distance to the horizon. Two observers need only to be about 60' off the ground to see each other at 19 miles (horizon distance: 9.5mi).

Anyone who has ever been out in the ocean or a large lake with a decent pair of binoculars can see this phenomena, so there's just no excuse for not accepting it.

 

[A.T.]

That's what I asked you to explain. What is this mysterious
component of Newtonian gravity that is "parallel to the local
surface"? Where does it come from?

It comes from the orientation of the geoid surface relative to Newtonian gravitation. As already explained, the geoid is shaped this way per definition .

 

[Jeff Root]

That's what I asked you to explain. What is this mysterious
component of Newtonian gravity that is "parallel to the local
surface"? Where does it come from?

It comes from the orientation of the geoid surface
relative to Newtonian gravitation.

I don't see it. The net gravitational force is toward the
opposite hemisphere. That is the opposite of what you are
claiming.

The diagram shows a cross-section through the Earth with the
axis of rotation vertical and the equator horizontal. The blue
arrows are vectors of gravitational strength at the surface.
Red arrows are vectors of "centrifugal force". Green arrows are
vectors of the net downward force. This net force is everywhere
perpendicular to the surface, so the surface is "level". There
is no gravitational force parallel to the local surface. No
force that can make a loose, frictionless object travel around
the nearest pole instead of around Earth's center.

Notice that the green vectors point toward locations on the axis
in the opposite hemisphere. The net force is deviated away from
Earth's center toward the equator, not toward the nearer pole.

-- Jeff, in Minneapolis

 

[jbriggs444]

View attachment 253614

You forgot to draw the normal force. If you are going to do a free body diagram, draw all the forces.

 

[FactChecker]

The surface of the Earth has always been under the influence of gravitational attraction and centrifugal force. The Ocean surface and the land surface (especially while still hot and molten) was free to flow toward the Equator if there was a net force in that direction. It piled up toward the Equator to form the shape that we have today. When the centrifugal force component toward the Equator was exactly balanced by the increased height toward the Equator, the surface shape stopped changing. I am ignoring local density differences and Lunar tides. Today, something that is constrained to follow the shape of the Earth's surface will, likewise, not want to move toward the Equator.

 

[A.T.]

View attachment 253614

There is no gravitational force parallel to the local surface.

The blue arrows are Newtonian gravitation, and they are not perpendicular to the surface, so they do have a component parallel to the local surface.

If you want to talk about net force and movement, you have to state the reference frame. See posts #59 and #68 on how to do this.

The net force in either frame includes the normal force from the surface, which is missing in your diagram.

 

[A.T.]

I don't see it.

This might help:

The description was already posted:

From the rotating frame: The object is at rest. There is no Coriolis force. There is still a gravitational force toward the Earth's center. There is a centifugal force outward from the Earth's axis. The two are not parallel. However, the Earth's surface is sloped just right so that the resultant of the upward normal force, the downward gravitational force and the outward centrifugal force is zero.

From the inertial frame: The object is in motion. It is following a circular path that moves with a point on the Earth's surface. The gravitational force is toward the Earth's center. The centripetal acceleration is toward the Earth's rotational axis. The two are not in parallel directions. However, the Earth's surface is sloped just right so that the resultant of the upward normal force and the downward gravitational force accounts for the centripetal acceleration.