First question: assuming no atmospheric drag, can you use a gun type launcher at the surface to put an inert satellite into a closed orbit that does not intersect the planet’s surface once per orbit? The scenario is different than for a rocket which burns for a long period of time, clawing for altitude while its lateral velocity is increasing. A gun-type launcher, ISTM, could send you away from the surface on a hyperbolic or parabolic trajectory, but anything short of that would bring you back down to the surface at periapsis.
Second question, related to the first: Could you hypothetically use a gravity-assist maneuver around an object to put yourself into an elliptical orbit that did not subsequently intersect that object’s orbit? Imagine shooting a probe out to Jupiter, but rather than having Jupiter whip it along a New Horizons- or Voyager-type escape trajectory it somehow slots it into an elliptical orbit that stays between the orbits of Saturn and Uranus without the need for additional course corrections by rocket or whatever. This situation seems analogous to the gun-type launch from the surface of a planet; I don’t see how it could work, but perhaps I’m wrong. As I see it for a closed orbit you could boost something out to beyond Jupiter at aphelion but it would always come back in to Jupiter’s orbit at perihelion.
If a closed two-body orbit passes through a point once, it will pass through that point repeatedly. This point could be the location of your gun, or the location of your flyby maneuver. In either case, your surmise is correct.
Thanks, Chronos. A follow-up, though: after a gravity boost outward by Jupiter to a more distant aphelion, you’ll cross through the same point again eventually, but there’s no guarantee that that point represents your perihelion, does it? I can imagine that there would be only one closed orbit from there that would touch Jupiter’s orbit just once (the slingshot point represents your perihelion), and many more that would cross it twice, with a perihelion inside Jupiter’s orbit. Does that make sense?
You can cross Jupiter’s orbit only once without it being your perihelion. There will be some other point in your orbit that’s at the same distance from the Sun, but there’s no reason that point has to be in the plane of Jupiter’s orbit. Most such orbits, in fact, would be in other planes.
So, I think the apparent question here is, could you use a gun-type launcher on the surface of the earth and use a lunar flyby to stabilize the orbit of your satellite. And I believe the answer is yes (ignoring the difficulties of shooting something out of a gun at 9km/s or so at the bottom of the atmosphere), but you’d end up with an orbit highly susceptible to being messed up by repeated encounters with the moon.
How about if we allowed for atmospheric drag. Could we fire a projective at some speed greater than escape velocity such that the atmosphere would slow the projectile down to escape velocity just as it exits the atmosphere?
… assuming it wouldn’t burn to a crisp doing Mach 30 …
No, because any gun-launched satellite will be on an orbital trajectory intersecting the surface of the planet (so, actually sub-orbital), no matter how high its apoapsis is. If you add more energy, you just add to the eccentricity of the orbit, which just means you’ll slam back into the atmosphere that much faster on your way back. To move from this to a stable orbit you need either to accelerate prograde in the top half of your orbit, or radially after you’ve cleared the atmosphere (either towards the planet if you’re still ascending, or away from the planet if you’re descending). Atmospheric drag gives you retrograde acceleration in the bottom half your orbit, which is exactly the opposite of what you need.
Disclaimer: everything I know about orbital mechanics I learned from Jebediah Kerman.
Sorry, I’m having trouble parsing this. If you cross Jupiter’s orbit twice, then the crossings are not your perihelion, right? Let’s keep things all in the ecliptic to make things easier for me to understand.
Picture Jupiter’s orbit, and that of a Halley’s Comet analogue that moves along the ecliptic. The comet comes in from afar, crosses Jupiter’s orbit on the way in, swings closer to the Sun, then passes Jupiter’s orbit again on the way out to aphelion. Could you not use a gravity-assist from Jupiter to put a probe into a similar orbit, with the probe crossing Jupiter’s orbit twice on every probe-orbit?
As a separate case, your probe gets an assist from Jupiter and swings into a bigger orbit that touches Jupiter’s orbit at only that one point, which is then the probe’s perihelion point.
I’m trying to determine whether the flyby point must become the perihelion of the new orbit or whether the perihelion of the new orbit can lie inside that of Jupiter.
I’m not trying to stabilize an orbit with a gun launch and a lunar assist; I’m trying to confirm my intuition that a slingshot will result in a slingee orbit that crosses the slinger’s orbit at least once but possibly more than that. If you throw in the possibility of things looping up out of the ecliptic, the geometry gets a bit too hairy for me to hold in my head.
Someone once tried to build a cannon satelite launcher. I believe his name was Gerald Bull. Obviously, it would have to accelerate once it reached orbit if it was not to come back to the earth, as stated above. I gather he spent a fair amount of money on it, but was never able to make it work. But the problem was engineering, not conceptual.
If you intersect Jupiter’s orbit twice, then those two points will not be your perihelion. But it’s also possible (and more likely) to intersect Jupiter’s orbit only once, and for that point to still not be your perihelion.