How would a Jupiter flyby have helped to get to the Sun? Why was it later ruled out?

The quote below surprised me. What were the orbital mechanical details of using a Jupiter flyby to get a probe from Earth so close to the Sun? Was a "U-turn" possible; single flyby of Jupiter into a super-low perihelion ellipse? What were the later constraints that then made this solution unacceptable

First definitions of Solar Probe missions (studies) at NASA/JPL were started in 1978. The original Solar Probe mission concept of 2005, based on a Jupiter gravity assist trajectory, was no longer feasible under the new guidelines given to the mission. A complete redesign of the mission was required to meet the mission constraints, which called for the development of alternative mission trajectories that excluded a flyby of Jupiter.

• Didn't Ulysses do a Jupiter flyby to get to the Sun? On bad device now so can't check easily. – Organic Marble Oct 24 '18 at 3:12
• Ulysses used Jupiter to get into a solar polar orbit, so it could look at the poles of the Sun. However it was in a 5 AU orbit, so I'd hard call that "getting to the Sun". – Mark Adler Oct 24 '18 at 3:22
• hardLY.......... – Mark Adler Oct 24 '18 at 4:23
• space.stackexchange.com/questions/6582/… – Heopps Oct 24 '18 at 16:50

A gravity assist at Jupiter would have been used to decrease Solar Probe (Plus)'s orbital speed, lowering its perihelion as explained well in this answer.

Credit: NASA/JHUAPL

In fact, for such an extreme low perihelion, the Jupiter gravity assist is much more fuel-efficient than a direct transfer (note - Parker uses multiple Venus gravity assists to save on fuel budget).

The Jupiter assist only requires ~ $$9kms^{-1}$$ delta-v from fuel with a further ~ $$5.6kms^{-1}$$ from the Jupiter assist. Compared to the direct transfer which requires ~ $$21kms^{-1}$$ - see the maths below.

9 km/s instead of 21 is a huge difference that would have allowed for a more massive probe. From a 1966 paper Gravity-Assisted Trajectories to Solar-System Targets:

When missions to less than 0.1 a.u. are desired, it is apparent that the only available route with existing chemical propulsion systems is via a Jupiter fly-by.

Parker Solar Probe obviously has the benefit of more modern propulsion systems and will utilise multiple Venus-assists to reach its final orbit, but it still required one of the highest $$C_3$$'s in history from one of the largest launch vehicles in history.

The Jupiter-Assist trajectory was eventually scrapped in 2007 for a number of reasons, the main ones being:

• Time: each of the sun-diving orbits takes around 6 years, giving only two opportunities for collecting data. Furthermore, the higher perihelion speed would make the observation windows even smaller.
• Heat: The probe would have had to be able to handle both the high temperatures at perihelion and extended periods at low temperatures at aphelion. These requirements would have incurred mass penalties.
• Power: The low solar intensity out at Jupiter's orbit would have pretty much precluded the use of solar power (9 metre panels aren't available to everyone), necessitating an internal power source which was an undesirable option.
• Communication: The larger distances involved would have required a larger antenna and therefore more mass. An early design concept actually had a hybrid combined Heat-shield/Antenna as a solution.

The original Solar Probe mission design actually had the final orbit being highly inclined rather than near the ecliptic plane, much like Ulysses but with a much lower perihelion.

Maths

We can use the vis-viva equation with the different stages of the Jupiter transfer to work out the total budget:

$$v = \sqrt{\mu\left(\frac{2}{r}-\frac{1}{a}\right)}$$

Our initial orbit is just Earth's orbit with $$a_{E} \approx r_{E} \approx 1.5\times10^{11}$$m and orbital speed ~ $$30kms^{-1}$$ (we'll ignore the Earth-escape requirements as they're similar for both options).

Our transfer orbit has aphelion at Jupiter's orbit and perihelion at Earth's, giving us $$a_{EJ} \approx 4.65\times10^{11}m$$ and $$r_{J} \approx 7.8\times10^{11}m$$. Our speed at perihelion is ~ $$39kms^{-1}$$, decreasing to just ~ $$7.4kms^{-1}$$ at aphelion. This is where our fuel savings come in - the low aphelion speed means we can get a much larger relative change in velocity for the same amount of fuel.

Our final, low-perihelion orbit has $$a_{JS} \approx 3.87\times10^{11}m$$ and $$r_{S} \approx 7\times10^{9}m$$, giving a speed at aphelion of ~ $$1.8kms^{-1}$$.

So our total expediture will be:

• Earth to Jupiter: $$39 - 30 = 9kms^{-1}$$
• Jupiter to Sun: $$7.4 - 1.8 = 5.6kms^{-1}$$
• Total: ~$$14.6kms^{-1}$$

Direct transfer option:

• Earth to Sun: $$30 - 8.9 = 21.1kms^{-1}$$
• @uhoh the image you link shows an earlier trajectory design where the Jupiter assist provides a large plane change which is difficult to display 2-dimensionally, rather than a prograde to retrograde switch. – Jack Oct 24 '18 at 10:55

The Jupiter flyby mission concepts were nuclear-powered. They were told to come up with a non-nuclear option.

• That's "part-b" but I'm still trying to understand how (or if) Jupiter was used directly to "get to the Sun" beyond "Jupiter is a big bucket of delta-v." Was Jupiter invoked also for a plane change only, or did a single swing-by somehow help lower perihelion? – uhoh Oct 24 '18 at 4:53