Let's assume there is unlimitedly rich eccentric person living nowadays, who has been just diagnosed with a kind of terminal cancer (estimates are 3 years left) and their last wish is to jump into a suitable capsule, which would be heading straight into the center of the Sun, watch the Sun as the spacecraft approaches (with suitable shield to give the best visual performance) and then terminally burn themselves together with the capsule whilst listening to the Voyager Golden Record, when the heat shield limit of the capsule is exceeded.

Two aspects of the question:

  1. Main Q: What is the most spectacular, yet realistic, trajectory (it has to be aiming the very center of the Sun as much as practically possible)?

With my limited knowledge of orbital mechanics, first a spacecraft would need to cancel Earth's speed around the Sun to reach zero speed (wrt the Sun), and then simply fall into the Sun. But I'm not sure the Earth wouldn't affect the "falling" trajectory exactly one year later, I.e. will the falling journey be quick enough in this scenario (remember, there are only 3 years left to build the rocket, spacecraft and actually fly)? Or are there better/more spectacular trajectories to fit within the given timeframe?

  1. Bonus Q: Is there hardware available nowadays to be capable of such a journey (at a chosen trajectory)?
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    $\begingroup$ Related: Why is it easier to escape the solar system than get to Mercury or the Sun? $\endgroup$
    – DrSheldon
    Jun 27 at 12:06
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    $\begingroup$ I don't think it's doable in your 3 year limit with any near-future propulsion technology. The only approach currently feasible would be to use Jupiter for a gravity assist, and it'll take about 5 years to get there. Your time limit more or less requires a direct burn that leaves the spacecraft with 30 km/s relative to Earth after it leaves Earth's sphere of influence. $\endgroup$ Jun 27 at 13:13

Reaching your "falling" trajectory means leaving the Earth with a $v_{\infty}$ of 29.8km/s. From low Earth orbit, that's a delta-v cost of 24.0 km/s, which is quite steep. If you waive the requirement of falling straight towards the centre of the Sun, and consider hitting the Sun good enough, the delta-v cost goes down to 21.3 km/s.

Your worry about the Earth affecting the "falling" trajectory can be put to rest. Consider the equation for the orbital period of an orbit:

$$T = 2\pi\sqrt{\frac{a^3}{\mu}}$$

Which means $T \propto \sqrt{a^3}$. Since the falling trajectory has a semi-major axis ($a$) that's exactly half of the Earth, the orbital period is $\frac{\sqrt{2}}{4}$ years, and since we are only interested in the inwards portion, the fall only takes roughly two months.

The 3 year limitation makes it difficult to get creative with trajectory design. In particular, it's not enough time to use Jupiter as a booster.

Nevertheless, you can do this:

  1. Escape Earth into an elliptic solar orbit with an aphelion of 3.64 AU. (delta-v of 5.55 km/s from LEO).
  2. At 3.64 AU, cancel your momentum (delta-v: 10.2 km/s)
  3. Fall down into the Sun.

This iternary takes exactly 3 years, and comes at a lower delta-v cost of 15.8km/s.


I don't know how exactly to quantify

...most spectacular, yet realistic, trajectory...


...it has to be aiming the very center of the Sun as much as practically possible...

is easy. You ask for companies to bid on a $C_3 = v_{Eorb}^2$ launch.

$C_3$ is the reduced kinetic energy (per unit mass) of an object leaving Earth in a geocentric frame. It's how much $v^2$ you have left after you loose the escape velocity by escaping Earth.

@PearsonArtPhoto's answer to What spacecraft has had the greatest total propulsive delta-v? explains that New Horizons had the greatest post-escape geocentric velocity of $\sqrt{170 \text{ km}^2 \text{/s}^2} \ = \ $ ~13 km/s.

But the orbital velocity of Earth is $\sqrt{\frac{GM_{sun}}{1 \ AU}} \ =$ 29.7 km/s.

That's way higher than what you can easily get even for New Horizons! According to this answer to Was there any launch vehicle possible that could have been used for a heavier New Horizons with enough fuel to enter Pluto orbit?:

New Horizons had a launch mass of 478 kg.

This answer to Mass of food per astronaut per year for an extended deep space excursion? says you'll probably need about 235kg of food and its packaging per year, but you'll need way more than that to stay alive, healthy and sane.

How long?

Answers to Time to fall into the Sun from Mars orbit tell us that the time it takes to fall into the Sun from 1 AU is $\sqrt{2}/8 \ \approx \ $0.18 year or about 65 days, so you won't actually be needing all of that food.

If you want to spiral in with a solar sail, read @SEstopfiringthegoodguys' answer to What is the optimal angle for a solar-sail deorbit towards the Sun when radial thrust is included?

If you can't quite get that 29.7 km/s for that $\sqrt{C_3}$ then read the amazing answers to Do you need 0 km/s velocity to crash into the sun?


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