If any of these definitions are wrong, please let me know

[Johnny5]

I am trying to understand exactly how the earth moves around the sun.

 

Specifically, I need to be aware of any anomalies in the earth's orbit over the past 6000 years or so.

 

I want to get an intuitive feel for just how much the positions of the other planets actually influence earths orbit.

 

Copernicus supposedly went against Ptolemy's teachings in the 1500s by speculating that the earth, and other planets went around the sun.

 

I don't really trust history, but at least you get a general feel for things.

 

Copernicus` book was umm, On the revolutions of the celestial spheres... I think, and Ptolemy's book was Amalgest.

 

But, and someone please correct me if I'm wrong, Copernicus still had the planets going around the sun in circles, it wasn't until Kepler came along, with his three laws (which I need to now derive), that the model of a planets path around the sun was changed to an ellipse.

 

In fact, I think that in between them, Tycho Brahe actually went back to an earth centered system.

 

But anyway, I was thinking of doing the analysis in the rest frame of the sun.

 

I am going to ignore the motion of all the planets except earth, and model the earth's orbit as an ellipse, just as Kepler did. (A small modification can be made later, by assuming that the barycenter of the earth/moon is what travels in an elliptical path, not the earth only, but for now we can ignore the moon).

 

And I am going to derive Kepler's three laws from Newton's formula for gravity, and basic assumptions about orbital motion.

 

Now, I realize that Newton was fixated on the path of the earth's center of inertia around the sun, and ignored the motion of the whole rigid body of earth. But later I plan to take this into account, since the earth is precessing.

 

Now, in order to develop an understanding of how the earth moves around the sun, in the rest frame of the sun, one has to wonder where the earth's north poles and south poles are, in the frame.

 

One might guess that the line through the magnetic poles of earth, is perpendicular to earth's orbital plane, but that isn't the case. Instead, the earth's axis of spin is tilted relative to the plane at 23 degrees 26 minutes 22 seconds, and points towards the north star, polaris, in the constellation ursa minor.

 

So, the analysis of motion is going to be carried out in a frame where the center of inertia of the sun is permanetly at rest. Then, it will be assumed that the earth traverses an elliptical path around the center of mass of the sun, and the plane this ellipse lies in, is called the ecliptic plane.

 

Here are some links to diagrams with the ecliptic plane in them, and discussion of the "celestial sphere".

 

Hyperphysics: Ecliptic plane

 

In the previous link, take specific notice of 'declination' and 'right ascension.' Knowledge of these terms is necessary, in order to understand how to locate a given star in the "celestial sphere".

 

In the next picture, you can actually see the positions of a few planets, simultaneously, in one image, and get a feel for the fact that there really is a "ecliptic plane."

 

Clementine spacecraft picture of Saturn, Mars, & Mercury simultaneously

 

 

You can call this frame S. The X,Y axes of frame S can lie in the plane, and the z axis runs through the center of the sun.

 

Now, i think that the earth is closest to the sun in the summertime, around June 21st, which is the summer solstice. On this day, if you are located anywhere on the tropic of cancer, which is at 23 degrees 26 minutes 22 seconds north latitude, and you look straight up into the air at noon, you will be looking right at the sun.

 

It may help you to take time to visualize this clearly.

 

Suppose that wherever you are on the surface of the earth, that you are standing on a tangent plane, and that there is an axis perpendicular to this plane which runs through the center of inertia of the earth, and your feet are standing on the tangent plane. Thus, this tangent plane touches the earth at only one point. So at noon on this day, if you tilt your head back 90 degrees, at 12 noon, so that you are looking stright up into the atmosphere, you will be looking right at the sun (but you have to be at 23 degrees north. And that is June 21st. And I think this is when the earth is farthest from the sun, but If I'm wrong someone please correct me.

 

So now we come to the first definition.

 

Apehelion: Point lying on the elliptical path of earth, which is farthest away from the center of inertia of the sun. Opposite of...

 

Perihelion: Point lying on the elliptical path of earth, which is closest to the center of inertia of the sun.

 

Here are some good pictures (the first one especially):

 

Solstices, and Equinoxes

 

 

 

23 degree tilted axis, in an elliptical orbit in the ecliptic plane

 

Ecliptic Plane: Mercury, Venus, Earth, Mars

[swansont]

So at noon on this day' date=' if you tilt your head back 90 degrees, at 12 noon, so that you are looking stright up into the atmosphere, you will be looking right at the sun (but you have to be at 23 degrees north. And that is June 21st. And I think this is when the earth is farthest from the sun, but If I'm wrong someone please correct me.

[/quote']

 

No, the aphelion is around July 4, and the perihelion is around January 4, give or take a day or so. Here is a table.

[Johnny5]

No, the aphelion is around July 4, and the perihelion is around January 4, give or take a day or so. Here[/url'] is a table.

 

Thank you Dr Swanson