This answer contains some nice plots of deep space spacecraft trajectories. Noticing that Voyage 2's heliocentric velocity dropped substantially just before 1990 I wanted to see why. Wikipedia's Voyager 2; Neptune describes its August 25, 1989 flyby.

But later in the mission the article shows the plot below. Since the planetary orbits are fixed I assume this is in an inertial frame.

  1. I see that Voyage 2 (red) and Pioneer 2 (green) have substantial clockwise (prograde) "knees" or bends or deviations in their trajectories in the space between Unanus and Neptune's orbit. Are these accurate?

  2. It shows all orbits traveling retrograde around the Sun until probably encountering an inner planet. That can't be right, can it?

  3. I also noticed that when trajectories change course, the radius of curvature of the deflection is several AU. For scale note that the first planet plotted is Saturn's a = 9.6 AU orbit.

Is it possible that the plot mixes frames somehow? I can't make heads or tails of these plots.

Wikimedia Outersolarsystem-probes-4407b.svg

Image cropped from source Voyager 1 extends to the right (purple) and Pioneer 10 extends to the left (dark blue).

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    $\begingroup$ No hyperbolas in SVG :( $\endgroup$ Oct 21, 2020 at 8:22
  • $\begingroup$ @SE-stopfiringthegoodguys I don't know much about SVG but I will have to learn soon. Are there at least splines of some kind? $\endgroup$
    – uhoh
    Oct 21, 2020 at 10:14
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    $\begingroup$ quadratic and cubic beziers. Also circles and ellipses. $\endgroup$ Oct 21, 2020 at 10:15

1 Answer 1


The diagram you show is the digital version of a drawing by someone with an Etch-a-Sketch: completely inaccurate. The diagram below is accurate, showing Pioneer 10 & 11 and Voyager 1 & 2 trajectories in a heliocentric, inertial reference frame, of course with the ecliptic N-S dimension collapsed. No retrograde, no dog-legs between planets.

Every now and then a spacecraft will do a broken plane maneuver (illustrative figure here) between planets but the trajectory-change angles involved are very small; by far the largest component of those maneuvers is in the ecliptic N-S direction, so they wouldn't show up on these diagrams anyway.

This is not to say that no mission headed to the outer solar system can launch retrograde with respect to Earth, i.e., slower in an inertial heliocentric frame than Earth. Multiple missions have used Venus gravity assists, along with Earth gravity assists, to get to Jupiter. To get to Venus you have to slow down from Earth's orbital speed. But this is a far cry from launching to retrograde motion in a heliocentric, inertial frame; the idea of doing that with current launch vehicles would get trajectory designers laughing.

enter image description here


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    $\begingroup$ Since the source of this image is NASA, it should be public domain, so you are free to replace the erroneous image on Wikipedia with this one. $\endgroup$ Oct 21, 2020 at 23:55
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    $\begingroup$ +1 just for "someone with an Etch-a-Sketch". Wikipedia sometimes is not the best source. $\endgroup$ Oct 22, 2020 at 5:48
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    $\begingroup$ @NickMatteo It's unfortunate, but at some point knowledgable people ask themselves "why bother?" There are far more people with Etch-a-Sketches than there are people with advanced degrees in aerospace engineering or other degrees that specialize in orbital mechanics. $\endgroup$ Oct 22, 2020 at 5:52
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    $\begingroup$ That was COOL. Somebody fixed the Wikipedia page using this image - less than 8 hours after @NickMatteo suggested it. I saw the suggestion and thought "I'll just do that" - and it was already done. $\endgroup$
    – JRE
    Oct 22, 2020 at 8:52
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    $\begingroup$ This visiualization of Voyager 1 & 2 trajectories is also very cool. It's a sort of "chase camera" following Voyager 2, with Voyager 1 showing up very close for much of the journey, and since it's a chase camera rather than an overhead view, the z-axis maneuvers are very clear. $\endgroup$ Oct 22, 2020 at 13:36

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