What's the closest that an Apollo mission passed GEO on it's way to the moon?












4














@Uwe's comment




No astronaut ever visited geostationary orbit at 22-23k miles to maintain or deploy satellites. The Apollo astronauts just rushed by on their way to the Moon and back.




below the question How far have astronauts been in space? has got me wondering...



Question: What's the closest that an Apollo mission has passed GEO on it's way to the moon? Did they end up always going substantially above or below it, or did they pretty much just pass right through due to the Earth's inclination.



It's not a profound question, GEO was a lot less populated fifty years ago of course.



While GEO could be abstracted as a mathematically zero-height line, if you'd like a height by which to define what "through it" means, then let's assume whatever a typical scatter would be in North-South station keeping in the day. Perhaps 1 degree or less?










share|improve this question




















  • 2




    Somewhat apropos: Not geostationary but geosynchronous, tundra orbits pass well north and south of the equator (typical inclinations are ~43-63°). Similar are molniya orbits (~63° inclination) that have a period of half a day. Both of these pass through or or orbit near (±10k km depending on the sat) the geostationary altitude (~36k km) during some or all of their orbits. Not sure if there were any on-orbit when Apollo flew but I know the Soviets were heavy users of them.
    – Alex Hajnal
    3 hours ago








  • 1




    I'm puzzled by what you are asking. Do you mean at what inclination north or south Apollo was when it passed 22k miles?
    – Rory Alsop
    3 hours ago










  • @RoryAlsop That's how I read it. Or more precisely roughly what was the distance (in km or mi) from where Apollo was at 22k mi and the equatorial plane at 22k mi. (I must say, to my eye "k mi" just looks wrong).
    – Alex Hajnal
    3 hours ago






  • 1




    @RoryAlsop that could be a way to address it. By "how far" I'm thinking of a linear measurement but an angle measured from Earth would be okay too. You're much better at 3D orbit scenarios than I am so in this case I think it's better if I don't over-constrain potential answers.
    – uhoh
    3 hours ago






  • 1




    I'm working on getting range data to make best estimate from first 2 orbit data
    – Rory Alsop
    2 hours ago
















4














@Uwe's comment




No astronaut ever visited geostationary orbit at 22-23k miles to maintain or deploy satellites. The Apollo astronauts just rushed by on their way to the Moon and back.




below the question How far have astronauts been in space? has got me wondering...



Question: What's the closest that an Apollo mission has passed GEO on it's way to the moon? Did they end up always going substantially above or below it, or did they pretty much just pass right through due to the Earth's inclination.



It's not a profound question, GEO was a lot less populated fifty years ago of course.



While GEO could be abstracted as a mathematically zero-height line, if you'd like a height by which to define what "through it" means, then let's assume whatever a typical scatter would be in North-South station keeping in the day. Perhaps 1 degree or less?










share|improve this question




















  • 2




    Somewhat apropos: Not geostationary but geosynchronous, tundra orbits pass well north and south of the equator (typical inclinations are ~43-63°). Similar are molniya orbits (~63° inclination) that have a period of half a day. Both of these pass through or or orbit near (±10k km depending on the sat) the geostationary altitude (~36k km) during some or all of their orbits. Not sure if there were any on-orbit when Apollo flew but I know the Soviets were heavy users of them.
    – Alex Hajnal
    3 hours ago








  • 1




    I'm puzzled by what you are asking. Do you mean at what inclination north or south Apollo was when it passed 22k miles?
    – Rory Alsop
    3 hours ago










  • @RoryAlsop That's how I read it. Or more precisely roughly what was the distance (in km or mi) from where Apollo was at 22k mi and the equatorial plane at 22k mi. (I must say, to my eye "k mi" just looks wrong).
    – Alex Hajnal
    3 hours ago






  • 1




    @RoryAlsop that could be a way to address it. By "how far" I'm thinking of a linear measurement but an angle measured from Earth would be okay too. You're much better at 3D orbit scenarios than I am so in this case I think it's better if I don't over-constrain potential answers.
    – uhoh
    3 hours ago






  • 1




    I'm working on getting range data to make best estimate from first 2 orbit data
    – Rory Alsop
    2 hours ago














4












4








4







@Uwe's comment




No astronaut ever visited geostationary orbit at 22-23k miles to maintain or deploy satellites. The Apollo astronauts just rushed by on their way to the Moon and back.




below the question How far have astronauts been in space? has got me wondering...



Question: What's the closest that an Apollo mission has passed GEO on it's way to the moon? Did they end up always going substantially above or below it, or did they pretty much just pass right through due to the Earth's inclination.



It's not a profound question, GEO was a lot less populated fifty years ago of course.



While GEO could be abstracted as a mathematically zero-height line, if you'd like a height by which to define what "through it" means, then let's assume whatever a typical scatter would be in North-South station keeping in the day. Perhaps 1 degree or less?










share|improve this question















@Uwe's comment




No astronaut ever visited geostationary orbit at 22-23k miles to maintain or deploy satellites. The Apollo astronauts just rushed by on their way to the Moon and back.




below the question How far have astronauts been in space? has got me wondering...



Question: What's the closest that an Apollo mission has passed GEO on it's way to the moon? Did they end up always going substantially above or below it, or did they pretty much just pass right through due to the Earth's inclination.



It's not a profound question, GEO was a lot less populated fifty years ago of course.



While GEO could be abstracted as a mathematically zero-height line, if you'd like a height by which to define what "through it" means, then let's assume whatever a typical scatter would be in North-South station keeping in the day. Perhaps 1 degree or less?







apollo-program trajectory geostationary trajectory-design






share|improve this question















share|improve this question













share|improve this question




share|improve this question








edited 3 hours ago

























asked 4 hours ago









uhoh

34.8k17119432




34.8k17119432








  • 2




    Somewhat apropos: Not geostationary but geosynchronous, tundra orbits pass well north and south of the equator (typical inclinations are ~43-63°). Similar are molniya orbits (~63° inclination) that have a period of half a day. Both of these pass through or or orbit near (±10k km depending on the sat) the geostationary altitude (~36k km) during some or all of their orbits. Not sure if there were any on-orbit when Apollo flew but I know the Soviets were heavy users of them.
    – Alex Hajnal
    3 hours ago








  • 1




    I'm puzzled by what you are asking. Do you mean at what inclination north or south Apollo was when it passed 22k miles?
    – Rory Alsop
    3 hours ago










  • @RoryAlsop That's how I read it. Or more precisely roughly what was the distance (in km or mi) from where Apollo was at 22k mi and the equatorial plane at 22k mi. (I must say, to my eye "k mi" just looks wrong).
    – Alex Hajnal
    3 hours ago






  • 1




    @RoryAlsop that could be a way to address it. By "how far" I'm thinking of a linear measurement but an angle measured from Earth would be okay too. You're much better at 3D orbit scenarios than I am so in this case I think it's better if I don't over-constrain potential answers.
    – uhoh
    3 hours ago






  • 1




    I'm working on getting range data to make best estimate from first 2 orbit data
    – Rory Alsop
    2 hours ago














  • 2




    Somewhat apropos: Not geostationary but geosynchronous, tundra orbits pass well north and south of the equator (typical inclinations are ~43-63°). Similar are molniya orbits (~63° inclination) that have a period of half a day. Both of these pass through or or orbit near (±10k km depending on the sat) the geostationary altitude (~36k km) during some or all of their orbits. Not sure if there were any on-orbit when Apollo flew but I know the Soviets were heavy users of them.
    – Alex Hajnal
    3 hours ago








  • 1




    I'm puzzled by what you are asking. Do you mean at what inclination north or south Apollo was when it passed 22k miles?
    – Rory Alsop
    3 hours ago










  • @RoryAlsop That's how I read it. Or more precisely roughly what was the distance (in km or mi) from where Apollo was at 22k mi and the equatorial plane at 22k mi. (I must say, to my eye "k mi" just looks wrong).
    – Alex Hajnal
    3 hours ago






  • 1




    @RoryAlsop that could be a way to address it. By "how far" I'm thinking of a linear measurement but an angle measured from Earth would be okay too. You're much better at 3D orbit scenarios than I am so in this case I think it's better if I don't over-constrain potential answers.
    – uhoh
    3 hours ago






  • 1




    I'm working on getting range data to make best estimate from first 2 orbit data
    – Rory Alsop
    2 hours ago








2




2




Somewhat apropos: Not geostationary but geosynchronous, tundra orbits pass well north and south of the equator (typical inclinations are ~43-63°). Similar are molniya orbits (~63° inclination) that have a period of half a day. Both of these pass through or or orbit near (±10k km depending on the sat) the geostationary altitude (~36k km) during some or all of their orbits. Not sure if there were any on-orbit when Apollo flew but I know the Soviets were heavy users of them.
– Alex Hajnal
3 hours ago






Somewhat apropos: Not geostationary but geosynchronous, tundra orbits pass well north and south of the equator (typical inclinations are ~43-63°). Similar are molniya orbits (~63° inclination) that have a period of half a day. Both of these pass through or or orbit near (±10k km depending on the sat) the geostationary altitude (~36k km) during some or all of their orbits. Not sure if there were any on-orbit when Apollo flew but I know the Soviets were heavy users of them.
– Alex Hajnal
3 hours ago






1




1




I'm puzzled by what you are asking. Do you mean at what inclination north or south Apollo was when it passed 22k miles?
– Rory Alsop
3 hours ago




I'm puzzled by what you are asking. Do you mean at what inclination north or south Apollo was when it passed 22k miles?
– Rory Alsop
3 hours ago












@RoryAlsop That's how I read it. Or more precisely roughly what was the distance (in km or mi) from where Apollo was at 22k mi and the equatorial plane at 22k mi. (I must say, to my eye "k mi" just looks wrong).
– Alex Hajnal
3 hours ago




@RoryAlsop That's how I read it. Or more precisely roughly what was the distance (in km or mi) from where Apollo was at 22k mi and the equatorial plane at 22k mi. (I must say, to my eye "k mi" just looks wrong).
– Alex Hajnal
3 hours ago




1




1




@RoryAlsop that could be a way to address it. By "how far" I'm thinking of a linear measurement but an angle measured from Earth would be okay too. You're much better at 3D orbit scenarios than I am so in this case I think it's better if I don't over-constrain potential answers.
– uhoh
3 hours ago




@RoryAlsop that could be a way to address it. By "how far" I'm thinking of a linear measurement but an angle measured from Earth would be okay too. You're much better at 3D orbit scenarios than I am so in this case I think it's better if I don't over-constrain potential answers.
– uhoh
3 hours ago




1




1




I'm working on getting range data to make best estimate from first 2 orbit data
– Rory Alsop
2 hours ago




I'm working on getting range data to make best estimate from first 2 orbit data
– Rory Alsop
2 hours ago










2 Answers
2






active

oldest

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0














Apollo 11 first entered a 103 nautical mile orbit, and midway through orbit 2 was boosted onto lunar trajectory. This was 2hrs 50mins into the mission, so from this point onwards, mission control were not considering orbits of the Earth.



Apollo 11 passed 22k nautical miles at 5hrs and 22 minutes into the mission.



2:54 p.m.- The spacecraft is reported 22,000 nautical miles from Earth 
and traveling at 12,914 feet per second. Crew members keep busy with
housekeeping duties.


This was during the Translunar Coast phase, which ran from 2hrs 44mins to 75hrs 74mins



Translunar Coast (Duration 73:10) 2:44 - 75:54 GET
After TLI, which places the spacecraft in a free lunar return trajectory,
the following major events occur prior to LOI:
(a) Transposition, docking and LM ejection, including SIVB photography
(b) Separation from SIVB and a CSM evasive maneuver
(c) SIVB propulsive venting of propellants (slingshot)
(d) Two series of P23 cislunar navigation sightings, star/earth horizon,
consisting of five sets at 06:00 GET and five sets at 24:30 GET
(e) Four midcourse corrections which take place at TLI +9, TLI +24,
LOI -22 and LOI -5 hours with DV nominally zero (See Table 1-1).
(f) Passive thermal control (PTC) will be conducted during all periods
when other activities do not require different attitudes.
(g) LM inspection and housekeeping
(h) LOI1, performed at 75:54:28 GET, ends the TLC phase.


There is nothing in the flightplan to indicate this was considered as a point of interest, in fact at that point the plan states:



Doff & Stow helmet, gloves and PGA's.


There is an interesting point on page 115 of the flight plan showing field of view at 7hrs 0 minutes into the mission, and it appears to be directly overhead Honduras, at 15N, but I don't have range data at that time stamp.





Weirdly, in hunting for info, far too many moon landing hoax pages seem to have relevant data but misunderstand or misuse it badly...






share|improve this answer





























    0














    If we want to know the distance of the Apollo astronauts to the GEO orbit, we have to consider the different planes.



    enter image description here



    Graphic from wikipedia.



    The GEO orbit's plane is the equatorial plane of Earth tilted by 23.44 ° to plane of the Earth's orbit.



    The plane of the trajectory from Earth to Moon is close to the plane of the Moon orbit tilted by 5.14 °.



    For the calculation I assume the axis of Earth lying in a plane htrough the centers of Earth and Moon as shown in the graphic.
    The angle between both planes is therefore 23.44 ° + 5.14 ° = 28.58 °. The radius of the GEO orbit is 42,164 km. We aply the formula c = 2Rsin(α/2) for the chord length of a circular segment and get the result 10,407 km. This is the distance at the closest approach between the Apollo trajectory and the GEO orbit. For a trajectory in a different plane we have to add or subtract the angle.






    share|improve this answer



















    • 1




      I think you missed the point that the two planes intersect. Depending on the position of the moon, Apollo might have passed right through GEO.
      – asdfex
      1 hour ago










    • A translunar trajectory isn't necessarily in the plane of the moon's orbit (I'm not saying it was equatorial, though)
      – pericynthion
      1 hour ago










    • @pericynthion That is why I wrote: "For a trajectory in a different plane we have to add or subtract the angle".
      – Uwe
      57 mins ago










    • @asdfex Of course the two planes do intersect. We have to consider the individual position of the Moon for each Apollo mission.
      – Uwe
      54 mins ago










    • @Uwe I don't down vote often, but I have here because this doesn't even begin to answer the question. You've just pasted an image and described what someone would do if they wanted to start to answer, but without actually doing it yourself. I'd say convert this to one of your excellent comments and delete this.
      – uhoh
      45 mins ago













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    2 Answers
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    2 Answers
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    active

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    0














    Apollo 11 first entered a 103 nautical mile orbit, and midway through orbit 2 was boosted onto lunar trajectory. This was 2hrs 50mins into the mission, so from this point onwards, mission control were not considering orbits of the Earth.



    Apollo 11 passed 22k nautical miles at 5hrs and 22 minutes into the mission.



    2:54 p.m.- The spacecraft is reported 22,000 nautical miles from Earth 
    and traveling at 12,914 feet per second. Crew members keep busy with
    housekeeping duties.


    This was during the Translunar Coast phase, which ran from 2hrs 44mins to 75hrs 74mins



    Translunar Coast (Duration 73:10) 2:44 - 75:54 GET
    After TLI, which places the spacecraft in a free lunar return trajectory,
    the following major events occur prior to LOI:
    (a) Transposition, docking and LM ejection, including SIVB photography
    (b) Separation from SIVB and a CSM evasive maneuver
    (c) SIVB propulsive venting of propellants (slingshot)
    (d) Two series of P23 cislunar navigation sightings, star/earth horizon,
    consisting of five sets at 06:00 GET and five sets at 24:30 GET
    (e) Four midcourse corrections which take place at TLI +9, TLI +24,
    LOI -22 and LOI -5 hours with DV nominally zero (See Table 1-1).
    (f) Passive thermal control (PTC) will be conducted during all periods
    when other activities do not require different attitudes.
    (g) LM inspection and housekeeping
    (h) LOI1, performed at 75:54:28 GET, ends the TLC phase.


    There is nothing in the flightplan to indicate this was considered as a point of interest, in fact at that point the plan states:



    Doff & Stow helmet, gloves and PGA's.


    There is an interesting point on page 115 of the flight plan showing field of view at 7hrs 0 minutes into the mission, and it appears to be directly overhead Honduras, at 15N, but I don't have range data at that time stamp.





    Weirdly, in hunting for info, far too many moon landing hoax pages seem to have relevant data but misunderstand or misuse it badly...






    share|improve this answer


























      0














      Apollo 11 first entered a 103 nautical mile orbit, and midway through orbit 2 was boosted onto lunar trajectory. This was 2hrs 50mins into the mission, so from this point onwards, mission control were not considering orbits of the Earth.



      Apollo 11 passed 22k nautical miles at 5hrs and 22 minutes into the mission.



      2:54 p.m.- The spacecraft is reported 22,000 nautical miles from Earth 
      and traveling at 12,914 feet per second. Crew members keep busy with
      housekeeping duties.


      This was during the Translunar Coast phase, which ran from 2hrs 44mins to 75hrs 74mins



      Translunar Coast (Duration 73:10) 2:44 - 75:54 GET
      After TLI, which places the spacecraft in a free lunar return trajectory,
      the following major events occur prior to LOI:
      (a) Transposition, docking and LM ejection, including SIVB photography
      (b) Separation from SIVB and a CSM evasive maneuver
      (c) SIVB propulsive venting of propellants (slingshot)
      (d) Two series of P23 cislunar navigation sightings, star/earth horizon,
      consisting of five sets at 06:00 GET and five sets at 24:30 GET
      (e) Four midcourse corrections which take place at TLI +9, TLI +24,
      LOI -22 and LOI -5 hours with DV nominally zero (See Table 1-1).
      (f) Passive thermal control (PTC) will be conducted during all periods
      when other activities do not require different attitudes.
      (g) LM inspection and housekeeping
      (h) LOI1, performed at 75:54:28 GET, ends the TLC phase.


      There is nothing in the flightplan to indicate this was considered as a point of interest, in fact at that point the plan states:



      Doff & Stow helmet, gloves and PGA's.


      There is an interesting point on page 115 of the flight plan showing field of view at 7hrs 0 minutes into the mission, and it appears to be directly overhead Honduras, at 15N, but I don't have range data at that time stamp.





      Weirdly, in hunting for info, far too many moon landing hoax pages seem to have relevant data but misunderstand or misuse it badly...






      share|improve this answer
























        0












        0








        0






        Apollo 11 first entered a 103 nautical mile orbit, and midway through orbit 2 was boosted onto lunar trajectory. This was 2hrs 50mins into the mission, so from this point onwards, mission control were not considering orbits of the Earth.



        Apollo 11 passed 22k nautical miles at 5hrs and 22 minutes into the mission.



        2:54 p.m.- The spacecraft is reported 22,000 nautical miles from Earth 
        and traveling at 12,914 feet per second. Crew members keep busy with
        housekeeping duties.


        This was during the Translunar Coast phase, which ran from 2hrs 44mins to 75hrs 74mins



        Translunar Coast (Duration 73:10) 2:44 - 75:54 GET
        After TLI, which places the spacecraft in a free lunar return trajectory,
        the following major events occur prior to LOI:
        (a) Transposition, docking and LM ejection, including SIVB photography
        (b) Separation from SIVB and a CSM evasive maneuver
        (c) SIVB propulsive venting of propellants (slingshot)
        (d) Two series of P23 cislunar navigation sightings, star/earth horizon,
        consisting of five sets at 06:00 GET and five sets at 24:30 GET
        (e) Four midcourse corrections which take place at TLI +9, TLI +24,
        LOI -22 and LOI -5 hours with DV nominally zero (See Table 1-1).
        (f) Passive thermal control (PTC) will be conducted during all periods
        when other activities do not require different attitudes.
        (g) LM inspection and housekeeping
        (h) LOI1, performed at 75:54:28 GET, ends the TLC phase.


        There is nothing in the flightplan to indicate this was considered as a point of interest, in fact at that point the plan states:



        Doff & Stow helmet, gloves and PGA's.


        There is an interesting point on page 115 of the flight plan showing field of view at 7hrs 0 minutes into the mission, and it appears to be directly overhead Honduras, at 15N, but I don't have range data at that time stamp.





        Weirdly, in hunting for info, far too many moon landing hoax pages seem to have relevant data but misunderstand or misuse it badly...






        share|improve this answer












        Apollo 11 first entered a 103 nautical mile orbit, and midway through orbit 2 was boosted onto lunar trajectory. This was 2hrs 50mins into the mission, so from this point onwards, mission control were not considering orbits of the Earth.



        Apollo 11 passed 22k nautical miles at 5hrs and 22 minutes into the mission.



        2:54 p.m.- The spacecraft is reported 22,000 nautical miles from Earth 
        and traveling at 12,914 feet per second. Crew members keep busy with
        housekeeping duties.


        This was during the Translunar Coast phase, which ran from 2hrs 44mins to 75hrs 74mins



        Translunar Coast (Duration 73:10) 2:44 - 75:54 GET
        After TLI, which places the spacecraft in a free lunar return trajectory,
        the following major events occur prior to LOI:
        (a) Transposition, docking and LM ejection, including SIVB photography
        (b) Separation from SIVB and a CSM evasive maneuver
        (c) SIVB propulsive venting of propellants (slingshot)
        (d) Two series of P23 cislunar navigation sightings, star/earth horizon,
        consisting of five sets at 06:00 GET and five sets at 24:30 GET
        (e) Four midcourse corrections which take place at TLI +9, TLI +24,
        LOI -22 and LOI -5 hours with DV nominally zero (See Table 1-1).
        (f) Passive thermal control (PTC) will be conducted during all periods
        when other activities do not require different attitudes.
        (g) LM inspection and housekeeping
        (h) LOI1, performed at 75:54:28 GET, ends the TLC phase.


        There is nothing in the flightplan to indicate this was considered as a point of interest, in fact at that point the plan states:



        Doff & Stow helmet, gloves and PGA's.


        There is an interesting point on page 115 of the flight plan showing field of view at 7hrs 0 minutes into the mission, and it appears to be directly overhead Honduras, at 15N, but I don't have range data at that time stamp.





        Weirdly, in hunting for info, far too many moon landing hoax pages seem to have relevant data but misunderstand or misuse it badly...







        share|improve this answer












        share|improve this answer



        share|improve this answer










        answered 2 hours ago









        Rory Alsop

        9,74324272




        9,74324272























            0














            If we want to know the distance of the Apollo astronauts to the GEO orbit, we have to consider the different planes.



            enter image description here



            Graphic from wikipedia.



            The GEO orbit's plane is the equatorial plane of Earth tilted by 23.44 ° to plane of the Earth's orbit.



            The plane of the trajectory from Earth to Moon is close to the plane of the Moon orbit tilted by 5.14 °.



            For the calculation I assume the axis of Earth lying in a plane htrough the centers of Earth and Moon as shown in the graphic.
            The angle between both planes is therefore 23.44 ° + 5.14 ° = 28.58 °. The radius of the GEO orbit is 42,164 km. We aply the formula c = 2Rsin(α/2) for the chord length of a circular segment and get the result 10,407 km. This is the distance at the closest approach between the Apollo trajectory and the GEO orbit. For a trajectory in a different plane we have to add or subtract the angle.






            share|improve this answer



















            • 1




              I think you missed the point that the two planes intersect. Depending on the position of the moon, Apollo might have passed right through GEO.
              – asdfex
              1 hour ago










            • A translunar trajectory isn't necessarily in the plane of the moon's orbit (I'm not saying it was equatorial, though)
              – pericynthion
              1 hour ago










            • @pericynthion That is why I wrote: "For a trajectory in a different plane we have to add or subtract the angle".
              – Uwe
              57 mins ago










            • @asdfex Of course the two planes do intersect. We have to consider the individual position of the Moon for each Apollo mission.
              – Uwe
              54 mins ago










            • @Uwe I don't down vote often, but I have here because this doesn't even begin to answer the question. You've just pasted an image and described what someone would do if they wanted to start to answer, but without actually doing it yourself. I'd say convert this to one of your excellent comments and delete this.
              – uhoh
              45 mins ago


















            0














            If we want to know the distance of the Apollo astronauts to the GEO orbit, we have to consider the different planes.



            enter image description here



            Graphic from wikipedia.



            The GEO orbit's plane is the equatorial plane of Earth tilted by 23.44 ° to plane of the Earth's orbit.



            The plane of the trajectory from Earth to Moon is close to the plane of the Moon orbit tilted by 5.14 °.



            For the calculation I assume the axis of Earth lying in a plane htrough the centers of Earth and Moon as shown in the graphic.
            The angle between both planes is therefore 23.44 ° + 5.14 ° = 28.58 °. The radius of the GEO orbit is 42,164 km. We aply the formula c = 2Rsin(α/2) for the chord length of a circular segment and get the result 10,407 km. This is the distance at the closest approach between the Apollo trajectory and the GEO orbit. For a trajectory in a different plane we have to add or subtract the angle.






            share|improve this answer



















            • 1




              I think you missed the point that the two planes intersect. Depending on the position of the moon, Apollo might have passed right through GEO.
              – asdfex
              1 hour ago










            • A translunar trajectory isn't necessarily in the plane of the moon's orbit (I'm not saying it was equatorial, though)
              – pericynthion
              1 hour ago










            • @pericynthion That is why I wrote: "For a trajectory in a different plane we have to add or subtract the angle".
              – Uwe
              57 mins ago










            • @asdfex Of course the two planes do intersect. We have to consider the individual position of the Moon for each Apollo mission.
              – Uwe
              54 mins ago










            • @Uwe I don't down vote often, but I have here because this doesn't even begin to answer the question. You've just pasted an image and described what someone would do if they wanted to start to answer, but without actually doing it yourself. I'd say convert this to one of your excellent comments and delete this.
              – uhoh
              45 mins ago
















            0












            0








            0






            If we want to know the distance of the Apollo astronauts to the GEO orbit, we have to consider the different planes.



            enter image description here



            Graphic from wikipedia.



            The GEO orbit's plane is the equatorial plane of Earth tilted by 23.44 ° to plane of the Earth's orbit.



            The plane of the trajectory from Earth to Moon is close to the plane of the Moon orbit tilted by 5.14 °.



            For the calculation I assume the axis of Earth lying in a plane htrough the centers of Earth and Moon as shown in the graphic.
            The angle between both planes is therefore 23.44 ° + 5.14 ° = 28.58 °. The radius of the GEO orbit is 42,164 km. We aply the formula c = 2Rsin(α/2) for the chord length of a circular segment and get the result 10,407 km. This is the distance at the closest approach between the Apollo trajectory and the GEO orbit. For a trajectory in a different plane we have to add or subtract the angle.






            share|improve this answer














            If we want to know the distance of the Apollo astronauts to the GEO orbit, we have to consider the different planes.



            enter image description here



            Graphic from wikipedia.



            The GEO orbit's plane is the equatorial plane of Earth tilted by 23.44 ° to plane of the Earth's orbit.



            The plane of the trajectory from Earth to Moon is close to the plane of the Moon orbit tilted by 5.14 °.



            For the calculation I assume the axis of Earth lying in a plane htrough the centers of Earth and Moon as shown in the graphic.
            The angle between both planes is therefore 23.44 ° + 5.14 ° = 28.58 °. The radius of the GEO orbit is 42,164 km. We aply the formula c = 2Rsin(α/2) for the chord length of a circular segment and get the result 10,407 km. This is the distance at the closest approach between the Apollo trajectory and the GEO orbit. For a trajectory in a different plane we have to add or subtract the angle.







            share|improve this answer














            share|improve this answer



            share|improve this answer








            edited 43 mins ago

























            answered 1 hour ago









            Uwe

            8,80322650




            8,80322650








            • 1




              I think you missed the point that the two planes intersect. Depending on the position of the moon, Apollo might have passed right through GEO.
              – asdfex
              1 hour ago










            • A translunar trajectory isn't necessarily in the plane of the moon's orbit (I'm not saying it was equatorial, though)
              – pericynthion
              1 hour ago










            • @pericynthion That is why I wrote: "For a trajectory in a different plane we have to add or subtract the angle".
              – Uwe
              57 mins ago










            • @asdfex Of course the two planes do intersect. We have to consider the individual position of the Moon for each Apollo mission.
              – Uwe
              54 mins ago










            • @Uwe I don't down vote often, but I have here because this doesn't even begin to answer the question. You've just pasted an image and described what someone would do if they wanted to start to answer, but without actually doing it yourself. I'd say convert this to one of your excellent comments and delete this.
              – uhoh
              45 mins ago
















            • 1




              I think you missed the point that the two planes intersect. Depending on the position of the moon, Apollo might have passed right through GEO.
              – asdfex
              1 hour ago










            • A translunar trajectory isn't necessarily in the plane of the moon's orbit (I'm not saying it was equatorial, though)
              – pericynthion
              1 hour ago










            • @pericynthion That is why I wrote: "For a trajectory in a different plane we have to add or subtract the angle".
              – Uwe
              57 mins ago










            • @asdfex Of course the two planes do intersect. We have to consider the individual position of the Moon for each Apollo mission.
              – Uwe
              54 mins ago










            • @Uwe I don't down vote often, but I have here because this doesn't even begin to answer the question. You've just pasted an image and described what someone would do if they wanted to start to answer, but without actually doing it yourself. I'd say convert this to one of your excellent comments and delete this.
              – uhoh
              45 mins ago










            1




            1




            I think you missed the point that the two planes intersect. Depending on the position of the moon, Apollo might have passed right through GEO.
            – asdfex
            1 hour ago




            I think you missed the point that the two planes intersect. Depending on the position of the moon, Apollo might have passed right through GEO.
            – asdfex
            1 hour ago












            A translunar trajectory isn't necessarily in the plane of the moon's orbit (I'm not saying it was equatorial, though)
            – pericynthion
            1 hour ago




            A translunar trajectory isn't necessarily in the plane of the moon's orbit (I'm not saying it was equatorial, though)
            – pericynthion
            1 hour ago












            @pericynthion That is why I wrote: "For a trajectory in a different plane we have to add or subtract the angle".
            – Uwe
            57 mins ago




            @pericynthion That is why I wrote: "For a trajectory in a different plane we have to add or subtract the angle".
            – Uwe
            57 mins ago












            @asdfex Of course the two planes do intersect. We have to consider the individual position of the Moon for each Apollo mission.
            – Uwe
            54 mins ago




            @asdfex Of course the two planes do intersect. We have to consider the individual position of the Moon for each Apollo mission.
            – Uwe
            54 mins ago












            @Uwe I don't down vote often, but I have here because this doesn't even begin to answer the question. You've just pasted an image and described what someone would do if they wanted to start to answer, but without actually doing it yourself. I'd say convert this to one of your excellent comments and delete this.
            – uhoh
            45 mins ago






            @Uwe I don't down vote often, but I have here because this doesn't even begin to answer the question. You've just pasted an image and described what someone would do if they wanted to start to answer, but without actually doing it yourself. I'd say convert this to one of your excellent comments and delete this.
            – uhoh
            45 mins ago




















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