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Link to mission report: https://www.hq.nasa.gov/alsj/a13/A13_MissionReport.pdf

So Im trying to do analysis on the mission phases of Apollo 13 but my part is to only focus on the flyby part. My partner needs information from me to figure out the Hohmann transfer from Earth to the point of issue, and then the Hohmann transfer from the point of issue back to Earth. What equations do I use to find what is needed to give to my partner to figure out Hohmann transfers? Also what parameters do my partners need to figure that out?

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    $\begingroup$ Apollo 13 never entered lunar orbit due to its accident. Do you mean the lunar orbit they would have entered if the mission had gone as planned, or the Earth parking orbit prior to trans-lunar injection? $\endgroup$
    – Russell Borogove
    Commented Nov 28, 2018 at 23:56
  • $\begingroup$ No, analyzing it at the closest approach to the moon and take that as the radius of the parking orbit. $\endgroup$
    – Vanessa
    Commented Nov 29, 2018 at 0:05

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Apollo 13 never entered a closed lunar orbit, but according to both Wikipedia and the Apollo Flight Journal, closest approach was about 254 km to the lunar surface. With the mean radius of the moon being 1737 km, this puts the orbital radius at about 1991 km.

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  • $\begingroup$ So Im trying to do analysis on the mission phases of Apollo 13 but my part is to only focus on the flyby part. My partner needs information from me to figure out the Hohmann transfer from Earth to the point of issue, and then the Hohmann transfer from the point of issue back to Earth. What equations do I use to find what is needed to give to my partner to figure out Hohmann transfers? $\endgroup$
    – Vanessa
    Commented Nov 29, 2018 at 0:29
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    $\begingroup$ By "point of issue" do you mean the point at which the accident occurred? Hohmann transfers only apply between circular orbits; 13 was on a quite eccentric elliptical at the time of the accident. What are you actually trying to do here? $\endgroup$
    – Russell Borogove
    Commented Nov 29, 2018 at 0:52
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    $\begingroup$ @Vanessa the more you can explain in detail, the easier it is for people to provide helpful answers. $\endgroup$
    – uhoh
    Commented Nov 29, 2018 at 3:40
  • $\begingroup$ yes, I mean where the accident occurred. How do I find the flyby portion of the phases in order to give my partner what they need to find the Hohmann transfers before and after the accident? And if it wasnt a Hohmann Transfer, what would the correct mission phases be? $\endgroup$
    – Vanessa
    Commented Nov 29, 2018 at 9:03
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    $\begingroup$ @Vanessa There was no Hohman transfer after the accident. At the point of the accident, Apollo 13 was on an elliptical orbit that intercepted the moon. After the accident, the were brought back with some small corrections to a free-return trajectory. $\endgroup$
    – Polygnome
    Commented Nov 29, 2018 at 10:09

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