The angular momentum of a planet is conserved if taken with respect to:
a)The center of the ellipse
b) The focus of the ellipse at the sun
c)The focus of the ellipse opposite the sun
d)Both foci of the ellipse
Hmmm. None of the answers are correct, as the focus of the ellipse is not at the center of the Sun. Consider Jupiter and the Sun. The Baricenter is one solar diameter from the center of the Sun, and both jupiter and the Sun rotate in an ellipse about that baricenter.
Now for Sun and smaller planets, the Sun is very close to the foci of the ellipse.
a) is a bad answer
b. is nearly right
Now, the real problem is that the system has to have conservation of angular momentum, and as discussed above, the Sun is also moving about the baricenter. The sum of the planet's angular momentum plus the angular momentum of the Sun about the Baricenter is then conserved.
So if one blithely assumes The sun's center is the foci (baricenter) , then its angular momentum is zero.
so, if the Sun has zero angular momentum, what about c)?
it would be true in that case, the angular momentum about the other foci would be conserved, however if the Sun is in however in a slight elliptical orbit, then c) is not true, as that the remote foci is not a point of rotational symettry of the system.
d) answed above.
So what does your teacher want as a "correct" answer. I would go with b), however, it is not a good question, and I would not argue with the teacher on this, because it depends on assumtions, "foci at the sun" is the main problem. In real systems, it the center of rotation (foci, or baricenter), is never at the center of one body in a two body system.
http://en.wikipedia.org/wiki/Barycentric_coordinates_%28astronomy%29#Two-body_problem
To determine which point the angular momentum of a planet is conserved with respect to, let's first understand what angular momentum is.
Angular momentum is a property of rotating bodies and is defined as the product of the moment of inertia and angular velocity. It is a vector quantity, meaning it has both magnitude and direction.
In the case of a planet orbiting the Sun, the planet's angular momentum is conserved. This means that its angular momentum remains constant throughout its orbit.
Now, let's examine the options:
a) The center of the ellipse: When calculating angular momentum with respect to the center of the ellipse, it will not remain constant throughout the planet's orbit. As the planet moves along its elliptical path, its distance from the center of the ellipse keeps changing, in turn, affecting the value of the angular momentum. Therefore, option a) is not correct.
b) The focus of the ellipse at the sun: Since the sun is located at one of the foci of the elliptical orbit, the distance from the planet to the sun remains constant. As a result, when calculating angular momentum with respect to the focus of the ellipse at the sun, it remains constant throughout the planet's orbit. Hence, option b) is correct.
c) The focus of the ellipse opposite the sun: This focus is not physically significant in terms of the solar system dynamics, so choosing this point would not ensure the conservation of angular momentum. Therefore, option c) is not correct.
d) Both foci of the ellipse: Using both foci of the ellipse is unnecessary because angular momentum is conserved with respect to the focus of the ellipse at the sun. Choosing both foci would not provide any additional insight or conservation. Thus, option d) is not correct.
In conclusion, the angular momentum of a planet is conserved when taken with respect to the focus of the ellipse at the Sun, which is option b).