Question

eccentricity
toggle the eccentricity and foci checkboxes and create different orbits. you should see the panel below.

1. changing the orbit, try to get the pink arrow to each label of the eccentricity panel (see picture on the left). describe the process you used to achieve this.
2. create two different orbits with the same eccentricity as eris. what is the same in those orbits, and what is different?
3. describe in your own words: what is eccentricity?
4. what observations can you make about the foci related to eccentricity?

how velocity affects the orbits
restart the sim. for these challenges, move the velocity arrow only.

1. discover how to create a circular orbit. sketch the velocity vector below:
2. create a highly eccentric orbit (eccentricity greater than 0.8) that doesnt escape or crash into the sun. what characteristics does the velocity have in this scenario?

discuss with your group to see the different conclusions your peers arrived at

Explanation:

1. To get the pink arrow to each label of the Eccentricity panel, one should adjust the orbital elements (such as the semi - major axis, velocity vector etc.) through trial - and - error while observing the changes in the orbit's eccentricity as shown in the simulation.
2. Orbits with the same eccentricity as Eris will have the same shape (in terms of how non - circular they are). Differences could include the size of the orbit (semi - major axis), the period of revolution, and the objects in the orbit.
3. Eccentricity is a measure of how much an orbit deviates from being a perfect circle. An eccentricity of 0 is a circle, values between 0 and 1 are ellipses, an eccentricity of 1 is a parabola, and values greater than 1 are hyperbolas.
4. The foci of an elliptical orbit are related to the eccentricity. As the eccentricity increases, the distance between the foci increases relative to the size of the orbit. For a circular orbit (eccentricity = 0), the two foci coincide at the center of the circle.
5. To create a circular orbit, the velocity vector should be perpendicular to the position vector from the central body (like the Sun) and have a magnitude that satisfies the centripetal force requirements for circular motion. The velocity vector will be tangent to the circular path.
6. For a highly eccentric orbit (eccentricity > 0.8) that doesn't escape or crash into the Sun, the velocity at the closest point (perihelion) must be high enough to move the object away from the Sun but not so high as to cause escape, and at the farthest point (aphelion) the velocity must be low enough to allow the object to fall back towards the Sun.

Answer:

1. Adjust orbital elements through trial - and - error.
2. Same: shape (non - circularity); Different: size, period, orbiting objects.
3. Measure of orbit's deviation from a circle.
4. As eccentricity increases, foci distance relative to orbit size increases.
5. Velocity vector perpendicular to position vector, tangent to circle.
6. High velocity at perihelion, low velocity at aphelion within non - escape/non - crash range.