I rarely disagree with the venerable Cecil Adams (in fact this is the first time), but I don’t understand the answer to the question of whether a fired bullet or dropped bullet would hit the ground first. He states that a bullet fired far enough would take longer to drop because of the curvature of the earth. What is this, Newtonia? I thought general relativity stated that the bullet would follow a curved path due to the gravity of the earth. Thus the bullet would hit the ground at the same time no matter what it’s initial velocity is upon leaving the gun. Therefore, if one could actually fire a bullet fast enough to leave the earth’s orbit, if this bullet were fired perfectly straight, couldn’t it circumnavigate the globe and hit the shooter in, say, the back of the foot, without ever traveling in anything but a perfectly straight line?
Or is there nothing more to gravity than the fact that it pulls stuff (including light) down.
Would that take into account the Earths orbital motion,the momentum of the whole Solar System,galaxy,local galactic cluste and of course the more scattered gravitational effects of the various physical bodies within the S.System?
The situation is sufficiently close to your “Newtonia” as to make no difference. For all practical purposes relativistic concerns don’t apply given the speeds involved.
If the bullet is fired fast enough it will go into orbit and (if we ignore air friction) never land (if we continue to ignore air friction, then if it is fired at just the right speed that orbit will cause it to come around and hit you in the back if you don’t duck ). If it is not quite fired fast enough then the orbit will slowly decay until it intersects the earth (i.e. the bullet lands). It will clearly take longer for that to happen than if the bullet falls straight toward the earth. The fact that the bullet is following a geodesic (“straight line”) according to general relativity is irrelevant.
Air friction will make it land a lot faster than if the bullet was shot in a vacuum, but the principle still applies.
I note that it conveniently avoids mention of the complications introduced by air. Though high school physics tends to encouarge simplifying assumptions, it’s a trifle naive to think that the effect of air would always be exactly equal in the case of a dropped and a fired bullet.
In fact, using the simplest (non-zero) model for air resisitance, the effects won’tt be exactly equal for the dropped and fired bullet. Air resistance is approximately proportional to the square of the speed of a moving object, so the horizontal and vertical motions of the bullet are not entirely separable. The fired bullet will actually have a greater vertical force from air resistance than will the dropped bullet, so even neglecting the curvature of the Earth (which effect would be small compared to the air resistance effect), the fired bullet would still take a slight bit longer to reach the ground.
[QUOTE=Canadjun]
. If it is not quite fired fast enough then the orbit will slowly decay until it intersects the earth (i.e. the bullet lands).
It’s not that the orbit will decay (we need air friction or some other loss for that), it’s that the orbital path intersects the Earth’s surface. As soon as the bullet is fired, the bullet is in an orbit around the center of the Earth. Unless the initial velocity is large enough, the path of this orbit goes through the Earth.
It’s not naive as long as the assumptions are stated and understood. That’s the way science (and engineering is done). Look at the simplest cases first and then look at how to move to a more general case. For example, I suppose you could say that Special Relativity is ‘naive’ since it is valid only in a flat spacetime according to General Relativity is not possible in a universe with non-zero mass-energy content.
It’s not naive as long as the assumptions are stated and understood. That’s the way science (and engineering) is done. Look at the simplest cases first and then look at how to move to a more general case. For example, I suppose you could say that Special Relativity is ‘naive’ since it is valid only in a flat spacetime according to General Relativity is not possible in a universe with non-zero mass-energy content.
Agreed. But in this case there was no statement about air - it’s simply ignored. My sense is that it could well have as much effect as the curvature of the earth, which the linked column considers at some length.
If you are in a car traveling at the speed of light and you turn on the headlights, what happens?
Ok, let’s assume the car is not actually traveling at the speed of light, but it is moving at a rate really, really close to the speed of light… to make it at least plausible
[hijack] 186,000 miles per second - not just a good idea; it’s the LAW. And if lesser things like spatial dimensions, mass and time have to be adjusted to make it work, the universe will do that for us at no extra, er, charge. Is how I understand it. [/hijack]
). If it is not quite fired fast enough then the orbit will slowly decay until it intersects the earth (i.e. the bullet lands). It will clearly take longer for that to happen than if the bullet falls straight toward the earth. The fact that the bullet is following a geodesic (“straight line”) according to general relativity is irrelevant.