Interesting things about Voyager 1 and 2 launches

There is something fascinating about science. One gets such wholesale returns of conjecture out of such a trifling investment of fact.

--Mark Twain

It's amazing how much we can do with such a small amount of data. The following analysis is based solely on the dates of launch and arrival of the Voyager spacecrafts, and an ephemeris of the planets.

Voyager 2 was launched on 1977-08-20T14:29:00Z, while Voyager 1 was launched later on 1977-09-05T12:56:00Z. Voyager 1 passed Voyager 2 on the way out (the exact time depends on how you define "pass") and arrived at Jupiter on 1979-03-05T12:05:26TDB, while Voyager 2 arrived on 1979-07-09T22:29:51TDB.

Notice that while the arrival reference is a full-blown set of orbital elements, we did not use these. Instead, we use the Lambert/Gauss targeting method to plot a course which departs from the center of the Earth on the indicated time, considers only the gravity of the Sun and ignores the gravity of the Earth, and arrives at the center of Jupiter at the indicated time. There is one unique trajectory which crosses the indicated places at the indicated times and is prograde.

So, even though Voyager 1 is launched later, it arrives first. This is for two reasons:

1. Voyager 1 has a higher heliocentric energy
2. Voyager 1 is launched on the "outside track". Normally the inside track is faster, but not in this case. If both spacecraft are going to intercept Jupiter, the first to arrive must be on the outside track because Jupiter is moving from "outside" to "inside".

We end up with the following picture:

There is a lot to look at in this picture, so here are the thousand words. Red is Voyager 1, blue is Voyager 2. The small white circle is the orbit of Earth, with the sun marked as a yellow dot, Jupiter the next larger white circle, and Saturn the largest. The tick marks are 30-day intervals starting at the launch date of Voyager 2. This means that the ticks for Voyager 1 and 2 are directly comparable. We see Voyager 1 pass at about the 4th tick mark. A zoom in reveals that from this perspective directly from Ecliptic North, the trajectories actually cross twice. Normally the trajectory diagrams don't show them crossing at all.

Another interesting thing is that the orbit of Voyager 2 if it did not intercept Jupiter, would have continued about 1AU past Jupiter's orbit. However, Voyager 1's orbit would have gotten almost out to Saturn. Did they use a larger launch vehicle for Voyager 1? No, both spacecraft had almost identical launch speeds (vinf=10.951km/s for Voyager 1, 10.316km/s for Voyager 2). The main difference is just the direction of launch. Voyager 2 was launched above the ecliptic plane (departure asymtote 17 deg above the ecliptic) while Voyager 1 was launched almost in the ecliptic (departure asymtote 4 deg above ecliptic). Also, Voyager 1 was launched closer to the direction of travel of the Earth. Voyager 2 was launched 18 degrees inward, while Voyager 1 was launched 4 deg outward.