Does the Earth circle the sun?

[N1LAF]

Does the Earth circle the sun?

Sounds like a trick question, but it isn't. Think about it. If you know, spit it out.

[WØTKX]

No. It orbits, and it's not "circular", unlike some forms of "logic".

:neener:

[KC2UGV]

http://www.thesportsbank.net/core/wp-content/uploads/2009/04/orbit.jpg

[N1LAF]

No. It orbits, and it's not "circular", unlike some forms of "logic".

:neener:

Does it orbit in a circle?

[ki4itv]

No, they both circle a common point relative to all the gravitational forces acting upon them.
This is how we find planets in other systems.

[WØTKX]

And, it's actually a spiral elliptical shape if you don't use an, erm... Heliocentric point of view.

That's a special word, heliocentric.

[ki4itv]

I was trying to stay in that 8th grade reading zone we all aspire too.
You kinda ruined it there, Dave :lol:

[ki4itv]

You might really wish to ask the right question, Paul.
Are you asking why it's going to take another 105 years to see the transit of Venus again?

[N1LAF]

You might really wish to ask the right question, Paul.
Are you asking why it's going to take another 105 years to see the transit of Venus again?

Clue - the transit prompted the thought... then it came to me... but nothing to do with the transit. Read your PM

[WØTKX]

Well, if you wanna get esoteric, I read something a long time ago that it's actually chaotic... something about too many masses affecting the system at the same time. Which makes sense to me. I dig astronomy and astrophysics from an amateur "fanboi" status.

I sense the game is afoot, however. It may be a trick question.

http://laughingsquid.com/wp-content/uploads/its-a-trap-20100127-143341.jpg

Seems the only way this "lib" can impress Paul is with a long boring dissertation about obscure
technical skills like typefaces and font management. I should have flown away and avoided it.

http://www.bigtimeattic.com/blog/uploaded_images/hamster_working_2.jpg

I accept defeat, rolled over and pissed myself.

http://plus4chan.org/b/co/src/133825303194.jpg

[N1LAF]

I think Corey gave up on this one...

[KC2UGV]

I think Corey gave up on this one...

I'm not bothering Paul...

But, if you like (Astrophysics isn't my strong suit):

The Earth, as all other bodies of the solar system (Sun included), orbit (Elliptical, generally), around the center of gravity of the solar system (Known as the Barycenter), which is a point about 800,000 Km from the Sun.

[N1LAF]

I'm not bothering Paul...

But, if you like (Astrophysics isn't my strong suit):

The Earth, as all other bodies of the solar system (Sun included), orbit (Elliptical, generally), around the center of gravity of the solar system (Known as the Barycenter), which is a point about 800,000 Km from the Sun.


Simple question, Corey, and it isn't really a trick question, but does the earth have a circular or elliptical circular orbit?

[KC2UGV]

Simple question, Corey, and it isn't really a trick question, but does the earth have a circular or elliptical circular orbit?

It's an eccentric circle, with a varying eccentricity between 0.005 (Mildly eccentric) and 0.058 (Highly eccentric).

I know Paul, Natural Cycles (TM).

[kf0rt]

The Google-fu is strong on this one. :lol:

[KC2UGV]

The Google-fu is strong on this one. :lol:

Well, I knew it's eccentricity varied, I googled the specifics :) I got it from a Gub'Mint website (NASA), so who knows if it's true and all, amirite?

[N1LAF]

It's an eccentric circle, with a varying eccentricity between 0.005 (Mildly eccentric) and 0.058 (Highly eccentric).

I know Paul, Natural Cycles (TM).

Are you sure? Care to try again?

Anyone else think they have the answer to this science riddle, PM me, and I'll let you know how close you are.

[KC2UGV]

Are you sure? Care to try again?

Anyone else think they have the answer to this science riddle, PM me, and I'll let you know how close you are.

It's an eccentric circle, with a varying eccentricity, orbiting the barycenter. This is a pretty well known fact, but like I said, NASA might be wrong. I mean, they only got the Mars rovers to Mars, which doesn't need to take into account gravity sling-shotting, with variable orbits of bodies or anything.

[N1LAF]

It's an eccentric circle, with a varying eccentricity, orbiting the barycenter. This is a pretty well known fact, but like I said, NASA might be wrong. I mean, they only got the Mars rovers to Mars, which doesn't need to take into account gravity sling-shotting, with variable orbits of bodies or anything.

What if I say it isn't an eccentric circle...

Don't feel bad that you don't know the solution to this science riddle, but once you know what it is, it will be very obvious.

[suddenseer]

My sunday school teacher said the earth is flat. Gawd said it, I believe it, that settles it.

[KC2UGV]

What if I say it isn't an eccentric circle...

Don't feel bad that you don't know the solution to this science riddle, but once you know what it is, it will be very obvious.

Ok, shoot. I'd love to hear how it's not an eccentric circle...

[ki4itv]

Most of us have answered this question correctly in various ways.
It's the question itself that makes the desired answer elusive.

[N1LAF]

Most of us have answered this question correctly in various ways.
It's the question itself that makes the desired answer elusive.

Yes! But it is an interesting (the answer).

[N1LAF]

Ok, shoot. I'd love to hear how it's not an eccentric circle...

Its in your PM...

[KK4AMI]

Google Sez!!! (In honor of Richard Dawson)
The shape of Earth's orbit can be nearly circular to slightly elongate and back again. The time it takes to go through a complete cycle from circular to elongate and back to circular is about 100,000 years.

[N1LAF]

Google Sez!!! (In honor of Richard Dawson)
The shape of Earth's orbit can be nearly circular to slightly elongate and back again. The time it takes to go through a complete cycle from circular to elongate and back to circular is about 100,000 years.

Can't be a circle or ellipse.... won't work.

[KK4AMI]

Oh Crap, I think I just stepped in to the prelude to another Global Warming thread :wall:

[N1LAF]

Oh Crap, I think I just stepped in to the prelude to another Global Warming thread :wall:

Nothing to do with global warming. Think of it as a scientific riddle.

[KK4AMI]

Nothing to do with global warming. Think of it as a scientific riddle.

Are you referring to the fact the sun and earth actually rotate around each other at a Earth/Sun center of mass?

[ki4itv]

He's actually thinking bigger.

[KK4AMI]

He's actually thinking bigger.

Bigger as in 3 Dimensional? THe Earth's orbit kind of wobbles? I give up. Its completely clouded over here, so I gotta live another 100 and some years to see Venus pass in front of the sun...groan

[WØTKX]

The secret word is heliocentric. Ahhhhhhhh!

http://www.toledoblade.com/image/2004/11/11/800x_b1_cCM_z/Pee-wee-s-silly-Saturday-mornings.jpg

[ki4itv]

You can view it here (http://www.solarham.net/), Mike.
Cool site.

[KK4AMI]

You can view it here (http://www.solarham.net/), Mike.
Cool site.
Thanks. You came up with that website pretty fast. Couldn't stand to see me live another 100, huh? :)

I thought as part of his parole, Pee Wee was not allowed to be caught with his hands down there again?

[WØTKX]

That site is in one of my "home tabs". :agree:

As far as the brain teaser goes... I'm a CNC software guy of many years.

Think "tool path". :lol:

[ki4itv]

Tool path.
Is that like a new name for "Pearl Necklace"?:lol:

[WØTKX]

Could be, in certain... ahem... applications.

NSFW


http://www.jerzeedevil.com/gallery/files/7/5/5/skeet.jpg

[W3WN]

Are you sure? Care to try again?

Anyone else think they have the answer to this science riddle, PM me, and I'll let you know how close you are.Well, I know it's technically complicated. Even though The Moon (Luna) orbits the Earth, the gravitational mass of Luna affects the position of Earth.

So it's not, strictly speaking, the Earth itself that is in an eccentric eliptical orbit, but the Earth/Moon tandem. The center of which is slightly off the center of the Earth itself.

But I'm no astrophysiscist... geez, I can't even spell that word right... either, so describing this accurately with the correct technical details is a little tough.

[ki4itv]

:lol:

[WØTKX]

Climb out of the (local gravity) well of perception, and see! :lol:

[N1LAF]

Well, I know it's technically complicated. Even though The Moon (Luna) orbits the Earth, the gravitational mass of Luna affects the position of Earth.

So it's not, strictly speaking, the Earth itself that is in an eccentric eliptical orbit, but the Earth/Moon tandem. The center of which is slightly off the center of the Earth itself.

But I'm no astrophysiscist... geez, I can't even spell that word right... either, so describing this accurately with the correct technical details is a little tough.

It is actually very simple, but not obvious. The moon isn't part of this in the BIG picture of things...

[N2CHX]

So....... What's the answer? I hate it when these question and answer sessions drag on and on and on..... :squint: :-p

[NQ6U]

You're all missing the point. Paul is a Republican--he thinks the sun revolves around the Earth! ;)

[ki4itv]

You're all missing the point. Paul is a Republican--he thinks the sun revolves around the Rich! ;)

Had to tweak that for you just a bit.

[N1LAF]

Hey, this is not the political forum now....

;)

[ki4itv]

Sorry 'bout that bro-man. ;)

[WØTKX]

You've forgotten a dimension, or a movement, if you will.
A movement in time, arguably, with a bow to an Albert.

http://static.guim.co.uk/sys-images/Guardian/Pix/pictures/2010/8/3/1280836135147/1960s-television-series-T-006.jpg

You have entered the Outer Limits. :lol:




Absolute, total spoiler... if you must, peek. :omg:

http://www.waterjournal.org/uploads/vol3/demeo/fig31.jpg

[N1LAF]

That's a pretty big clue there, Dave...

BIG spoiler.

[WØTKX]

Well, the natives are getting restless. Watch your head and all that. :lol:

[WØTKX]

FWIW, the movements are not even that simple. Think of how the perigee and apogee points "orbit" around as well. :lol:

Crazy. Like when Tesla visualized the whirling fields when inspired to make the AC motor.

[N1LAF]

I PM'd a number of Islanders on request, as a precautionary measure. But it was a neat scientific based fact, that is not so obvious, easy to understand. Nothing wrong with a good brain teaser once in a while

[KK4AMI]

Well I guess I always was a two dimensional thinker.

[suddenseer]

Does the Earth circle the sun?

Sounds like a trick question, but it isn't. Think about it. If you know, spit it out.Define "circle".

[KC2UGV]

I PM'd a number of Islanders on request, as a precautionary measure. But it was a neat scientific based fact, that is not so obvious, easy to understand. Nothing wrong with a good brain teaser once in a while

It's obvious, and easy to understand. Once you lay out the vantage point.

Case in point: Is it what you think if you are at Sol? How about 0,0 Galactic? How about 0,0 Andromeda?

[N1LAF]

Define "circle".

To be at the same point 360 degrees later. The forward motion of the sun, planets prevent this.

[N1LAF]

It's obvious, and easy to understand. Once you lay out the vantage point.

Case in point: Is it what you think if you are at Sol? How about 0,0 Galactic? How about 0,0 Andromeda?

Because we make the sun as a reference point, and as a reference point, it is a circle (or ellipse). The reality that the sun is racing through the galaxy, so in absolute, 3D terms, the motion of the earth and the other planets is like a corkscrew.

[KC2UGV]

Because we make the sun as a reference point, and as a reference point, it is a circle (or ellipse). The reality that the sun is racing through the galaxy, so in absolute, 3D terms, the motion of the earth and the other planets is like a corkscrew.

Absolute is referential....

[W5GA]

Absolute is referential....
You go wash your mouth out right now!!

[W3WN]

Absolute is referential....I thought it was a vodka?

[KC2UGV]

I thought it was a vodka?

That too :)

[WØTKX]

Define "circle".

Got your ummm, errr... "defined point". ;)

Where is the line of a circle, exactly? :hyper:

https://www.projectrhea.org/rhea/images/a/a7/Cartoon.jpg

[suddenseer]

That site is in one of my "home tabs". :agree:

As far as the brain teaser goes... I'm a CNC software guy of many years.

Think "tool path". :lol:Does that sentence begin with G01 ?

[suddenseer]

Got your ummm, errr... "defined point". ;)

Where is the line of a circle, exactly? :hyper:

https://www.projectrhea.org/rhea/images/a/a7/Cartoon.jpgI kinda get that. lets go to a 2D view along the line that the sun is heading to, and going from. Project the earth orbit onto a plane perpendicular to that line, voila, we have an parabolic thing that has circular tendencies.

[W3WN]

Got your ummm, errr... "defined point". ;)

Where is the line of a circle, exactly? :hyper:

https://www.projectrhea.org/rhea/images/a/a7/Cartoon.jpgHmmm. That graphic is very familiar. Reminds me of an avatar I've seen somewhere... where, oh where, was that again? :sarcasm:

[WØTKX]

I'm well aware of it. But is it irony? ;)

[n2ize]

Assuming a planet orbits the sun is the motion of the planet planar ? (i.e. does the path of motion lie in a plane ? Assuming it is planar if we think of a planet (say the earth) and we think of a position vector (a line) from the sun to the earth what can we say about the area that will be swept out by this line with respect to intervals of time ?

[NQ6U]

If I get what you're saying correctly, John, the area swept in a given time will be equal no matter the position of the planet. Johannes Kepler figured that out.

[n2ize]

Because we make the sun as a reference point, and as a reference point, it is a circle (or ellipse). The reality that the sun is racing through the galaxy, so in absolute, 3D terms, the motion of the earth and the other planets is like a corkscrew.

Well, it's sort of like taking a weight on the end of a string while you are in moving car. If you keep the weight stationary (in other words you don;t swing it or twirl it) then from the reference point of the car itself the weight is stationary and not moving. But, if you look at it from the reference point of an observer both the car and the weight are moving together so, the path of the weight in 3-Space is the same as the path of the car. Now to make it a bit more complex start swinging the weight like a pendulum or twirling it in a circle. From within the car it's simple periodic motion or circular motion. But from outside the car things are more complex as the exact path the weight has taken in 3-space is going to involve both the motion of the car and the motion of the weight inside the car.

Another example are the lights that attatch to the wheel of a bicycle. From the frame of reference of the bike itself the light traces out a circular path. But, if you are observing it from a distance as the bike moves it will no longer trace out a circle but rather it will trace out a cycloid.

In either case, provided the path of the bike or the car is simple (such as a linear or circular path) it is easy to determine an equation for the position of the weight (or light) in space at a given time. You can use vector calculus. For a complex path through space (such as the solar system moving through space) it's a bit more complicated. ;)

[suddenseer]

What's my Vector Victor?


http://www.youtube.com/watch?v=fVq4_HhBK8Y

[n2ize]

If I get what you're saying correctly, John, the area swept in a given time will be equal no matter the position of the planet. Johannes Kepler figured that out.

Well, what it actually says is that motion is planar and that the area swept out is proportional to time "t".

[WØTKX]

Does that sentence begin with G01 ?

Well, if you wanna go.. errr... ummmm... "straight". :wiggle:

G02 or G03 needs to be in there somewhere. :spin:

[KG4CGC]

Well, if you wanna go.. errr... ummmm... "straight". :wiggle:

G02 or G03 needs to be in there somewhere. :spin:

The shortest distance between point A and point B is a folded plane.

[NQ6U]

The shortest distance between point A and point B is a folded plane.

http://4.bp.blogspot.com/--Rp1F-8Wgxk/TuElaSDf_eI/AAAAAAAABiE/syz5SvIV1GI/s1600/paper-airplane.jpg

[N2RJ]

Hmmm. That graphic is very familiar. Reminds me of an avatar I've seen somewhere... where, oh where, was that again? :sarcasm:

Yeah no kidding.

[N2RJ]

That's a pretty big clue there, Dave...

BIG spoiler.

That's what I was thinking.

In 2 dimensions it is elliptical.

In 3 dimensions, the Earth's orbit tilts up and down over a period of orbits (hence why we can see the transit of venus every what, 115 years, then the next 8 years on the way back up.) So it is actually not perfectly circular or elliptical either.


But even in 2 dimensions there's also the perihelion and aphelion, where the Earth gets closer to and further away from the sun, a range of about 5 million km, so it does not make a perfect circle or ellipse with the Sun at the center either.

[KG4CGC]

http://4.bp.blogspot.com/--Rp1F-8Wgxk/TuElaSDf_eI/AAAAAAAABiE/syz5SvIV1GI/s1600/paper-airplane.jpghttp://www.engineering.com/GamesPuzzles/Flight.aspx

[n2ize]

To be at the same point 360 degrees later.


No that does not define a circle. That does not define a circle because there are many other closed curves through which you can traverse through 360 degrees and still end up at the same point. Think in terms of polar, cylindrical or spherical coordinates in which a point is defined in terms of angle and distance from an origin. Traverse 360 degrees around an ellipse and you will be at the same point. Traverse 360 degrees around a cardioid and you will be at the same point. Ditto foir a rectangle, a triangle, or virtually any simple closed curve .in such a coordinate

I think a better definition (and probably what you meant) would be a set of points all at equal distance from the origin (or center) for all 0 <= x <= 360. If you really think about it a circle is a special case of an ellipse so, you could actually call a circle an ellipse. The geometric relation between a circle and an ellipse is evident when described as a conic section of a right circular cone. If you cut a cone with a plane perpendicular to it's axis you get a circle. If the plane is at an angle you get an ellipse.

[NQ6U]

http://www.engineering.com/GamesPuzzles/Flight.aspx

I already finished that one! Great game, too. Did you try "Sugar Sugar?"

[KG4CGC]

I already finished that one! Great game, too. Did you try "Sugar Sugar?"

Yeah. We were doing Sugar Sugar before we did flight. Flight is pretty whimsical. I like to see how long I can go before I have no other options left and have to start using jets and rudder.

[N7YA]

5984

[KC2UGV]

What's my Vector Victor?


http://www.youtube.com/watch?v=fVq4_HhBK8Y

Huh?

[N1LAF]

No that does not define a circle. That does not define a circle because there are many other closed curves through which you can traverse through 360 degrees and still end up at the same point. Think in terms of polar, cylindrical or spherical coordinates in which a point is defined in terms of angle and distance from an origin. Traverse 360 degrees around an ellipse and you will be at the same point. Traverse 360 degrees around a cardioid and you will be at the same point. Ditto foir a rectangle, a triangle, or virtually any simple closed curve .in such a coordinate

I think a better definition (and probably what you meant) would be a set of points all at equal distance from the origin (or center) for all 0 <= x <= 360. If you really think about it a circle is a special case of an ellipse so, you could actually call a circle an ellipse. The geometric relation between a circle and an ellipse is evident when described as a conic section of a right circular cone. If you cut a cone with a plane perpendicular to it's axis you get a circle. If the plane is at an angle you get an ellipse.

Yeah, in a two dimensional plane, already been there.

With all the planets, it becomes a complex corkscrew momentum

[n2ize]

Yeah, in a two dimensional plane, already been there.

With all the planets, it becomes a complex corkscrew momentum

I know that, however your definition if a circle (circular path) is still incorrect, whether it be in a 2 dimensional plane or oriented in 3-space there are many simple closed paths other than a circle that would fit your definition. Since the plane is a subspace of 3-space we can look at it as planar motion as the plane transitions through space.

[N1LAF]

I know that, however your definition if a circle (circular path) is still incorrect, whether it be in a 2 dimensional plane or oriented in 3-space there are many simple closed paths other than a circle that would fit your definition. Since the plane is a subspace of 3-space we can look at it as planar motion as the plane transitions through space.

Circumference of Circle = PI x diameter = 2 PI x radius
where PI = PI = 3.141592...

Area of Circle:
area = PI r2

http://www.math.com/tables/geometry/circles.htm

Are these equations valid in the 3D orbits of planets?

[NQ6U]

The orbit of a planet not circular, it describes an ellipse. I do not think that PI applies.

[N1LAF]

A circle is the set of points that are equidistant from a special point in the plane.

A plane is a flat surface that extends without end in all directions.

http://www.mathgoodies.com/lessons/vol2/geometry.html


A closed plane curve consisting of all points at a given distance from a point within it called the center.

http://dictionary.reference.com/browse/circle

So, does planetary orbits fit the definition as circular in 3 dimensional space, without using the sun as reference?

[N8YX]

All this talk of pie has made me hungry.

[n2ize]

Circumference of Circle = PI x diameter = 2 PI x radius

where PI = PI = 3.141592...

Area of Circle:
area = PI r2

http://www.math.com/tables/geometry/circles.htm

Are these equations valid in the 3D orbits of planets?

You are missing the entire point that I am making. What I am trying to point out is is that your definition of a circular path is not entirely correct since there are numerous simple closed curves (other than circles) that fit the criteria you described. The equation for area and circumference of a circle are not entirely relevant to this discussion since to describe planetary motion we would be more interested in examining position vectors expressed in parametric form (i.e. vector equations).. In the plane we would be looking at equations that approximate an elliptical orbit and, if we are to consider the motion of the plane through 3-space we would have to add additional parameters

In answer to your question no, the formulas don't apply if the orbital path in the plane is non-circular (elliptical). But assuming it were actually circular since you can have a circular path in 3-space and any circle in 3-space can be defined in terms of a 2-dimensional subspace (i.e a projection) . Think of it in terms of the earth orbiting the sun in a plane and envision the plane in motion through space.In terms of vectors the path of the planet in the plane would be a component of the vector equations for it's position in space.

Said differently, for an observer standing somewhere out in space the position of a given planet at some time "t" would be given by a set of parametric (vector) equations. The 2-dimensional motion in the plane would be a component of those equations i.e. the projection of that motion onto some plane subspace of 3-space.

[n2ize]

Now for a better question. Does the earth move under my feet ?

[suddenseer]

I mentioned projecting a plane normal to the line that the Earth appears to be moving. I just had my second bowl of killer shit, and i don't care anymore.

[N1LAF]

Now for a better question. Does the earth move under my feet ?

You have to define a reference point now

;)

[N1LAF]

You are missing the entire point that I am making. What I am trying to point out is is that your definition of a circular path is not entirely correct since there are numerous simple closed curves (other than circles) that fit the criteria you described. The equation for area and circumference of a circle are not entirely relevant to this discussion since to describe planetary motion we would be more interested in examining position vectors expressed in parametric form (i.e. vector equations).. In the plane we would be looking at equations that approximate an elliptical orbit and, if we are to consider the motion of the plane through 3-space we would have to add additional parameters

In answer to your question no, the formulas don't apply if the orbital path in the plane is non-circular (elliptical). But assuming it were actually circular since you can have a circular path in 3-space and any circle in 3-space can be defined in terms of a 2-dimensional subspace (i.e a projection) . Think of it in terms of the earth orbiting the sun in a plane and envision the plane in motion through space.In terms of vectors the path of the planet in the plane would be a component of the vector equations for it's position in space.

Said differently, for an observer standing somewhere out in space the position of a given planet at some time "t" would be given by a set of parametric (vector) equations. The 2-dimensional motion in the plane would be a component of those equations i.e. the projection of that motion onto some plane subspace of 3-space.

At the end of the day, the planetary orbits are actually a corkscrew motion, not circular, in an absolute galactic coordinate system

[KC2UGV]

At the end of the day, the planetary orbits are actually a corkscrew motion, not circular, in an absolute galactic coordinate system

Well, as seen from 0,0,0 Milky Way; it's not a corkscrew. It'd be a speeding forwards, then slowing down, speeding forwards, then slowing down, with a slight waver in it's path :)

[N2RJ]

At the end of the day, the planetary orbits are actually a corkscrew motion, not circular, in an absolute galactic coordinate system

I would like to see the reasoning behind that.

[KC2UGV]

At the end of the day, the planetary orbits are actually a corkscrew motion, not circular, in an absolute galactic coordinate system

And, which Galactic Coordinate System? The standard one, uses Sol as it's 0,0,0

[n2ize]

At the end of the day, the planetary orbits are actually a corkscrew motion, not circular, in an absolute galactic coordinate system

I am fully aware of that. That is what I wrote above. The only thing I was attempting to do was to better define "circle" or "circular path" in terms of closed curves. Regardless of whether we are talking about astronomy it still boils down to Mathematics and the principles of analytical geometry and coordinate systems and transformations. A component of the "corkscrew motion" you are describing is the elliptical motion of planets in the plane. To an observer in the plane the planet moves in an elliptical orbit Now if we take that plane of planetary motion and move it through space (lets say in a straight line perpendicular to the plane of motion for simplicity) an observer at some reference point (origin) in space would observe (say off to the side somewhere would observe a spiral (corkscrew path). Now if that observer were to be smart enough to write down the equations of that corkscrew path the planar path would be a component of that motion.

An analogy would be I am riding a bicycle at night in a straight line path while twirling a flashlight in a plane perpendicular to the direction I am riding. To me sitting on the bicycle I am moving with the flashlights plane of motion and to me it traces out a circular path in a plane. But if you are sitting on a bench observing me riding past the path of the light to your frame of reference is a corkscrew path. the planar motion of the light as I twirl it is a component of that corkscrew.

I am not trying to criticize your example. Matter of fact I like this example because when we think of planetary motion we often only think only of the elliptical orbit in the plane (as if the plane were stationary) as opposed to the frame of reference of a point in space in which it is moving in the plane as the plane of motion is hurtling through space.