The discussion centers around the effects of Earth's rotation on objects that leave the ground, specifically addressing the conditions under which a stone would no longer follow the Earth's rotation and the implications of jumping or being airborne. Participants explore concepts related to orbital mechanics, gravitational effects, and the behavior of the atmosphere in relation to Earth's rotation.
Participants express differing views on the mechanics of jumping and its effects on following the Earth's rotation, with no consensus reached on the implications of these actions. The discussion also includes competing explanations for why the atmosphere rotates with the Earth, indicating a lack of agreement on the underlying principles.
Some claims depend on specific assumptions about altitude, speed, and the effects of gravity and atmospheric drag, which remain unresolved. The discussion includes various interpretations of motion and reference frames that may not be fully clarified.
maverick_starstrider said:The second the rock leaves the ground it is no longer following the Earth's rotation.
Really. The minute you leave the ground, you are following a path independent of the Earth's rotation. You actually follow an orbital path which intersects the surface of the Earth. Even if you jump straight up, you will not come back down exactly where you jumped. For low height jumps, you will not notice any difference, but as you increase the height of the jump the difference will increase.Bjarne said:So when jumping I am not following the Earths rotation ? Really?
How can we calculate ?
But do not confuse this with following a path independent of Earth's gravitational pull.Janus said:Really. The minute you leave the ground, you are following a path independent of the Earth's rotation.
DavidSnider said:If I were in a stationary position in space and looked at a jet traveling 1000MPH on Earth would it appear to be fixed in place?
DaveC426913 said:assuming by 'fixed in place' you mean 'in your line of sight as the Earth turns under it', yes.
maverick_starstrider said:well no, generally when we say that a plane is going 1000mph we're implying that we mean RELATIVE to the surface of the earth.
Not unless you jump straight sideways you aren't!maverick_starstrider said:when you feet leave the ground you are veering on a path that is tangentional to the rotating path you were taking when your feet were on the ground...
russ_watters said:Not unless you jump straight sideways you aren't!
When you are standing still on the ground, your direction of motion is tangential to the rotating path of the surface of the earth. When you jump, your direction of motion is some angle above the tangent. Not a big angle, but an angle, nonetheless.
Without the atmoshpere, the stone traveling east at the equator would orbit the Earth faster than the Earth rotates until it's at an altitude of 35,786 km == 22,236 miles above ground, where the orbital rate would match up with the surface of the earth:Bjarne said:I mean in which altitude will the stone will no longer be able to follow the earth’s rotation.
What?Bjarne said:Which law of nature is responsible for that the atmosphere follows the Earth's surface?
Density off course, - but which equation?
Right...russ_watters said:I think he's asking why the atmosphere rotates with the earth.[quote fixed]
If the atmosphere were not rotating with earth, there'd be aerodynamic drag causing it to speed up and rotate with the earth.
I mean aerodynamic drag! It's the thing that pushes your hand back when you stick it out the window of a moving car.Bjarne said:What do you mean: "aerodynamic drag".
If you could "stop" the atmosphere rotating, then the wind speed at ground level near the equator would be about 1000 mph. It would rip anything and everything off the ground, but in so doing, those things would slow the wind down a little. And even after the Earth was swept mostly smooth in those first few seconds, there'd be friction between the wind and the ground. A lot of friction. It would take only minutes for the wind at ground level to lose most of that speed. Then viscous friction between molecules in the air would eventually slow the rest of the atmosphere. Would it take days or weeks? I don't know. But it wouldn't be a very long time. It certainly wouldn't be years.Lets image we could stop the atmosphere rotating, - and push the STOP.
How fast would it begin to rotate again after pushing START ?
Janus said:Really. The minute you leave the ground, you are following a path independent of the Earth's rotation. You actually follow an orbital path which intersects the surface of the Earth. Even if you jump straight up, you will not come back down exactly where you jumped. For low height jumps, you will not notice any difference, but as you increase the height of the jump the difference will increase.
Janus said:It takes some orbital mechanics. First you have to determine the properties of the orbital path you take from the initial speed of your jump and your linear velocity at your latitude due the Earth's rotation. Then you need to calculate the time it takes for you to travel the segment of your orbit from when you left the surface to when it intersects the Earth again. You will also need to calculate how many degrees of on orbit you traveled. Compare this to the number of degrees the Earth turned while you were "in the Air". Use the difference between the two and the radius of the Earth to find the distance between the point you jumped and the point where you landed.
Red_CCF said:so what is the difference between Earth's rotation and an orbital path?
Red_CCF said:I didn't quite understand what you meant by the orbit intersecting with the Earth
[/URL]Janus said:In the following image the green circle is the surface of the Earth, the red dot its center, and the black ellipse the orbital path. The Earth is rotating clockwise.
As you jump up, you are moving up and to the right with with the Earth. This puts you in a path that is an ellipse with one focus at the center of the Earth. We are concerned with the part from when you leave the surface to when you return to the surface. This is the part of the ellipse outside of the green circle.
http://home.earthlink.net/~parvey/sitebuildercontent/sitebuilderpictures/jump.gif
Red_CCF said:Thanks for the reply
I didn't quite understand the diagram. When you jump shouldn't you have the same linear velocity as the Earth so you would end up landing at the same spot but in that diagram it is more like a projectile motion where the object traveled faster than the Earth's rotation. Also I thought that the center of ellipses were at the center of the Earth but that does not seem to be the case in that diagram. I think I'm misunderstanding the diagram somehow, can you clarify some of my misconceptions? Thanks for any help that you can provide
Janus said:I modified the diagram to illustrate the point better. The diagram shows the view from someone not sharing the Earth's rotation. The angle between the red lines is how much the Earth rotates while you are in the air. Note that it rotates a bit more than the arc you travel from jumping to landing.
As to the ellipse, you are mistaken. The center of the Earth would be located at one of the foci of the ellipse, not its center. It is an orbital trajectory, and this is a property of elliptical orbits.
Here's a little on elliptical orbits:
http://www.windows.ucar.edu/tour/link=/physical_science/physics/mechanics/orbit/ellipse.html