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Suppose you have a hypothetical spacecraft launched from Earth.

When it escapes from Earth's gravity it will still be orbiting the sun at roughly the same velocity as the earth, approximately 30km/s relative to the center of the sun. Say the spacecraft then thrusts in the opposite direction, until its velocity relative to the center of the sun is reduced to 0 while keeping its other positional attributes as close to unchanged as possible. Now the hypothetical spacecraft is (for some brief instant in time) essentially stationary relative to the sun.

My question is, what happens next? I'd expect that the spacecraft would immediately begin to fall directly into the sun. Is that the case, and if so, how long would it take to get there and what would the acceleration profile be like?

And if one were to deliberately send a probe into the sun, is there any practical merit to doing it that way as opposed to simply thrusting directly towards the sun while retaining the lateral velocity imparted by the earth?

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    $\begingroup$ For what it's worth, getting an extra 30 km/s delta-V after leaving Earth's Hill sphere is astonishingly difficult. About the best we can do is Dawn's recent 10 km/s budget, using ion engines over multiple years. $\endgroup$ – Nathan Tuggy Oct 8 '15 at 6:37
  • $\begingroup$ In theory you could do it using only an extra ~19km/s delta-V if you orient your launch so that the craft escapes away from the direction of Earth's orbit, I think? $\endgroup$ – aroth Oct 8 '15 at 6:39
  • $\begingroup$ Give or take, but that's still almost twice what we can manage at present. $\endgroup$ – Nathan Tuggy Oct 8 '15 at 6:42
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    $\begingroup$ Sure, but it would be much cheaper to accelerate in the velocity direction to reach Jupiter, and then use a Jupiter gravity assist to dive into the Sun. $\endgroup$ – Mark Adler Oct 8 '15 at 20:36
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You can; burning retrograde with respect to the sun lowers your perihelion. If you do it long enough your orbit will intersect the sun. If you ignore gravity assists this is the cheapest way of impacting the sun. Because the sun is not a point mass you don't even need to reduce your velocity to 0.

Thrusting directly towards the sun would eventually work, but would be extreme expensive. (With infinite thrust this approach would be roughly $\sqrt 2$ times as expensive as burning retrograde; you are changing your velocity vector 90 degrees rather than eliminating your velocity. With less thrust I think it would be even less effective).

A more effective way is to make the retrograde(with respect to the sun) burn while still in the Earths sphere of influence. This in order to utilize the Oberth effect.

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Bottom line, from low-Earth orbit (these are all impulsive burns), you need 21.3 km/s to dive directly into the Sun with a single burn. (Your "horizontal" thrusting.) Seems a bit excessive.

You can do much better than that if you instead raise your aphelion, and once you get to aphelion, lower your perihelion. Depending on how far out you're willing to go, and how long you're willing to wait to get to the Sun, you can reduce the total of the two burns to as low as 8.75 km/s (the amount need to escape from the Sun directly from low-Earth orbit). For example, if you're willing to go out to the distance of Uranus, you can get it down to 10 km/s total. This is about the total $\Delta V$ of the launch vehicle that got you to low-Earth orbit. Still too high.

You can do way better if you use a Jupiter gravity assist. One of those along with a modest maneuver at Jupiter closest approach will send you right to the surface of the Sun. (I haven't done the arithmetic, but I'm guessing just a few hundred m/s burn at Jupiter.) You can go directly to Jupiter from low-Earth orbit for 6.3 km/s. Now at least we're getting into the realm of something feasible.

Of course, you don't need to go directly to Jupiter. You can use a Venus-Earth-Earth gravity assist to get to Jupiter (like Galileo did). You just have to live with an extra three years of flight time. Now you only need 3.5 km/s from low-Earth orbit to get to Venus. Plus that burn at Jupiter.

So instead of the 21.3 km/s required for your direct approach of slowing your orbit around the Sun, you can dive into the Sun for less than 4 km/s by stealing tiny bits of energy from Venus, Earth, and Jupiter. That, and some careful navigation.

You could also do just Venus flybys, but many of them. I'm not sure how many, but quite a few. Solar Probe Plus will take seven Venus flybys and six and a half years to get to 8.5 solar radii. You want to get to zero solar radii.

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Putting on the brakes vs making a left turn? Putting on the brakes is cheaper.

You would not have to kill all the 30 km/s. Getting your perihelion below the sun's surface takes about 27 km/s. As Taemyr notes, doing the burn deep in earth's gravity well confers an Oberth benefit. From low earth orbit, it'd take about 21.5 km/s for injection to a heliocenric orbit with a sun grazing perihelion.

I think the way I'd do it is send the probe towards Venus. From low earth orbit a trans venus injection takes about 3.5 km/s.

Venus arrival Vinf would be about 2.7 km/s. If the hyperbola's periapsis is at 300 km altitude, turning angle would be 122º. 2*2.7*sin(122º/2)=4.7. So a Venus Hohmann swing by can provide 4.7 km/s.

Moreover, the 10.5 km/s Venus fly by can provide a nice Oberth benefit. A small burn at the Venus hyperbola's periapsis can get a lot of bang for the buck.

I don't have time to do the numbers at the moment. Will try to return to this later.

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Assuming you can afford to wait quite a while there's a surprising, cheaper option:

Burn for the stars.

You're looking at only about 1/3 of the delta-v as would be needed to kill your orbital velocity. Now, you go flying way out there, the farther the better (but the slower.) Lets just figure we start out with a minimum-energy burn for Pluto. When we get there in a century we burn the rest of our fuel to completely stop. Even with this we still used only half the delta-v--we can use a rocket of less than 1/10th the size. Living to see our probe hit the sun is another matter, though...

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The original question has two parts, A) "what happens next?" B) "is there any practical merit in doing it that way?"

It appears to me that all the comments and answers have addressed another question, something like "what's the best way to do it?". I wouldn't knock them beyond that, some of them appear really interesting.

My humble answer to "what happens next?": First, in idealised circumstances of there being just the probe and the Sun then the two objects will move under the acceleration resulting from their gravitational attraction, as always. In this case it will look, to the external observer, as if the probe is simply falling towards the sun.

See the first equation in https://en.wikipedia.org/wiki/Gravity for guidance in working out the acceleration profile and eventually the travel time.

In the real circumstances of the solar system as we know it, I have little idea and would be interested to know, to what extent other solar system bodies might interfere, and this is going to depend a lot on the initial conditions as to what bodies might have some influence.

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  • $\begingroup$ "It appears to me that all the comments and answers have addressed another question, something like 'what's the best way to do it?'" - Spot on. I've got some great suggestions regarding the best way to drop something into the sun, and I've learned a lot from them. For instance, that dropping something into the sun isn't as intuitively easy as it would seem. And I appreciate that. But the original question was more about "what would happen if..." than "what's the best way to actually do it". $\endgroup$ – aroth Oct 9 '15 at 14:54

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