[theleopard] was responding to an anno by [AbsintheWithoutLeave] which introduced the vacuuming thing - but I think some of us may have missed [Awol]'s subtle (vacuum based) joke.

//how hard would you have to hit a lunar golf ball to put it in orbit?// About one sixth as hard as you would have to hit it to put it into Earth orbit.

Right. Well. Assuming a circular orbit, with Kepler's & Newton's shenanigans, there's a F=Gm1m2/r.r equated with F=m.v.v/r and a little bit of jiggery pokery. Unfortunately, I can't remember any more of my school physics.

Yes [Paulo], there's definitely a lack of seriousness in there somewhere! And I have to admit to wanting to throw in a pun too.

Even though I don't play golf, I admit it should be awesome to play it on the moon. I mean, if they could slim those spacesuits down a bit. At least enough so that you could swing a golf club. But imagine, without air drag and with only a sixth of Earth gravity, those golf balls could go pretty far. Maybe enough so that they would have to forbid golf playing inside flight paths.

You can't put a golf ball into orbit by hitting it from the surface of the moon. If it doesn't escape to infinity, it'll be in an orbit which intersects the moon's surface, so at some point it'll hit the ground.

To get into orbit you need to perform a "circularising" manoeuvre when the ball has reached the right altitude.

No, [Wrongfellow] is right, any ballistic orbit will include it's starting point, so you need to Tee off in a tower and then take down the tower. The lack of atmosphere should allow a highly eliptical orbit with an apogee of a few feet.

Really? A trajectory is normally considered parabolic, but that's a simplification based on the assumption that the surface from which a thing is ballisticated is a flat surface.

I agree that a straight-up launch would require a secondary, sideways thrust to get it to go around the planet, that's fair enough - but say you launched something at 45° (or some other non perpendicular trajectory) and imparted just enough energy to mean that the peak of the parabola was such that the object would have enough "sideways" motion to slip into a circular orbit. It's the same thing as [Wrongfellow]'s suggestion, only you're giving the object the sideways thrust at the beginning, simultaneous to giving it the upwards push.

Won't work, I'm afraid. Orbits are ellipses (assuming the parent body is a point mass, which I think is reasonable for this discussion) and an orbiting body can only move from one possible ellipse to another through the application of an acceleration.

So if you accelerate the body from ground level, it will always end up moving on an elliptical path which intersects the ground, no matter what angle you accelerate it at.

To put a body into a genuine orbit, you have to get it onto an elliptical path that doesn't intersect the ground at any point, and so the final application of acceleration must necessarily happen far from the ground.

Or another way to look at it is that Newtonian mechanics is fully reversible. Imagine the time-reversed equivalent of your scenario: a body in a stable circular orbit which suddenly decides to plunge parabolically groundwards. Why did it do that? It can only do that if you apply a force to it.

Wait a minute - let's take Wrongfellow's argument about reversible physics a bit further here - and imagine a satellite in orbit whose orbit is slowly but steadily decaying - it will eventually come crashing back to earth and all without anyone prodding or poking it while it is in orbit.

I guess we could say that this satellite's original orbit just wasn't 'stable' - But stability is relative! - that satellite may have been in orbit for 20 years, but in geological terms, the orbit would be seen as a flash in the pan.

And so, if a satellite's orbit can naturally decay into a death spiral, then so mightn't there be a *perfect* ballistic trajectory that might work in reverse?

The orbit decays because it's not in a perfect vacuum; it's being prodded and poked by molecules of air.

The time-reversal of a satellite's orbital decay is a situation where those stray air molecules etc are colliding with it in just the right way to gradually speed it up and boost it into a higher orbit.

Theoretically possible, but in practice entropy is against you.

(And herein lies a very interesting question: if physics is perfectly reversible, where does the "arrow of time" come from?)

Bit of a leap here, but isn't there an analogous thing to reversing the arrow of time and the idea of being able to calculate the nth Prime Number?

By which I mean that the nth Prime is dependent on all n-1 primes prior to it - in the same way that the nth moment is dependent on the n-1 moments prior to it.

Also, considering direction of time is odd when you're doing sums.

There is another force available which could, in theory, circularise the orbit - the Earth's gravity. It would be a particularly tricky three-body problem, and a damn tricky shot.