Astronomy Help with ellipses?

Question

Use this image for all the questions: http://i53.tinypic.com/53k6k6.gif


*A mystery spacecraft is in orbit about the Sun in the orbit shown. Find its semi-major axis

1. 66 AU

2. 20 AU

3. 80 AU

4. 14 AU

5. 26 AU

6. 54 AU

7. 40 AU

*A mystery spacecraft is in orbit about the Sun in the orbit shown. Find its: aphelion

1. 80 AU

2. 14 AU

3. 20 AU

4. 40 AU

5. 66 AU

6. 54 AU

7. 26 AU

*A mystery spacecraft is in orbit about the Sun in the orbit shown. Find its: perihelion

1. 20 AU

2. 80 AU

3. 54 AU

4. 66 AU

5. 40 AU

6. 26 AU

7. 14 AU

*A mystery spacecraft is in orbit about the Sun in the orbit shown. Find its orbital eccentricity

1. 0.00

2. 0.35

3. 0.54

4. 0.83

5. 1.5

6. 0.40

7. 0.65

Use this image: http://i53.tinypic.com/53k6k6.gif for all questions

Answer 1

The sun is drawn too far toward the center of the ellipse for the ellipse to occur in the plane of the paper. If the ellipse were in the plane of the paper, the foci should be shown as closer to the ends of the ellipse.



So I am thinking that this ellipse is tilted with respect to the plane of the paper, such that the major axis is in the plane of the paper, but the minor axis is slightly fore and back, and what we are seeing is the projection of the ellipse on to the plane of the paper.



Going on that assumption, then

semimajor axis, a=40

center to focus distance, ae = 26

eccentricity, e = ae/a = 0.65

perihelion, p = a − ae = 14

aphelion, q = a + ae = 66

semiminor axis, b = a√(1−e²) = 30.39737

b cos θ = 20

The inclination of the ellipse with respect to the paper, θ=48.9°

The line of nodes is identical with the major axis.

The argument of the perihelion is either 0° or 180°, depending on which way the ellipse is tilted and on the direction of motion in the orbit.

Answer 2

*A mystery spacecraft is in orbit about the Sun in the orbit shown

. Find its semi-major axis 40 AU



Find its: aphelion 66AU



Find its perihelion 14AU



Find its orbital eccentricity 0.65

Answer 3

An eclipse is while merchandise 'b' passes between products 'a' and 'c' and completely obscures the view of the two 'c' while seen from 'a' or viceversa. it is in many circumstances as a results of scale of merchandise 'b' or it is distance relative to the viewer to apear to be the same length as merchandise 'a' or 'c'. It occurs between us and the solar as a results of fact the moon's distance between us is in basic terms top to look to be the same length as a results of fact the solar while seen from the earth. So, in concept if any 3 products in area can fulfill the factors, there will be an eclipse. i do no longer see how we are in a position to calculate the place else 3 products might seem in this way from us in basic terms viewing from the earth. you will possibly prefer to be status on the two merchandise 'a' or 'c' to verify the eclipse.

Answer 4

Q1 A7

Q2 A5

Q3 A7

Q4 (takes too much math! we'll leave this as an exercise for the student.)_