Challenge answers

 

 

Part 3

 

Going direct from the help page we know initially:

 

STEREO A

 

Semi-major = a_{(STEREO A)} = 0.961 AU

 

Aphelion = 1AU (given)

 

STEREO B

 

Semi-major = a_{(STEREO B)} = 1.04 AU

 

Perihelion = 1 AU (given)

 

We also have the formulas for each spacecraft:

 

(1)   (2)

 

 

(3)   (4)

 

 

Equation 2 (aphelion for STEREO A) can be rearranged as:

 

 

and so:

 

(rounded to 3 significant figures)

 

 

Equation 3 (perihelion for STEREO B) can be rearranged as:

 

 

and so:

 

(rounded to 3 significant figures)

 

 

Now we have:

 

 

STEREO A

 

a_{(STEREO A)} = semi-major = 0.961 AU

Aphelion = 1AU

Eccentricity = 0.0406

 

 

STEREO B

 

a_{(STEREO B)} = semi-major = 1.04 AU

Perihelion = 1 AU

Eccentricity = 0.0412

 

 

We can now find the Perihelion for STEREO A and the Aphelion for STEREO B:

 

 

(to 3 significant figures)

 

 (to 3 significant figures)

 

and so we are finished:

 

 

STEREO A

 

a_{(STEREO A)} = semi-major = 0.961 AU

Aphelion = 1AU

Perihelion = 0.922 AU

Eccentricity = 0.0406

 

 

STEREO B

 

a_{(STEREO B)} = semi-major = 1.04 AU

Aphelion = 1.086

Perihelion = 1 AU

Eccentricity = 0.0412