# B Coriolis problem - Point mass movement upon release from earth

#### zanick

Summary
How long would a point mass take to reach the equator if released at a position on the 45th parallel?
If there was no atmosphere and a point mass was released at the 45th parallel and able to counteract the centripetal force of gravity (hovering 10ft off the surface), how long would it take before it ended up at the equator.

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#### olgerm

Gold Member
What are its initial velocity and ecxact initial position(also height)?

#### zanick

10ft off the ground... and no added momentum.

#### olgerm

Gold Member
Never. It would just fall to ground. effect of corialisi force is very small and is not directed towars equator. it only affects pointamsses longitude not lattitude.

#### A.T.

Added to what? State the initial velocity and the reference frame it is measured in.

#### jbriggs444

Homework Helper
Summary: How long would a point mass take to reach the equator if released at a position on the 45th parallel?

If there was no atmosphere and a point mass was released at the 45th parallel and able to counteract the centripetal force of gravity (hovering 10ft off the surface), how long would it take before it ended up at the equator.
Forever. It will stay in place. The geoid is not a sphere.

• vanhees71

#### zanick

Never. It would just fall to ground. effect of corialisi force is very small and is not directed towars equator. it only affects pointamsses longitude not lattitude.
I mentioned that the object was hovering... not in contact with the earth. (say it was hovering with small jets only counteracting the centripital force due to gravity)
actually, coriolis can effect objects in motion east or west toward the equator. (makes objects deflect to the right in the n-hemisphere)
Forever. It will stay in place. The geoid is not a sphere.
why will it stay in place? when it leaves the ground it will be retaining the momentum (as measured from the inertial reference frame) it will remain in a curved path due to the centripetal force / thrust balance (i.e. maintained altitude) but will take a southbound path (as seen from the non inertial frame of reference) . If we assume a sphere and not a geoid, how does that change the thought experiment? (let's ignor elevation changes and gravitational variations and assume a sphere)

#### zanick

Added to what? State the initial velocity and the reference frame it is measured in.
from the inertial reference frame, its initial velocity is 500mph. in the non inertial reference frame, its has no velocity.

#### jbriggs444

Homework Helper
I mentioned that the object was hovering... not in contact with the earth. (say it was hovering with small jets only counteracting the centripital force due to gravity)
actually, coriolis can effect objects in motion east or west toward the equator. (makes objects deflect to the right in the n-hemisphere)
why will it stay in place? when it leaves the ground it will be retaining the momentum (as measured from the inertial reference frame) it will remain in a curved path due to the centripetal force / thrust balance (i.e. maintained altitude) but will take a southbound path (as seen from the non inertial frame of reference) . If we assume a sphere and not a geoid, how does that change the thought experiment? (let's ignor elevation changes and gravitational variations and assume a sphere)
It is motionless in the rotating frame. Zero coriolis force. The hovering force exactly counters the force of "gravity" which is not radial but is, by definition, vertical -- normal to the geoid.

• vanhees71

#### zanick

It is motionless in the rotating frame. Zero coriolis force. The hovering force exactly counters the force of "gravity" which is not radial but is, by definition, vertical -- normal to the geoid.
correct, BUT we know that gravity (and the balance mentioned for hovering) will allow the object to be "forced" to rotate ….we know this because its path is circular and there for has an acceleration due to the change of velocity (not magnitude but direction) and that force id 90 degree inward... centripetal. Now, how does a point mass traveling to the right on the sphere in the non inertial reference frame, not travel southward because it would now be traveling in a straight line from the non inertial reference frame? I guess the same reason might be due to why you cant orbit around the tropic of cancer .

#### A.T.

• vanhees71 and jbriggs444

#### zanick

It's a thought discussion. assume a sphere. also, Coriolis would effect that point mass if it had an apparent deflection (verse its previous path) based on the sphere's spin.

#### jbriggs444

Homework Helper
It's a thought discussion. assume a sphere. also, Coriolis would effect that point mass if it had an apparent deflection (verse its previous path) based on the sphere's spin.
A point mass which is motionless in the rotating frame experiences zero Coriolis force in the rotating frame.

A point mass which is not subject to gravity will fly away in a straight line, escaping to infinity.

A marble rolling on the surface of a hypothetical perfectly spherical Earth will roll downhill toward the equator.

#### zanick

Thanks Jbriggs.. I'm having a hard time with the point mass or marble that is not touching the sphere, not starting to move toward the equator even if it has a 0 velocity in the rotating frame. could it be related to the impossibility of an artic orbit?

#### A.T.

I'm having a hard time with the point mass or marble that is not touching the sphere, not starting to move toward the equator even if it has a 0 velocity in the rotating frame.
On a sphere it will drift towards the equator.

#### jbriggs444

Homework Helper
Thanks Jbriggs.. I'm having a hard time with the point mass or marble that is not touching the sphere, not starting to move toward the equator even if it has a 0 velocity in the rotating frame. could it be related to the impossibility of an artic orbit?
Centrifugal force on a spherical earth causes an equator-ward drift. The impression from the point of view of a person standing on such a hypothetical planet is that it slopes [very slightly] downward toward the equator. On the real Earth, the geoid bulges upward at the equator, exactly cancelling this, so that the marble stays in place.

#### Janus

Staff Emeritus
Gold Member
correct, BUT we know that gravity (and the balance mentioned for hovering) will allow the object to be "forced" to rotate ….we know this because its path is circular and there for has an acceleration due to the change of velocity (not magnitude but direction) and that force id 90 degree inward... centripetal. Now, how does a point mass traveling to the right on the sphere in the non inertial reference frame, not travel southward because it would now be traveling in a straight line from the non inertial reference frame? I guess the same reason might be due to why you cant orbit around the tropic of cancer .
If you cancel gravity completely than the object travels in a straight line and fly off into space. From the frame of the person standing on the surface, this will appear to be a curved trajectory(Coriolis effect).
To have it "hover" a fixed distance above the ground (assuming a spherical Earth), Then you need to just cancel enough gravitational pull to allow it to "orbit" the Earth at the tangential speed it has at the 45th parallel.
You would also have to insure that the thrust is always oriented towards the center of the Earth.
Such a "forced orbit" would follow a great circle.
The orbit would have a period of just under 34 hrs, and the object would take just under 8.5 hrs to reach the Equator.
Coriolis effect comes into play when you trace this trajectory against the rotating surface of the Earth; the object will tend to "drift" relative to to surface of the Earth.

• jbriggs444