View Full Version : earth orbit around sun

WolfKC

2004-May-26, 10:39 PM

I know the earth's orbit is eliptical, and I know it's tilt that affects the seaons.

I've read that earth is closes to the sun in January. Does this mean it's not equally close in July and furthest in march and October therefore not symetrical?

cyswxman

2004-May-26, 10:42 PM

It's an elliptical orbit, but the sun isn't at the center of the ellipse, but offset somewhat. As a result, perigee occurs in early January, with apogee in early July.

Brady Yoon

2004-May-26, 11:01 PM

I know the earth's orbit is eliptical, and I know it's tilt that affects the seaons.

I've read that earth is closes to the sun in January. Does this mean it's not equally close in July and furthest in march and October therefore not symetrical?

When astronomers say the tilt of the Earth's axis affects the seasons, they mean that it is the most important factor. If the Earth's axis was perpendicular to the ecliptic, there would still be seasons, albeit very small variations.

The Earth's orbit is elliptical; however, the distance of the sun isn't a significant factor compared to the tilt of the Earth's axis when it comes to heating. This is why the southern hemisphere is hotter than the northern hemisphere*. The Earth is close to perihelion in January, which coincides with the Southern summer, but the Earth is near aphelion at the time of northern summer. In theory, the Southern Hemisphere should have larger temperature ranges.

*However, because the Southern Hemisphere has more water, it acts as a giant heat reservoir and temperature ranges there are actually smaller than in the North.

WolfKC

2004-May-27, 01:21 AM

I know the earth's orbit is eliptical, and I know it's tilt that affects the seaons.

I've read that earth is closes to the sun in January. Does this mean it's not equally close in July and furthest in march and October therefore not symetrical?

When astronomers say the tilt of the Earth's axis affects the seasons, they mean that it is the most important factor. If the Earth's axis was perpendicular to the ecliptic, there would still be seasons, albeit very small variations.

The Earth's orbit is elliptical; however, the distance of the sun isn't a significant factor compared to the tilt of the Earth's axis when it comes to heating. This is why the southern hemisphere is hotter than the northern hemisphere*. The Earth is close to perihelion in January, which coincides with the Southern summer, but the Earth is near aphelion at the time of northern summer. In theory, the Southern Hemisphere should have larger temperature ranges.

*However, because the Southern Hemisphere has more water, it acts as a giant heat reservoir and temperature ranges there are actually smaller than in the North.

I appreciate the response, but the question isn't about seasons or seasonal heating...... it's simply if the orbit is symetrical, and I supposed I should add to that if it's centered. Perhaps I should assume by definition that it's not centered and symetrical becuase otherwise there wouldn't be a single closest point, there would be 2. Thinking about that is what led to the question. :)

Jpax2003

2004-May-27, 02:02 AM

I appreciate the response, but the question isn't about seasons or seasonal heating...... it's simply if the orbit is symetrical, and I supposed I should add to that if it's centered. Perhaps I should assume by definition that it's not centered and symetrical becuase otherwise there wouldn't be a single closest point, there would be 2. Thinking about that is what led to the question. :)Perhaps you are thinking that the orbit is an ellipse with the sun in the geometric center of the ellipse. This is incorrect. The sun is located at one of the foci (plural of focus) of the ellipse. There are two foci for an ellipse. Geometrically there is a midpoint on a line between these foci. The difference between the foci and the midpoint (of what would be the center of a circle) is called the eccentricity*. If an ellipse has an eccentricity of zero then it is called a circle.

Due to the Law of Gravitation, as we understand it, the orbit must be an ellipse. The orbit may be circular (or nearly so) or it can be eccentric. But either way the sun must be at a focus (single, or one of two) but not in between.

As far as seasons go, it would be nice if the earth's tilt caused the solstices to coincide with appehelion/perihelion, but they don't. Perhaps in the future, with the precession of the earth's poles, that may be the case.

*Actually, I forget if eccentricity is measured from focus to focus, or focus to midpoint, but I think you get the idea (one would be half of the other).

Spaceman Spiff

2004-May-27, 02:22 PM

I know the earth's orbit is eliptical, and I know it's tilt that affects the seaons.

I've read that earth is closes to the sun in January. Does this mean it's not equally close in July and furthest in march and October therefore not symetrical?

Perihelion, Earth's closest approach to the Sun, occurs near January 4. Aphelion, Earth's farthest point from the Sun, occurs near July 4. The actual calendar dates can vary by a calendar day. If one discounts small effects, then yes Earth's orbit is symmetric about these two points: for equal time intervals on either side of the two extremes, the distances are the same (again discounting tiny effects due to long term changes in Earth's orbit, and the Sun's small motion about the Sun-Jupiter center of mass and perturbations therefrom due to the pull of the other planets).

WolfKC

2004-May-27, 06:26 PM

http://www.chipman.org/starhoax/orbit.gif

Keeping it generalized, not to scale, not looking for extream precision...

Figure 2 is true and Figure 1 is not?

Glom

2004-May-27, 06:36 PM

The first is certainly wrong. The second looks odd but it emphasises that the sun is not at the geometric centre of the ellipse. It is at one focus.

bmillsap

2004-May-27, 07:45 PM

To add one clarification, in case you intended your picture to look this way - as Spaceman Spiff pointed out, the orbit IS symmetric along a line connecting the foci of the ellipse, which would also connect the closest and farthest points of the orbit. So in the second picure if you intend the 94 and 92 to be the farthest and closest points, the Sun would be offcenter toward the 92, but it would be STRAIGHT down in the orientation of your picture - it would not also be shifted right to left. The line connecting 94 and 92 would bisect the Sun. Like I said, I can't tell if you meant to make if offcenter both ways, though.

Glom

2004-May-27, 09:34 PM

Wolf, I don't know how much you know about the geometry of ellipses, but for the benefit of those who know little...

If you have two fixed points A and B, an ellipse is the locus of points C that satisfy the equation, AC + BC = a constant. That is, when you add the distance between the point C and point A to the distance between point C and B, you'll always get the same answer for all points on the ellipse. Essentially, it means that the triangle ABC has a constant perimeter, but since AB is a constant, we can omit it from the equation.

So to draw an ellipse, take two thumbs tacks and place them at where you want the points A and B to be. Then encircle the thumb tacks and a pencil with a circle of string of length according to your choosing. Using the pencil to keep the string taut, draw a shape around the tacks, remembering the string must be kept taut. That shape will be an ellipse.

The points A and B are the foci of the ellipse. A circle is just a special kind of ellipse where the two foci are coincident (that is they are at the same). The geometric centre of the ellipse is the point halfway between the foci. We tend to denote the distance between the a focus and the centre as c. For a circle, c = 0.

You'll notice that the line connecting the two points that are furthest away, the major axis, is the line of the foci. The ellipse is symmetical about the major axis and also symmetrical about the minor axis. The minor axis is the shortest line that can be drawn between two points on the ellipse that goes through the centre. All points on this line are equidistant from the two foci. The major axis is perpendicular to the minor axis. We call the two points at the end of the major axis, the apses.

If you consider one of the apses, the distance to the nearest focus and the distance to the furthest focus add together to equal the length of the major axis. But of course, remembering the definition of an ellipse, the distance between each focus and a point on the ellipse must add to this for all points. Hence, the constant described above is equal to the size of the major axis. However, we tend to state use the semi-major axis, half the major axis, more and we denote it with by a. Similarly, we tend to denote half the semi-minor axis by b, although we don't use it often.

So, going back to the definition of the ellipse. For two fixed points A and B, an ellipse is the locus of all the points C where AC + BC = 2a.

An interesting result of this is that since the two ends of the minor axis are equidistant from each focus, it follows that the distance must be the semi-major axis, a.

So we have a, the semi major axis, and c, the distance between the centre and a focus. How do we relate them? If we take the ratio c/a, we get the eccentricity, e, which is essentially a measure of how stretched the ellipse is. For a circle, c = 0, so e = 0. As c gets bigger, and it must always be less than a or we no longer have an ellipse, the ellipse becomes more and more stretched. Eccentricity is a useful ratio because it defines the shape of the ellipse. It is common that we define the size and shape of an ellipse by the semi-major axis and the eccentricity. We usually disregard c, since we know that if we ever needed it, it is given by c = ea.

So we have a, which is the semi-major axis, which is half the distance between the furthest points on the ellipse. We have b, which is the semi-minor axis, which is half the distance between the closest diametrically opposed points, which is given be b² = a² - c² = a²(1-e²). We have c which is have the distance between the foci. which is given by c=ea. We have e, which is the eccentricity, which is the determiner of the shape of the ellipse.

One last value of importance is the parameter, p, sometimes called the semilatus rectum. This is the distance between a focus and a point on the ellipse where the line between the two is perpendicular to the major axis and parallel to the minor axis. It turns out that the parameter is given by p = a(1+e²). This is useful because in defining a polar function, which gives us an ellipse.

r = p/(1 + e cos t), where t is the angle between the pole and r is the radius at that angle. This equation has its origin at one focus of the ellipse NOT at the geometic centre. It can be seen that when t = 90°, r = p and hence the semi latus rectum is the distance straight up from the focus to the ellipse. If we didn't define the semi latus rectum, the polar equation would be r = a(1+e²)/(1 + e cos t), which is slightly more long winded. Therefore, having it is useful because it simplifies the equation and has physical significance of its own.

Since a circle is just where the two foci are coincident, c=0 and hence e=0. Therefore, from the polar equation, we can see that for a circle, r is a constant and is given by r = a = p = b.

The polar equation is useful to us because in application to two body orbital mechanics, we find that the minor mass orbits the major mass in the path of an ellipse where the major mass is at one focus of the ellipse.

Now that we are in a situation where we consider one focus more important than the other, some more terms come to mind. We must remember that we are dealing with ellipses were 0 < e < 1. As can be seen, for t = 0°, r is a minimum and hence at this point on the ellipse, the orbiter is closest to the attractor. We call this point the periapsis and usually donate is rp. From the polar equation of the ellipse, it is given by, rp = p/(1+e) = a(1-e). At the same time, for t = 180°, the distance between the prime focus and the ellipse is greatest. This point is called the apoapsis and is where the orbiter is furthest from the attractor. It is given by, ra = p/(1-e) = a(1+e).

For a circular orbit, since the two foci are coincident at the centre, the attractor is at the centre and hence the periapsis and apoapsis are undefined.

For those who dare to read further, you may be wondering what happens when e is not less than 1 but in fact equals or is greater than 1. This is where it gets freaky. You can try to plot the graphs of various conic sections, the general term for shapes that follow the aforementioned polar equation, on graph paper or on a graphic calculator.

For a conic to have e=1, two possible conditions are possible. The first is degenerate conic, which is a straight line, where p = 0 and things get irritating. The other possibility is the ultimate extension of an ellipse. If you keep the parameter constant, but increase the eccentricity and therefore the semi major axis, you are effectively stretching the ellipse further and further. As e approaches 1, a, and c for that matter, approaches infinity. At this point, we have a parabola. For e>1, the conic is a hyperbola, which is even screwier, has negative c and a and two different curves.

WolfKC

2004-May-27, 11:59 PM

bmillsap, didn't mean to offset the sun to the left. :)

Glom, :o more than I ever knew there was to know about ellipses. :)

tracer

2004-May-28, 12:21 AM

The second looks odd

That's partly because the second looks like the orbit of the Earth is supposed to be perfectly circular, with the sun offset from the center.

The orbit of the Earth is elliptical, as in the first picture -- but the sun is offset from the center, as in the second picture.

milli360

2004-May-28, 01:48 AM

The orbit of the Earth is elliptical, as in the first picture --

Actually, the orbit of the Earth is elliptical, more as in the second picture. :)

Assuming that the Earth goes from 92mm (million miles :) ) to 94 mm, the semimajor axis is 93 mm. Using the info Glom set out so handily, the semiminor axis would be the square root of 93^2 minus 1^2. That's 92.995 mm. Almost circular--except the sun is offset down from the center by a million miles.

It's a bit more than that, but you get the picture.

GR8AUPAN

2014-Feb-21, 03:53 AM

I appreciate the response, but the question isn't about seasons or seasonal heating...... it's simply if the orbit is symetrical, and I supposed I should add to that if it's centered. Perhaps I should assume by definition that it's not centered and symetrical becuase otherwise there wouldn't be a single closest point, there would be 2. Thinking about that is what led to the question. :)

The problem I have with this whole "sun not being exactly in the center of the earth's orbit thing" is that gravity is supposedly a constant according to Newton. If that is still true in this case, then one would think that the earth in its orbit would increase in speed from Aphelion to Perihelion and decrease from Perihelion to Aphelion as it moves closer to and further from the sun's gravitational center just as a penny would moving toward the center of the earth when dropped from a tall building (understanding that earth is in an orbit, not a free fall). I think that the relationship of gravity between two objects in space would still have an inverse proportion to the distance between them whether or not they are in orbit. Gravity - albeit different from that of Earth's, should still be a constant pull rate relative to any two masses regardless of the environment they reside in. The speed variance should also occur even if the sun was indeed at the midpoint of the ellipse's major axis (which apparently it’s not?). Maybe the earth does indeed increase and decrease speed in relation to the sun throughout its orbit, I have no idea. If you take Einstein's approach, the earth being a single entity - should attempt to travel along the straightest line possible, but in a spherical path due to his distortion of space-time. Obviously an ellipse is not travelling a spherical path, but a plane over the surface of an ovoid. At any rate, I feel that neither theory explains why 1.) The earth orbits along an ellipse or 2.) The sun is not at the midpoint of said ellipse's main axis or 3.) Why spring and autumn aren't "shorter" than summer and winter because of this. Where's the bust?

antoniseb

2014-Feb-21, 10:49 AM

Welcome, GR8AUPAN, I'm not sure why you resurrected at ten-year-old thread (I guess it came up in a search engine).

So, Winter in the Northern Hemsiphere IS shorter than Summer (There's a reason February is short). That reason IS that the Earth moves faster closer to perihelion (Early January).

You made a few other statements about Newton, Einstein, and approaches... I don't think they provide much difference in terms of this measurement.

NEOWatcher

2014-Feb-21, 01:17 PM

The problem I have with this whole "sun not being exactly in the center of the earth's orbit thing"...

Probably because you have some of the science wrong.

Maybe the earth does indeed increase and decrease speed in relation to the sun throughout its orbit, I have no idea.

That was my first clue. This is a basic idea in Newton's theory. Orbits sweep out an equal area over an equal time. That means the speed changes depending on where you are in the ellipse.

If you take Einstein's approach, the earth being a single entity - should attempt to travel along the straightest line possible, but in a spherical path due to his distortion of space-time.

It's not a spherical path, it's a curved path due to the curvature of space-time.

Why spring and autumn aren't "shorter" than summer and winter because of this.

The orbit has basically nothing to do with the seasons on earth. It's all about the tilt.

Jeff Root

2014-Feb-21, 01:47 PM

The problem I have with this whole "sun not being exactly

in the center of the earth's orbit thing" is that gravity is

supposedly a constant according to Newton.

Gravity is directly proportional to the total mass involved

and inversely proportional to the square of the distance

between the two objects you are considering. In all other

ways I guess you could say it is constant, yes.

If that is still true in this case, then one would think that

the earth in its orbit would increase in speed from Aphelion

to Perihelion and decrease from Perihelion to Aphelion as it

moves closer to and further from the sun's gravitational

center ...

Exactly correct.

I think that the relationship of gravity between two objects

in space would still have an inverse proportion to the distance

between them whether or not they are in orbit.

Definitely.

Gravity - albeit different from that of Earth's, should still be

a constant pull rate relative to any two masses regardless

of the environment they reside in.

Yes, I don't know what kind of "environment" you have in

mind, but I think what you're saying here is correct.

The speed variance should also occur even if the sun was

indeed at the midpoint of the ellipse's major axis (which

apparently it’s not?).

It is not.

An elliptical orbit is an idealization which really only works

perfectly for a two-body system. But lots of situations can

be analyzed as if they were systems consisting of only two

bodies. The Sun and Earth is such a system. Ignoring all

other masses in the Universe, the Earth is in an elliptical

orbit around the Sun, where the Sun is at one focus of the

ellipse.

You may well ask why the Sun is at one focus rather than

the other. How does the Sun know which focus it should

be at? The answer of course is that the Sun doesn't know

the ellipse exists. The ellipse only exists because the Earth

is orbiting the Sun. The locations of the Sun and Earth over

time define the ellipse and its foci.

This is in contrast to something like a teeter-totter, which

exists before anyone comes along to sit on it and occupy

the two seats. Unlike a teeter-totter, the ellipse doesn't

exist on its own, independent of two objects to define it.

The Sun is said to be at one focus of Earth's orbit because

it is so MUCH more massive than Earth. The actual location

of the focus is more precisely described as the barycenter

of the Sun-Earth system. The center of mass or center of

gravity of the two bodies considered together as a system.

Earth orbits around this point, and the Sun orbits around it.

The orbits are both ellipses, and the two ellipses have the

same shape -- that is, the same proportions between their

major and minor axes. The ellipses differ only in size.

The ellipses are also in the same plane.

Because the Sun is so much more massive than Earth, its

ellipse is very small. The Sun moves very little while Earth

moves a lot. So the focal point is inside the Sun. In the

case of Jupiter, which is both far more massive than Earth

and much farther from the Sun, the barycenter and thus the

focus of the ellipse is a little way outside the Sun.

As the Sun and Earth orbit each other, their positions in their

orbits are perfectly synchronized so that they are always on

opposite sides of their respective ellipses. Earth is farthest

from the focus at the same moment the the Sun is farthest.

That is also the moment when Earth is moving slowest and

the Sun is moving slowest. And so forth.

Maybe the earth does indeed increase and decrease speed

in relation to the sun throughout its orbit, I have no idea.

You have it right.

If you take Einstein's approach, the earth being a single entity -

should attempt to travel along the straightest line possible, but

in a spherical path due to his distortion of space-time.

I'm pretty familiar with relativity, but I don't know what you

mean by "spherical path". It isn't a description I've seen before.

Could you explain that?

Obviously an ellipse is not travelling a spherical path, but a

plane over the surface of an ovoid. At any rate, I feel that

neither theory explains why 1.) The earth orbits along an ellipse

or 2.) The sun is not at the midpoint of said ellipse's main axis

or 3.) Why spring and autumn aren't "shorter" than summer and

winter because of this. Where's the bust?

One way to look at it is to say that Earth orbits in an ellipse

because the total momentum of the system is constant. There

is no mechanism to add or remove momentum from the system,

so it can't increase or decrease.

But mainly you can look at it in terms of gravitational force and

speed:

When Earth is at perihelion, its closest point to the Sun, it is

moving too fast to be in circular orbit at that distance, so it

rises away from the Sun. But gravity is strong there, quickly

slowing the Earth as it rises. So it can't keep rising forever.

The Sun's pull on the Earth does get weaker as they get farther

apart, so the speed isn't reduced so quickly, but the speed is

reduced until Earth is no longer rising. It has reached aphelion,

its farthest point from the Sun. Now it is moving too slowly to

be in a circular orbit at that distance, so it falls toward the Sun.

As it falls, it gains speed. When it has gained back all the

speed it lost when it rose away from the Sun, it will again be

at perihelion, and moving too fast to stay in circular orbit.

An elliptical orbit is a constant transfer of energy between the

kinetic energy of speed when the bodies are closer together,

and the potential energy of gravity when the bodies are farther

apart. The energy keeps being traded back and forth between

kinetic and potential, but like the momentum, the total is

constant, because there is no mechanism to add or remove

energy from the system.

Does that also answer your questions 2 and 3?

-- Jeff, in Minneapolis

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