Question

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ii. elliptical orbits
(1) click the reset button. check the following boxes: voci, axes, eccentricity and visibility. in the space below, draw and label the orbit of the planet as it appears on the simulation.

a) what is the semi - major axis (a)?:

b) what is the semi - minor axis (b)?:

c) what is the focal distance (c)?:

d) an ellipse has two foci. on the simulation they are marked with a blue x. what is at one focus and what is at the other focus?

(2) click on and drag the planet around to change the eccentricity of its orbit. what happens to the shape of the planet’s orbit and the distance between the foci when the eccentricity increases?

a) what is the shape of the orbit when the eccentricity is zero?

b) what is its shape when the eccentricity is greater than zero?

c) change the orbit so that the length of the semi - major axis is greater than 1.50 au and the eccentricity of the orbit is greater than 0.45.

d) what eccentricity did you choose?:

e) enter the following distances below:
semi - major axis: \t semi - minor axis: \t focal distance:

f) using the eccentricity equation, confirm by calculation the eccentricity of the planet’s orbit. show your work.

Explanation:

This problem is about elliptical orbits, which falls under the subfield of Physics (Astronomy) in Natural Science. However, since the question here is about identifying the subfield and providing a general approach, we'll focus on the physics aspect. The problem involves concepts like semi - major axis, semi - minor axis, focal distance, and eccentricity of an elliptical orbit, which are key concepts in celestial mechanics (a part of astronomy/physics).

Step 1: Identify the core concepts

The problem deals with the geometry and properties of elliptical orbits. Concepts such as semi - major axis (\(a\)), semi - minor axis (\(b\)), focal distance (\(c\)), and eccentricity (\(e=\frac{c}{a}\)) are central here. These are concepts from the study of orbits, which is a part of physics (specifically astronomy or astrophysics).

Step 2: Relate to the subfield

In the Natural Science discipline, the subfield that best applies here is Physics, specifically the area of Astronomy (or Astrophysics) as it deals with the orbits of planets (or celestial bodies). The study of elliptical orbits and their properties is a fundamental part of understanding the motion of celestial objects, which is within the purview of physics.

Answer:

The subfield that best applies to this problem is Physics (specifically Astronomy/Astrophysics) under the Natural Science discipline.