Orbits are impossible: a conundrum

[siarad]

Newton explained gaining orbit by shooting an arrow with increasing speed until it no longer fell to the ground but orbited around the Earth.<br /><br />I can't see how this is possible so upgrading to a modern idealized experiment & making more laws obvious.<br /><br />No force can have an effect at right angles to it's line of action<br /><br />Gravity acts equally on all objects<br /><br />Push a cue ball across a table & as it leaves the edge cause it to trigger the drop of another one.<br />No matter how fast the cue ball goes across the table both balls reach the ground at the same time.<br /><br />The line of action of the force of the ball is at right angles to gravity so has no effect. Similarly gravity's line of action is at right angles to the motion of the ball thus having no effect.<br />This makes an orbit according to Newton impossible.<br /><br />Any takers?

 

[nacnud]

<font color="yellow">No matter how fast the cue ball goes across the table both balls reach the ground at the same time.</font><br /><br />True if the ground was a flat plate, but its not it’s a sphere. So if you push one ball fast enough then by the time the first ball has reached the ground the second ball is at the same altitude but the ground has fallen away so it travels further. <br /><br />Move the ball fast enough and the ground falls away at the same speed the ball is falling, the ball is then in orbit.<br />

 

[CalliArcale]

<blockquote><font class="small">In reply to:</font><hr /><p>No force can have an effect at right angles to it's line of action <p><hr /></p></p></blockquote><br /><br />I see the confusion. Basically, that's not what's happening here.<br /><br />Disregarding friction with the pool table and wind resistance, there are two forces involved here. One is gravity. The other is the force imparted by the pool cue. This force is over the moment the ball rolls away, and in accordance with Newton's First Law, the ball remains in motion in a straight line. But then it reaches the edge of the table. Assuming the table has no walls (so it's not a normal pool table at all), the ball rolls off the edge. There is nothing now to counteract gravity, and the ball is accelerated downwards by the constant force of gravity. This happens to be at a ninety-degree angle to the ball's current direction of travel. There is no other force now acting on the ball but gravity. It drops at 9.8 meters per second per second (or meters per second squared). This means that if the ball were falling far enough to take a second to do it, it would be travelling 9.8 meters/second by the end, but if it fell far enough to take two seconds, it would be travelling 19.6 meters/second. That's important to understanding this -- gravity <i>accelerates</i> falling objects.<br /><br />Now, if you drop a second cue ball at exactly the same altitude as the table but off to one side, it'll take just as long to hit the ground as the ball that was pushed off the table. This is because it, too, is being accelerated downward at 9.8 m/s^2. The difference is that the first ball will land directly below where it was dropped (proving that gravity is not somehow acting at right angles to itself) wheras the first ball will land some distance away, since it did not lose any of its initial momentum when it left the table. If you hit a third ball harder than the first, it will land further away than the first ball. But it too will lan <div class="Discussion_UserSignature"> <p> </p><p><font color="#666699"><em>"People assume that time is a strict progression of cause to effect, but actually from a non-linear, non-subjective viewpoint it's more like a big ball of wibbly wobbly . . . timey wimey . . . stuff."</em>  -- The Tenth Doctor, "Blink"</font></p> </div>

 

[siarad]

So Newton thought the Earth was flat! joking <img src="/images/icons/laugh.gif" /> It can't be possible to fire a rocket into orbit in the time it takes a ball to drop off a table plus a tiny little bit.<br />Sorry Calli you must've taken a long time to reply & I'm not being entirely serious but it is interesting as to why that ball would follow the curvature of the Earth & not fly directly into space as it's speed must be very high & would be following a curve not the straight line it follows in orbit.<br />I seem to have lead you astray by poor posting as I was questioning Newtons idea & I did say it was a conundrum.

 

[Leovinus]

How about this. Standing on a small round asteroid with very low gravity (assume your boots are nailed to the ground), you could throw a baseball into orbit (or even catch it as it comes around). <div class="Discussion_UserSignature"> </div>

 

[thalion]

It would follow a curve because the ball really is falling "around" the curvature of the Earth. It would only fly off in a straight line if its velocity were very high, greater than escape velocity (if its velocity were exactly escape velocity, it would be an open parabolic curve).

 

[siarad]

You've made my point. The speed would have to be way beyond the escape velocity in order not to fall back to Earth in the time it takes another ball to fall from a table 3 feet high. However I can't seem to work out whether the Earths curvature affects it. I started thinking about this after seeing a program about MagLev launch as it seems less energy is needed to reach orbit by horizontal launch, except for the buckling of the airframe of course. <img src="/images/icons/laugh.gif" /><br />Calli<br />I'm not convinced as above.

 

[CalliArcale]

<blockquote><font class="small">In reply to:</font><hr /><p>It can't be possible to fire a rocket into orbit in the time it takes a ball to drop off a table plus a tiny little bit.<p><hr /></p></p></blockquote><br /><br />The secret is that it's not just "plus a tiny little bit". It's plus a LOT. That's why Newton figured that it was all hypothetical, that nobody could possibly really do it. The technology of his time simply wasn't capable of scaling up that much.<br /><br />The speed you have to go in order to go all the way around the Earth without hitting the ground is very very very very fast. In fact, it is physically impossible to travel that fast at sea level; the air is too dense. No materials made today can make it possible. Besides, the drag would totally strip away your forward velocity; you'd have to keep thrusting constantly, which would really be cheating. <img src="/images/icons/wink.gif" /> I think the ISS goes the equivalent of Mach 17. For comparison, the fastest conventional manned aircraft, the SR-17, can only squeak out a bit over Mach 3. <img src="/images/icons/shocked.gif" /><br /><br />Additionally, they don't launch rockets parallel to the ground. They point them up a bit. An old ballistics trick is to aim up a bit to get the projectile to hit further downrange. And what's more, they do in fact cheat -- rockets add thrust until they reach orbit. Nobody has yet built a gun that can manage an orbital shot, though the technology is now conceivable, and some practical designs have been tossed around. The main problem with a cannon such as Newton suggested is that the payload has to endure a really massive acceleration. The Shuttle accelerates to 17,500 MPH in just over eight minutes. This would have to do it in just a few seconds. Passengers would be turned into pate!<br /><br /><blockquote><font class="small">In reply to:</font><hr /><p>I'm not being entirely serious but it is interesting as to why that ball would follow the curvature of the Earth &amp</p></blockquote> <div class="Discussion_UserSignature"> <p> </p><p><font color="#666699"><em>"People assume that time is a strict progression of cause to effect, but actually from a non-linear, non-subjective viewpoint it's more like a big ball of wibbly wobbly . . . timey wimey . . . stuff."</em>  -- The Tenth Doctor, "Blink"</font></p> </div>

 

[spacester]

<font color="yellow">Newton explained gaining orbit by shooting an arrow with increasing speed until it no longer fell to the ground but orbited around the Earth. </font><br /><br />Well then Newton explained it wrong. The arrow needs a rocket engine to perform a delayed burn to change its flight path, even if you give it plenty of speed leaving the bow to provide ample orbital energy.<br /><br />An arrow fired from any planet will do one of two things, and neither of them are "achieving orbit".<br /><br />It will either escape the planet's gravity field or it will fall back to the surface.<br /><br />What was all that stuff about the right angles? <img src="/images/icons/laugh.gif" /> <div class="Discussion_UserSignature"> </div>

 

[siarad]

That's what I think, you can't just throw something into orbit.

 

[siarad]

Surely an orbit is a straight line else a force would be necessary to curve it which is not felt. Indeed IronSun says gravity is not a force to my reply over another conundrum of the direction of gravity

 

[jitte]

I've got a page about gravitys role in orbital mechanics and spaceflight, if you're interested.<br /><br />Gravity Rules <br /><br />----------------------------

 

[siarad]

Thanks I've read it before & it's very good.<br />Not being scientific I like to be able to think things up for myself even though I appear silly at times. Hopefully at least I end up understanding. <img src="/images/icons/laugh.gif" />

 

[jitte]

I didn't think you looked silly. <img src="/images/icons/smile.gif" /><br /><br />They were right though. Once the arrow has sufficient velocity it falls around the planet. Its orbit is an ellipse.<br /><br />----------------

 

[nacnud]

<font color="yellow">Well then Newton explained it wrong. The arrow needs a rocket engine to perform a delayed burn to change its flight path, even if you give it plenty of speed leaving the bow to provide ample orbital energy. </font><br /><br />Newton got it right, but he didn't explain it in that way. He put a cannon on top of a very tall mountain, so high it was above the atmosphere. If fired fast enough a projectle from the cannon could go all the way round the earth and hit the top of the mountain again after completeing a single orbit.<br /><br />Here is the picture from his <i>Principia Mathematica</i>

 

[spacester]

<img src="/images/icons/cool.gif" /> nice illustration, talk about a classic! lol, I guess siarad mis-quoted the old bird. <img src="/images/icons/wink.gif" /><br /><br />siarad: "not being scientific, I like to think things up for myself . . . "<br /><br />My gosh, don't you realize you're describing the best kind of scientist?!? As long as he verifies his speculation, of course. Which is what you're doing, right?<br /><br />So you get a nomination from me for an honorary sdc science diploma just for that. <img src="/images/icons/laugh.gif" /><br /> <div class="Discussion_UserSignature"> </div>

 

[siarad]

Me honourable! na but thanks I feel honoured <img src="/images/icons/laugh.gif" /><br /><br />Calli I'm glad you think it's fun, life should be. Mine has been from working on an aircraft in difficulty at 50,000 feet, IRBM, oil rigs, industry, supertankers, universities & even down a coal mine.<br />I'm left with day dreams now & can pursue things I've missed, an interest in space being one. You guys are so much more knowlwdgeable than me I'm using you to short cut me to understanding. Not that I don't read but have problems with words, it's just I don't always agree with the accepted conclusions & can't figure out why as now.<br /><br />After 4 hours of disturbed sleep as all the replies sunk in I finally decided to jot some notes which follow:<br /><br />Clearly I have difficulty with Newtons arrows going straight. Presumably this is why my brain came up with the table but why the second ball?<br />Is it a timing problem or does it's position mean something?<br />Both, I've got it <b>both</b>.<br />A rocket firing to reach orbit is already falling during it's impulse time like the second ball, it's <b>inside</b> an ellipse reaching for the edge.<br />My table ball has not reached the falling time because it's already <b>outside</b> the ellipse during it's impulse time, it's on a <b>tangent</b> so will either fall to earth or take a hyperbola but never an ellipse.<br />Over to you guys.

 

[Leovinus]

It would hit the mountain again only if it were the North or South Pole. Otherwise, the Earth's rotation would move the mountain out of the way as the projectile came back around. <div class="Discussion_UserSignature"> </div>

 

[Leovinus]

Maybe you can think of an orbit as being a straight line in curved space. <div class="Discussion_UserSignature"> </div>

 

[nacnud]

Yeah I was over simplifying, I should have said that the projectile will return at the same altitude as the mountain top thanks for the correction <img src="/images/icons/smile.gif" />. Another point to note in the case of trying to get a object into orbit through a single impulsive force is that it will have the altitude of the firing point as the minimum height of the orbit. The only way to raze the minimum high would be to use a second impulse, most effectively at the maximum height of the orbit.<br /><br />There was a good thread on this before the crash, IIRC mostly about how the moon was formed due to the impact of another body. It took a while to work out how the moon could form if a single impulse (the impact) can only put material into sub orbital parabolas or escape velocity hyperbolae as any orbit would interest the ground level after a single revolution. I think it was determined that the gravitation of the ejected material must have perturbed the orbits of some the ejecta enough to stabilise them long enough for the moon to start coalescing. I whish I could still link to that thread, ho hum.<br />

 

[igorsboss]

Please consider Newton's thought experiment, in which an object is launched into orbit by shooting it out of a horizontal cannon on a high mountaintop.<br /><br />It is sometimes argued that this wouldn't work because the object would circle the planet just once, then collide with the mountaintop.<br /><br />I would like to point out that the planet is rotating on its own axis. So, by the time the object returned to the starting point, the mountain would have moved out of the way. There is no need to duck.

 

[iron_sun_254]

<font color="yellow">It would hit the mountain again only if it were the North or South Pole. Otherwise, the Earth's rotation would move the mountain out of the way as the projectile came back around.</font><br /><br />Actually, if it were anywhere on the equator it would do so as well so long as you pointed it directly east or west.

 

[CalliArcale]

<blockquote><font class="small">In reply to:</font><hr /><p>Maybe you can think of an orbit as being a straight line in curved space.<p><hr /></p></p></blockquote><br /><br />To elaborate on Leo's answer, Newton regarded gravity as a force acting at a distance. So, the orbit is curved because the object is continually being deflected from its straight trajectory by the force of gravity.<br /><br />Einstein, however, said that this wasn't really accurate. Einstein said that gravity isn't a force, but rather the warping of spacetime. So the object really is travelling in a straight line, but that line is being bent into a curve due to the warping of spacetime by a very massive object.<br /><br />So while it isn't entirely accurate the gravity is a force that deflects the trajectory of an object, it is sufficiently accurate to make the math work out right for celestial mechanics in most cases. Exceptions include times when the object is very small and very close to a very large object. For instance, using pure Newtonian science, the orbit of Mercury doesn't work out quite right. Mercury's orbit was actually used as the first observational test of relativity -- and relativity succesfully predicts Mercury's orbit. Don't ask me to explain that, though. I've barely got my head around Newtonian physics. <img src="/images/icons/tongue.gif" /> <div class="Discussion_UserSignature"> <p> </p><p><font color="#666699"><em>"People assume that time is a strict progression of cause to effect, but actually from a non-linear, non-subjective viewpoint it's more like a big ball of wibbly wobbly . . . timey wimey . . . stuff."</em>  -- The Tenth Doctor, "Blink"</font></p> </div>

 

[rocketbodypart]

I am thinking you become part of an orbit. You will either be sucked back into the atmosphere, and burn a-la a nice little sparkle to the naked eye, or you become one with an orbit. <br /><br />Maybe in order to become part of the orbit, you do need to have some sort of straightening device, so that the orbit accepts you in its plane.

 

[siarad]

Yes that's what I think & have only pictorially set it out above. I think Newton was wrong 'cos a horizontal launch is a special case being the divider between elliptical & parabolic orbits.<br />I was hoping someone could do the maths.