An ongoing debate in our household is whether or not it is worth spending the extra delta-v to shoot things directly into the sun, instead of just sending them onto an escape trajectory out of the solar system.
@sophieschmieg if you have the delta v to get an escape trajectory then you can get to the sun with only a tiny bit more: go for the escape trajectory, drift out until your orbital velocity is very small, then do a tiny retrograde burn to cancel it out exactly. You're now on course to hit the sun.
Downside is this method takes a LONG time. I think you can get there way quicker with gravity assists from say Venus.
@sophieschmieg on second look, I'm not sure this method is actually a win? We start at earth with Scott 30km/s velocity around the sun, but escape velocity is 600km/s???
So is firing directly at the sun actually the cheaper option?
@sophieschmieg oh no I'm missing pertinent facts like the fact that escape velocity gets smaller the further away you are from the body.
The Voyagers are on escape trajectories at only 17km/s and 15km/s.
@0x2ba22e11 the energy of an orbit is E = 1/2m v² - GmM/x. At infinity we want to be just out of the gravity well, so E = 0. This means that anywhere in that orbit we have 1/2mv² = GmM/x, i.e. v = √2*√(GM/x).
For a circular orbit otoh, we have ma = GmM/x², and a = v²/x, so v = √(GM/x). This is the Delta v cost of shooting directly into the sun. The cost to escape otoh is (√2-1) times as much, and therefore smaller.
Of course you can do a bielliptic transfer and first go to a higher orbit, where the orbital velocity is lower, and burn retrograde then, where in the limit the cost is the same.
You can brake in Sun's atmosphere, so you "just" need to get to an orbit with low enough perihelion. That doesn't change the conclusion though (I think? ISTR that bielliptic transfers work similarly for elliptical source and destination orbits, but Wikipedia says nothing about that).
@robryk @0x2ba22e11 yeah, at that point it doesn't really make a difference whether you impact or just hit the atmosphere. If you're anywhere but low orbit, you usually only care about atmospheric breaking to keep your Kerbals alive, not to save Delta v.