We are spinning about a 1000miles per hour on the surface of the Earth. How much does this spin lessen our weight than if the Earth was not spinning?
Thank you
I googled and got lucky:
The radius of the Earth at the equator is 6378137 meters, so each sidereal day (86164 seconds) you travel 40075017 meters (circumference) for a tangential velocity of 465 m/s (1038 mph) on the equator. Scale that by the cosine of your latitude for anywhere else (spherical approximation).
Your centripetal acceleration (v^2/r) at the equator i 0.034 m/s^2 at the equator, or 0.35% of 1 g (9.8055 m/s^2).
So your weight is about 0.35% less than without rotation at the equator. At 40 degrees latitude, it’s 0.20% less.
edit: Yay! My numbers are close!
Um, what’s the definition of ‘weight’ in use here?
You bet it does. And it was that very centrifugal force (yeah, I know, a pseudo-force) that allowed Loránd Eötvös (Wiki him; it’s a great experiment) to show the equivalence between inertial and gravitational mass which had previously been more or less assumed.
It certainly does decrease the force yiou feel at your feet of your weight pulling down (centrifugal force is, after all, a “fictitious force”, the result of our viewing our rotating frame of reference as a stationary one)Centrifugal force - Wikipedia
The same effect works on the earth around us, as well, with the result that the ground and water bear the effects of the interplay of gravitational force and the centrifugal effect, with the result that the ground and water appear perfectly perpendicular to the way things fall, even though such a perpendicular won’t pass perfectly through the center of the earth (unless you’re at the equator or one of the poles).
I wonder if this effect is significant enough (as in enough) to give an edge to a high or long jumper who is competing at or near the equator. Quick estimate indicates that we would be talking about a quarter of an inch or so, which probably would be washed out by various other factors.
xkcd covered that a while back xkcd: Local g
Most of the difference is due to the shape of the Earth though, and not centrifugal force, unless you want to quibble that the shape of the Earth is also a result of the centrifugal force.
As a semi-related aside, in some sense, the Mississippi River flows uphill. That is to say, the mouth of the river is further from the center of the Earth than the head is.
Thank’s. You’ve just made my brain hurt.
Huh. never thought of that. So is it the spinning of the earth that makes it flow?
No. The difference in elevation above sea level between upriver and the mouth does, just like you thought. Remember, some rivers flow AWAY from the equator, too. The Earth may be an oblate spheroid, but the surface is wrinkled (mountains, etc), which influences the local motion of surface water far more than minor differences in gravitational strength, or centripetal acceleration. “Sea Level” actually reflects the oblate spheroid shape, too, disregarding tides. In the same sense that Chronos was talking about, a seaport on the Equator is “higher” than one on the Baltic, although they are both approximately at sea level.
BTW, note the word “approximately”. I don’t want to get into a discussion of the small gradients between oceans, which is much smaller than the difference between the polar and equatorial diameters of the Earth.
No, enipla had it right: It is the rotation of the Earth that causes the flow of the Mississippi. It’s also the rotation of the Earth that causes the oblateness of the shape, but that doesn’t mean that it’s wrong.
And locally, like on the scale of determining which channel the river follows, it is the wrinkles in the shape of the surface that matter, but on a scale of the whole river, those are insignificant compared to the oblateness and centrifugal force.
Yeah, I did some calculations on the subject a while back. The oblateness results in a large force along the earth’s surface in the northward direction, the Earth’s rotation causes an equally large force along the surface in the southward direction, and the height of the river’s source above sea level causes a small force southward. The conflicting forces of oblateness and rotation are almost 100 times greater than the force caused by altitude differences relative to sea level.
OK, I’ll be damned, although I find it hard to believe. Then how come the Nile flows away from the equator, opposite the direction of the Mississippi in the same hemisphere? It arises near the equator, and flows generally northward, feeding the Med at about 30 N. Or the Parana, which also flows away from the equator in more temperate latitudes (south in the southern hemisphere). And in general, a look at a map of the major rivers of the world doesn’t appear to me to bear this out. You find them flowing in all sorts of various directions, seemingly in conformance with topographical features. If the oblateness and centrifugal force were the overriding features, I’d expect a map of the major rivers to show a pattern illustrating it.
Accepting the information given by others the conclusion must be:
It’s the oblateness and rotation that causes sea-level to be what it is. Without the spin, sea level would be different, and the Mississippi would run the other way, because sea level would differ in such a manner as to make the end higher than the origin.
The Nile however has a steeper course overall and would run the same way, only faster.
Oh, I see what you mean. The effects of oblateness and centrifugal force cancel each other out, allowing rivers to flow in whatever direction the local topographical features direct. However, for rivers that flow towards the equator (in either hemisphere), this means that the river will be flowing “uphill” in the sense that the mouth of the river is further from the center of the earth than the source of the river is - meaning that if the earth were magically not rotating, but still retained its oblate shape (I said “magically”!) the river would flow the other way.
For rivers that flow away from the equator, removing the rotation would leave the direction of flow unaltered (but the speed of flow would vastly increase).