OK I deleted a post I was about to make but this post prompts me to make it anyway, as confusing as it may be but if you sift through my jumbled post you will find the Voyager spacecrafts didn't achieve solar escape velocity until they got a gravity assist from Jupiter, and possibly also Saturn.
So here goes.
reply to post by -PLB-
And I guess Illustronic was right all along, although he didn't worded it that well (its not pulled into solar orbit, it already was in solar orbit to begin with)
If it is in earth orbit it is in solar orbit by proxy, but not independently. JUNO was placed into earth parking orbit for a half an hour, before its Centaur booster re-fired it off into solar orbit well under 23,000 mph in respect of earth. It entered solar orbit because the combined speed (of earth's orbit and 23,000 mph) was not 42km/sec. 66,600 mph + 23,000 = 91,600 mph, 94,000 mph at 1 AU is what is required for solar escape velocity, (judging from past math calculations by CLPrime I have no reason to believe 42k/sec is off).
Now New Horizons spacecraft left earth orbit at over 36,900 mph (speed record) so it never entered solar orbit, it passed the moon's orbit in less than 9 hours from liftoff, passed Mars's orbit in less than 3 months, and passed the orbit of Jupiter in 13 months for a slingshot up to over 38,000 mph.
Interesting paragraph from Wiki;
New Horizons is often erroneously given the title of Fastest Spacecraft Ever Launched, when in fact the Helios probes are the holders of that title. To be more specific New Horizons achieved the highest launch velocity and thus left Earth faster than any other spacecraft to date. It is also the first spacecraft launched directly into a solar escape trajectory, which requires an approximate velocity of 16.5 km/s (36,900 mph), plus losses, all to be provided by the launcher. However, it will not be the fastest spacecraft to leave the Solar System. This record is held by Voyager 1, currently travelling at 17.145 km/s (38,400 mph) relative to the Sun. Voyager 1 attained greater hyperbolic excess velocity from Jupiter and Saturn gravitational slingshots than New Horizons. Other spacecraft, such as Helios 1 & 2, can also be measured as the fastest objects, due to their orbital velocity relative to the Sun at perihelion. However, because they remain in solar orbit, their orbital energy relative to the Sun is lower than the five probes, and three other third stages on hyperbolic trajectories, including New Horizons, that achieved solar escape velocity, as the Sun has a much deeper gravitational well than Earth.
That makes a little more sense if I add;
The Star 48B third stage is also on a hyperbolic Solar System escape trajectory, and reached Jupiter before the New Horizons spacecraft. However, since it is not in controlled flight, it did not receive the correct gravity assist, and will only pass within 200,000,000km (120,000,000 mi) of Pluto.
So what I am gathering from all of that is the speed New Horizons left earth orbit at a combined hyperbolic trajectory of 103,500 mph is near the minimum required for a solar escape velocity at 1 AU from the sun, which converts to 46.3 km/sec. But in all fairness I also find'
After the Star 48B burn, the payload had reached escape velocity not only with respect to the Earth but also relative to the Sun (The velocity was 16.2 km/s relative to the Earth and I estimate an asymptotic velocity of 12.3 km/s, corresponding to 42.6 km/s relative to the Sun and leading to a heliocentric eccentricity of around 1.05).So which is it, 46.3 or 42.6?
Today there is at least one Apollo third stage booster still in solar orbit and a little over a year ago was spotted and at first mistaken as a NEO asteroid, until it got close enough to identify as being what it is.
The interesting fact of the Helios spacecrafts is their orbital apogee extends inside the orbit of Mercury which is how they reach a higher speed than Mercury at its perihelion, around 150,000 mph. I also understand a recent sun grazer comet was measured at reaching a speed of over 300,000 mph at its perihelion, which at the distance it missed the sun by is still not high enough to reach solar escape velocity.
So going back to the Apollo days, none of the Apollos reached solar escape velocity and that is why their flight trajectories were an arc, (a portion of its solar orbital trajectory). So if they missed the moon they would be in solar orbit today, and unpowered could never achieve earth orbit due to the speed they are moving.
Now all of this is relative to the sun or the earth but does anyone have any numbers on what is required to achieve galactic escape velocity? Where would one find data to support calculations for that?