the separation of the foci of an ellipse that describes a planet's orbit derermines
A eccentricity of the orbit
B period of the orbit
C size of the orbit
D all of the above.
I think it is A because the closer the foci, the more circular versus elliptical the orbit is.
Size is determined by the major axis. Period: square of the period is equal to the cube of the semi-major axis.
The foci are only mentioned in regards to shape/eccentricity.
Am I missing something? What can I research? Thank you for your help.
You are correct in considering the separation of the foci as a determinant of the eccentricity of the orbit. The closer the foci, the more circular the orbit becomes, while a larger separation indicates a more elongated elliptical shape.
To further support your answer, you can also research Kepler's laws of planetary motion. Kepler's first law states that planets move in elliptical orbits with the Sun at one of the foci. This reinforces the idea that the separation of the foci determines the shape of the orbit.
Regarding the other options, you mentioned that the size of the orbit is determined by the major axis. This is also correct since the major axis represents the longest distance between two opposite points on the ellipse, which can be considered as the size or extent of the orbit.
As for the period of the orbit, you correctly mentioned that the square of the period is equal to the cube of the semi-major axis. This means that the period of the orbit is related to the size of the orbit. However, it is not directly determined by the separation of the foci.
In conclusion, the separation of the foci of an ellipse that describes a planet's orbit primarily determines the eccentricity of the orbit (option A). The size of the orbit is determined by the major axis, and the period of the orbit is related to the size of the orbit but not directly determined by the foci distance.