Orbiting Planets: True Anomaly, Argument of Perihelion?

[Philosophaie]

In the case of orbiting planets does the True Anomaly(=0) start at the Argument of Perihelion equal to R at R<1*a and at a minimum? And at 180 + Argument of Perihelion equal to R at R>1*a and at a maximum? Is this true?

 

[Philosophaie]

The True Anomaly (v) is the angle of the Argument of the Perihelion and the position of the Earth at a given date. At v=0 the northern hemisphere of Earth in at its winter solstice (Jan 3 this year) but the distance from the sun is actually the closest because at v=0 it is at its perihelion. This may sound strange with the Earth being the closest to the sun and the tilted Earth being at the shortest day of the year but think it out and it makes sense. Finally when v=180deg the distance from the sun is maximum and is at its aphelion. The northern hemisphere is at its summer solstice.

 

[D H]

True anomaly is zero at periapsis by definition. What is your real question here?

Your last post in another thread resulted in that thread being locked. Try not to repeat that mistake in this thread.

You seem to have some serious misunderstandings of orbits. So, orbital mechanics in a nutshell. A good place to start with orbital mechanics is the simplest of all cases: a central mass and an object with negligible mass orbiting that central mass. The small mass accelerates toward the large central mass such that the magnitude of the acceleration is inversely proportional to the square of the distance between the two objects. Because the small mass is tiny compared to the central mass, the central mass can be viewed as essentially fixed in space.

The mathematics of central force motion (of which gravitation is just one example) dictate that the motion must follow a conic section (hyperbola, parabola, ellipse, or circle) whenever the magnitude of the force is inversely proportional to the square of the distance from the central force. You can find a proof of this in practically any sophmore/junior level classical mechanics physics text. A couple are Classical Mechanics by Goldstein and Classical Dynamics of Particles and Systems by Thornton and Marrion. No other forces are needed to make this small body follow an ellipse (or a parabola, or a hyperbola).

The next step is to a pair of masses orbiting one another such that the mass ratio of the smaller to the larger can no longer be treated as nearly zero. The motion is a bit more complex because the larger mass is noticeably attracted toward the smaller mass. By a neat little trick, the case of two comparable masses reduces to the case of a negligible mass orbiting a central mass. This is once again discussed in classical mechanics texts. The two masses will orbit the center of mass, each following similar conic sections.

Finally, the realistic case of multiple bodies. The classical mechanics texts will cover some special cases of this "N-body problem". They will not cover things like the solar system. For that, you need a more advanced text.