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# Stupid question about flying and earth's rotation

Posted on 2004-10-21
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Hello,

I have a really stupid question.  I'm going to Las Vegas next week and when I was booking my flight I noticed something strange.  From New York to Vegas non-stop takes over 5 hours.  Now the strange part to me, and only me becasue my friends think I'm stupid for asking.  If Vegas is three hours behind that means it takes the earth about three hours to rotate to the point where NY is.  So if I just decided to hover over NY in about 3 hours I'd be over Vegas.  Now of course Vegas is actually further south than New York but even than if I just flew a little south and hovered it would take me 3 hours to reach Vegas.  Now a plane isn't hovering it's flying towards the place you want to go.  So a plane traveling towards Vegas should take less than 3 hours, right?  I mean it makes sense to me, what am I missing.

Just to add to my confusion it turns out the flight back is less than 5 hours, how is that possible?

Thanks,
Joe

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Question by:jvieira
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snoyes_jw earned 60 total points
ID: 12374841
Hovering relative to some absolute point in space, or relative to the sun, yes.  But remember that when you leave the ground in your hovercraft/helicopter/antigravity device, you have momentum, and until you apply a force, you will continue to move along with the earth.

The reason the flight back is shorter is because you happen to have head winds when flying west, tail winds when flying east.
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rjkimble earned 90 total points
ID: 12375666
Planes travel in the air, just the way boats travel in the water. Because the air is being pulled along by the earth's rotation, at the equator so-called calm air is actually traveling over 1000 miles per hour. The plane you're traveling in is flying relative to that. The points snoyes_jw makes are also quite valid. Just remember, you're traveling relative to the surface of the earth, and the earth's rotation brings everything along with it.

FWIW, there is an an apparent accelation, known as the Coriolis acceleration, that appears to act on objects flying above the surface of the earth. Although negligible for most purposes, for objects that fly ballistically at high speed or over long distances, you have to take this acceleration into consideration. You can read more about it at Eric Weisstein's World of Physics:

http://scienceworld.wolfram.com/physics/CoriolisAcceleration.html
http://scienceworld.wolfram.com/physics/CoriolisForce.html
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ID: 12378870
The atmosphere rotates with the earth.  That is why your idea doen't work.  Otherwise, we would have a constant wind of approximately 1000 miles per hour.  Talk about a hurricane.
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ID: 12380588
I think your friend was right in stating that it's a stupid question.... :p (I can understand the confusion though)
The earth rotates in 24 hours. Imagine you'd be standing at the equator. There the surface rotates at 460 meters/sec (40,000,000 / (24 * 3600)). According to your theory, you'd land approximately 460 meters away from a point where u just jumped straight up and stayed in the air for one second... :D I don't think this needs any further explination that this theory is incorrect. I think snoyes_jw did a good job in explaying that the flight industry does know how to calculate flight timetables after 70, 80, 90 years of flight???

Cheers and have a nice (hovering) flight....
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ID: 12383459
you kinda answered your own question here...

So if I just decided to hover over NY in about 3 hours I'd be over Vegas
If you "hovered over NY" you would still be in NY!!

Also keep in mind even IF it did work the way you stated planes dont travel directly to thier destination they go by jet streams :)

-Navicerts
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ID: 12383874
>> Also keep in mind even IF it did work the way you stated, planes don't travel directly to their destination; they go by jet streams :)

That depends a lot on the location and strength of the jet streams. In the summer, they're generally too far north to affect travel over the continental U.S. Also, many long range flights to involve long "direct" segments, where the plane flies on internal (inertial/GPS) navigation equipment by a great circle route from one point to another. There are also "highways in the sky" -- jet routes -- that work a lot like roads on the ground. The jet streams do affect the altitudes at which jets fly -- higher when traveling east and lower when traveling west -- as well as the direction they head into the wind, but the routes they fly are determined by their ground track. That's what ground controllers are looking at, and it's really what's most important anyway.
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ID: 12383890
ahh, isn't more efficient fuel consumption another reason for using jet streams?

-Navicerts
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Author Comment

ID: 12389304
Okay,

I think I'm starting to get this.  I kind of remember something like this in highschool physics.  You drop a quarter in a moving car, if you're in the car than the quarter drops straight down.  If your outside the car the quarter does not drop staight down, it moves forward and drops down.  So when the plane takes off it's still moving with repsect towards the earth's rotation.  And one of the reasons why it's faster comming back is because it's not going against the jet stream, although that seems to depend on the time of year.  Am I close?
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ID: 12389897
>> I think I'm starting to get this.  I kind of remember something like this in highschool physics.  You drop a quarter in a moving car, if you're in the car than the quarter drops straight down.

Correct.

>> If your outside the car the quarter does not drop staight down, it moves forward and drops down.

Also correct.

>> So when the plane takes off it's still moving with respect towards the earth's rotation.

Exactly.

>> And one of the reasons why it's faster coming back is because it's not going against the jet stream, although that seems to depend on the time of year.  Am I close?

Very. In fact, you pretty much have it figured out. The earth's rotation and curvature modify things a bit, but you have grasped the essence of the situation.
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Expert Comment

ID: 12402115
the confusing thing is that if you went not in a plane but a space shuttle and 'hovered' over NY then you are absolutly correct in 3 hours you would be over las vagus

:-p) think of it as there being no air "pushing" you along
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Expert Comment

ID: 12402148
hmm, i still say you cant "HOVER OVER NY" and end up anywhere aside from NY.  Now, if there was another way to identify the postion you were hovering like an atmospheric location i suppose, i don't know if that exsists though :)

-Navicerts
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LVL 33

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ID: 12402860
The moving air has only a minor effect.  The root issue here is inertia, as in Newton's First Law of Motion, "An object in motion will stay in motion, and an object at rest will stay at rest, unless acted on by an unbalanced force."  The effect would be the same if you were on the moon with little or no atmosphere.
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Expert Comment

ID: 12411974
The reason your trip from Las Vegas to NY would be shortert is due to the winds.  When travelling from NY to Vegas, you will be facing a very strong headwind, causing you to fly slower. This is due to the prevailing westerlies.  When you flie back, those prevailing westerlies are a tailwind, and will help you travel faster towards NY.
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ID: 12412642
Your question is not stupid, it is a very good question. It took Sir Isaac Newton to come up with the answer. It's actually Newton's first law of motion. Once you know his other two laws and his universl law of gravitation you know pretty much all you need to know to describe motions on the earth. Check this out:

http://www.321books.co.uk/encyclopedia/physics/newtonian-mechanics/newtons-laws-of-motion.htm

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ID: 12412847
i suppose you could even say you are correct in a way.  Depends on what exactly you mean twhen you said "hover".  If you meant "hover in respect to the universe" then you are correct.  People just assume that when someone says hover they mean in respect to the earth.

-Navicerts
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ID: 12415649
Actually, "hovering" absolutely stationary at one fixed point in the universe would probably place you out of the planet's atmosphere pretty durn quick.  Yes, the Earth is rotating on it's axis, but it is also rotating around the sun.  Our solar system is also moving within the Milky Way galaxy, and this galaxy is also moving.  I'm not even convinced the concept of "stationary" in an absolute sense is even possible, let alone figuring out how to know you're not still moving relative to *something* that science may or may not have yet discovered.

Quick and dirty calculations of Earth's orbit around the sun gave me a figure of about   2,500,000 mph.  Even stopping immediately (physically impossible...there must be some deceleration time), staying absolutely stationary for one second, and instantly accelerating back to Earth speed would put you about 700 miles away...in a direction likely not on the surface of the planet.  You may be underground or in orbit.  That is still only considering Earth's orbit speed around the sun...then there is the solar system's speed, the galaxy's speed, etc.  Approximately half of every day we are going faster than the other half of the day relative to a fixed point in the universe, since half the time our rotation is going the same direction as the Earth's orbit path, and the other half of the day we are going against the orbit as the Earth rotates.  Same concept applies to the solar system and galaxy rotation.  Part of the year we are going faster than other parts compared to an absolute fixed position...if there is such a thing ;).  It all is further complicated by angles of rotation planes which I convieniently ignored in the quick and dirty calcs above (also assumed a circular orbit of Earth which is blatantly incorrect....just needed rough enough numbers to show we're going far faster than 1,000mph and it was easier to rough out <speed of light in miles/sec> * 60 sec/min * 8 min = Earth orbit radius then multiply by 2pi for a circumference, divide by 365 to get a day's distance, and divide by 24 for mph).  It would have taken me longer to look up an accurate number on google and I apologize, but the distance of our orbit is a factoid that left my brain about 20 years ago and just wanted some rough numbers.
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ID: 12415877
Newton believed in absolute position but was not convinced it existed. Einstein destroyed the whole concept -- that's the meaning of "relativity". There is no absolute position, only relative position:

http://www.321books.co.uk/encyclopedia/physics/newtonian-mechanics/absolute-position.htm

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ID: 12419515
"and instantly accelerating back to Earth speed would put you about 700 miles away"

unless of course you are standing on the wrong side of the world and find that the earth comes crashing towards you and flattens you as you try to move 700 miles into the earths core ;-p) any volenteers to try this out?
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ID: 12420930
well @ 2.5 mph you would be more likley to put a giant creater in the earths surface and possibly end all life on earth (assuming you were in a commerical plane)

-Navicerts
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ID: 12421207
the human body isnt very dense so wouldnt it just go splat ? or burn/evaporate in the atmophere?
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ID: 12421217
i would think so... i was assuming you were in a commercial air plane
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ID: 12421380
lol im not awake yet ;)
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ID: 12433084
There is still something i can't get:

"An object in motion will stay in motion, and an object at rest will stay at rest, unless acted on by an unbalanced force."
Okay, that's why when you lift yourself off the earth, you are not put 700 miles away as fixnix said.

If I understand well, an object on the surface of the earth has a momentum that will lead it to keep the earth rotation motion if the object is lifted off, say for example an helicopter.

Now, what I don't understand is that this effect must end at one moment :
Imagine a rocket taking off vertically from the earth. So it's got a momentum that allows it to follow the earth rotation and find itself at the same position relative to distant stars after 24 hours (with the hypothesis that the movement around the sun and around the galaxy is irrelevant for a 24 hours duration).

I can imagine this rocket keeping a vertical motion that leads it to fight against earth gravity and remain stationnary up its takeoff place for 24 hours. Its momentum will lead it to follow the earth rotation, meaning that after 12 hours it will stand at the symetrical point from the center of the earth in a distant stars referential.

That is conceavable if the rocket stands say a few hundreds kilometers from the earth surface (like the space shuttle), but imagine now that the rocket keeps going ahead vertically for days, weeks, months, ... It will then be far away from the earth, but if Newton's principle is respected, if will still be up its takeoff place on the surface of the earth.

See the problem ? After 12 hours, the rocket should be at the symetrical point from the center of the earth in a distant stars referential, and that point is twice the distance from the rocket to the earth. How can the rocket fly this distance in 12 hours, though it took months to fly half this distance.

Hope I am clear. Where's the bug ?

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ID: 12433357
Say the radius of the earth is x. On the surface, the rocket has a certain 'speed': (x*2*Pi) / 24 km/u (=40000 / 24 = 1667 km/h, if the rocket would be launched from somewhere near the equator). The rocket maintains its speed, no matter what its new upward speed is and no matter how far from earth, until another force is released on the rocket.. So, let's say the rocket is at 100.000 km away from earths core, it still caries its momentum, 1677 km/h sideways, circling around earth. But the earth rotates faster... the earth rotates 40.000 km in just 24 hours, where the rocket would need ((100.000 * 2 * Pi) / 1667 = ) 377 hours... This is because the increase of the radius... So if you'd be inside the rocket, you would see the earth rotate underneath you, in stead of seeming to stand still. Another example: Imagine a spiral track with a cart on it. Put the cart in the middle and give it a push. Image the cart won't slow down... It'll take the cart longer and longer to finish a circle as it goes...
However, a rocket will not only go upward... as it goes upwards, it tries to fight its momentum by steering against the earth rotation, so a part of it's upward force is used to fight its momentum...

Sorry if I'm mistaken in some english terms.... English and technological/scientific words is not one of my strong points...

Cheers
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ID: 12433565
Your quote of Newton's first law is missing an important few words, and drop the "unbalanced".

Corrected: "An object travelling at constant velocity in a straight line will stay moving at a constant velocity in a straight line , unless acted on by an external force. If is stationary it will remain stationary uness actedon by an external force."

The rocket does not follow the earth's rotation. When it takes off there are two components to its motion: (i) There is the motion "straight up" imparted by its rocket thrusters. (ii) There is another straight line motion at right angles to this imparted by the earth's motion (" a constant velocity").

Of course, earth's gravity ("external force") will cause the horizontal motion to deviate from a straight line, but gravity gets weaker as the rocket moves vertically (and horizontally) away from the earth due to Newton's universal law of gravitation:

http://www.321books.co.uk/encyclopedia/physics/newtonian-mechanics/newtons-universal-law-gravitation.htm

Weeks & months into flight and the earh's gravitational attraction will be very small but the craft will still have the horizontal velocity originally given to it by the earth's rotation.

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ID: 12433891
IThema - are you saying the rocket will continue to orbit the earh at 1667 km/h even when it gets clear of the solar system?

If so, you are wrong.

The only thing causing the rocket to orbit the earth is Earth's gravity. And by the time it clears the solar system that effect will certainly be 0, near as d**n it. The rocket will still have a STRAIGHT LINE component of its velocity still intact from the 'slingshot' effect of the earth's rotation imparted to it when it launched.

The only force the rocket is fighting against is earth's gravity (ignoring friction and other heavenly objects!)

Come on everybody,start thinking, this isn't rocket science. Er... :-)
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ID: 12434112
I'm saying the same as u do: The rocket has its forward velocity, and it's 'horizontal' velocity, given by the earth rotation.... that's about 1667 km/h if the earth would rotate and stand still in space and the rocket would be launched from somewhere near the equator...

I'm saying that the earth radius is +/- 6400 km... I'm saying that when a rocket rises 6400 km (so it's 12800 km away from the centre-point of the earth) and then reverses it's thrusters to come to a sudden upward halt (not rising anymore), it would rotate 180 degrees around the centre-point of the earth in 24 hours while the earth rotates 360 degrees in 24 hours...

Correct me if I'm mistaken...
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ID: 12436550
mal4mac is right.  An object in motion travels in a straight line.  Imagine that the rocket reaches the 6400km, stops its "vertical" motion, and then through some sort of cosmic blackhole blip, the earth vanishes completely.  The rocket would not orbit the point in space where the earth used to be; it would head off in a straight line parallel to a tanget to the missing earth's surface.  It would travel a distance equal to one earth circumference in 24 hours.  Since the earth doesn't disappear, we have gravity.  If it hits the right distance from the earth, the rocket will fall into orbit.  If it's too low, it will spiral down around the earth until it crashes.  If it's too high, it will spiral up and away until it heads off into space.
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ID: 12437345
"An object in motion travels in a straight line."

-- if not acted on by an external force.

"Parallel to a tangent to the missing earth's surface"

There are an infinite number of tangents to the missing earth's surface, which one were you thinking of?

A black hole would swallow the rocket as well, better just leave it at a blip :-)
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ID: 12437986
the tangent that goes through the point at which the rocket left the earth's surface, or near that point anyway.

And it was really more of a deep purple or navy blue hole anyway, not really black, so the rocket escaped and was completely unaffected by the change in gravity.
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ID: 12441879
Yeah, I rethought my theory after I wrote my last post. The 'rotation' is indeed only caused by the gravity of the earth. Without gravity, it will have a constant 'horizontal' speed in addition to any 'vertical' speed; it won't orbit earth...
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ID: 12441901
This got me wondering about the range of distances & velocities needed to maintain an orbit, escape velocity and the like. Rather than task my poor brain with numbers I did a Google search and found this excellent article:

http://electronics.howstuffworks.com/satellite3.htm

This links to NASAs orbital calculator which shows that the rocket would only need to move at the speed of a slow car to maintain an orbit around the earth if the rocket were as far away as the sun (I'm guessing NASA are assuming the rest of the universe has been swallowed by that dark purple black hole).

Also NASA says: "The orbital velocity at 12800.00 kilometers is 4.56 km/sec! The period of the orbit is 440.52 minutes."

If you throw an object straight up, it will rise until the the negative acceleration of gravity stops it, then returns it to Earth. Gravity's force diminishes as distance from the center of the Earth increases, however. So if you can throw the object with enough initial upward velocity so that gravity's decreasing force can never quite slow it to a complete stop, its decreasing velocity can always be just high enough to overcome gravity's pull. The initial velocity needed to achieve that condition is called escape velocity.

Escape velocity (ignoring air friction) is about 7 miles per second, or 25,000 miles per hour. Given that initial speed, an object needs no additional force applied to completely escape Earth's gravity. You can see why rockets need to be so big & expensive!

Some (simple) equations here:

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Author Comment

ID: 12453579
Well it turns out you're all wrong.  The correct answer is don't go to Vegas and if you do go to Vegas don't gamble and if you do gamble and lose don't take any cash advances on your credit card.  Because if you do all these things you will have no money and a huge credit card bill.  Thank god for overtime.

snoyes_jw and rjkimble both gave me the info I needed to understand this with rjkimble giving me a little more information.  I'll assign the points them both.  Although it seems like you guys have taken this to an all new level.  I'm not sure if you can keep posting comments if I close the question.  Does anyone know?  Or if you've finished I'll just close the question and assign the points.

Thanks,
Joe
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LVL 33

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ID: 12453677
Yes, we can continue to post to a closed question.  But few people ever do.
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ID: 12456063
Yeah, stay home and read Feynman's lectures on physics (33% off on Amazon.com!). He'll teach you the physics, statistics and a scientific mind set that will give you (i) the ability to think through problems like the 'hovering plane' and (ii) enough knowledge to know that gambling is for fools or MIT professors of mathematics who know how to card count*. (iii) the ability to coast through most physics-oriented science courses,so you can land a high paying, interesting job and not even need to think that gambling could be a 'way out' (iv) hours of enjoyment so you won't feel the need of gambling 'for entertainment'.

Brits please read this post carefully as Blair seems determined to turn the whole of Britain into Las Vegas.

* even then they'll probably get found out and may end up with concrete overshoes - so (ii) really resolves to 'gambling is for fools'
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ID: 12471615
Hello jvieira,

You should also know this:

Have you ever heard about shortest join between two points? This is geodetic. Two dimensional surface of earth is curved with space-time. Geodetic's are circles and their center is in middle of the earth. Pilots are folowing geodetic lines because they are the shortest lines between airports.

http://www.flightgear.org/Docs/Scenery/CoordinateSystem/CoordinateSystem.html
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