How much velocity can I shed?

Factual Questions
1

The Holidays were really good to me—Santa brought me a rocket ship![sup]*[/sup]

So I’ve packed a lunch (so shedding mass is out) and I want to get my velocity as close to zero as possible.

I take off and get into orbit. If I go high enough, can I just turn around and fly opposite the rotation of the Earth and effectively stop orbiting and end up as a fixed point in the Earth’s sky? As in I’d be sitting three degrees off Beetlejuice and every night people can go out and wave. Can I reach that point and still be between the Earth and the Moon?

But even if I’m still compared to the Earth’s rotation, I’m still orbiting the sun, right? How do I stop? Can I start on the side of the Earth opposite to its orbit and fire my engines until the Earth starts moving away? If the Earth is orbiting the sun at about 67,062 MPH, and I know the output of my engines, weight of craft, etc., I can calculate how long I have to floor it before I reach that speed. If I start out in the opposite direction and cut my engines just as I reach that speed, would I pretty much sit there for a year until the Earth came wizzing by again?

But even then I’m still chugging along with the solar system, aren’t I? If I take a few measurements from distant stars, I can get an idea of how the solar system is moving within the galaxy, right? Can I stop my motion relative to the solar system? Which way to I fly?

And if I do that, aren’t I still moving along the galactic plane? Taking new measurements from distant galaxies, can I zoom in the opposite direction the galaxy is spinning and become still relative to its spin—so if I sit there long enough the next arm will come washing over me, or if I wait long enough (I’d better pack a big lunch), the arm with the Earth and sun will do another flyby?

But the Milky Way itself is moving through space. Can I use the same measurements I took to figure out how the arms are spinning and stop moving relative to the galaxy?

Now what? Is this as ‘stopped’ as I can get? Assuming infinite fuel, is this level of stopping possible?

I think I understand why “stopped” is a meaningless concept absent some point of reference to be stopped relative to, but could I reach a point such that for all intents and purposes, for every measurement I can make I appear to have no velocity?

Despite my efforts, do I appear to move to observers in different parts of the universe? How?

[sup]*Okay, it’s the cardboard box the Dudeling’s toys were shipped in; but I’ve got a box of crayons and some scissors.[/sup]

2

in the scenario you paint moving at the same velocity as the Mily Ways Galactic centre would probably be the most meaningful. Sure with enough fuel you could do that. You’ll see the arms spiral past you and the solar system go past every 240 million years or so, give or take.

3

As I understand it, the simple answer is ‘no’. It’s not as if your spaceship will be so small relative to the moon that gravity won’t pay attention to it.

For anything we puny humans can put into space, the mass tends to factor out of the orbital calculations. Geostationary orbit is ~22,300 miles high, regardless of mass; doesn’t matter if it’s a satellite or an astronaut’s glove. At that altitude, a circular orbit takes 24 hours.

The distance from the earth to the moon is about 239,000 miles. At that altitude, an orbit takes about 27 days[sup]1[/sup]. And if you’re not orbiting, you’re falling.

However, there are myriad complications to all this. You posit a spacecraft with infinite fuel. A helicopter generates downward thrust equal to its weight and hovers just fine. You could use your rocket engines to do the same thing; get where you want to be, figure out the resulting gravitational pulls, and counteract it with thrust from the rocket.

And real-world orbits have their own oddities. There may be certain key positions within the earth-moon or earth-sun systems where the pulls toward different objects are sufficient to do what you describe.

We’re thirty-thousand light years from galactic central point.
We go 'round every two-hundred-million years.

It is a matter of some joy to me that the numbers in Monty Python’s Galaxy Song are roughly accurate.

  1. The size of the moon may complicate the issue a bit. It’s sufficiently massive that the common center-of-gravity of the two bodies is a non-trivial matter. The orbital period for a small object at the same distance may not be 27.3 days, but I don’t think it would differ by too much.
4

I think a key point is that you can really only be stopped relative to one other object. If you pick a geostationary orbit, the sun and moon will appear to move.

I guess you could park in one of the Lagrange points, and be motionless relative to the Earth and moon, assuming they work the way I remember. But even then, the two spheres will rotate, so you’d be moving relative to their surfaces.

5

‘Stopped’ as you’ve noted is a completely relative concept. However I would choose the cosmic microwave background frame which the Earth is moving ~600 km/s relative to. This is the frame where you can most consider yourself at rest relative to the rest of the universe.

However even then there will still be recession velcoities, so that even other objects in the cosmic microwave background frame will appear to recede.

6

To be a fixed point in the sky, you have to fly in the same direction as the rotation of the earth, not opposite it.

7

Not only that, but if you go with the OP’s first idea of trying to go round the other way so you remain ‘at rest’ w.r.t the Earth (its centre, that is, not a point on its surface) then… well… you won’t be at rest for very long!

8

Yes.

Those observers are moving with respect to each other. So you can pick one and be motionless with respect to it - but all the others will see you as in motion.

9

As I understand the OP, Rhythmdvl is positing the opposite—that is, for an observer on the surface of the Earth, the rocket ship will appear as a fixed point with respect to the background stars. Hence, “…I’d be sitting three degrees off Beetlejuice [Betelgeuse—DHMO]…”

A re-statement of this thesis might be: the rocket ship will always occupy a point along the line from the center of the Earth to the background stars, appearing as a motionless point in the firmament.

My celestial mechanics is a little rusty, but I cannot construct a stable orbit where that would be true. The rocket would have to move around the Sun with the Earth in its orbit to allow it to remain motionless relative to the stars. My back-of-the-envelope calculation says the rocket will orbit the Earth-Moon system at a distance of 1.35 million miles in order to have a period of one year.

Also, to achieve an orbit with these parameters, there is no advantage to “If I go high enough, can I just turn around and fly opposite the rotation of the Earth…?” You would merely launch your rocket into a “retrograde” orbit, meaning it will take up an East-to-West orbit from the moment of lift-off, rather than the more traditional West-to East.

I’ll leave the remaining calculations to another time.

10

No need to, as the OP postulates infinite fuel (presumably with all the benefits and none of the annoyances of infinite mass).

Though it should be noted that if you are closer to the Earth than the Moon, parallax issues will make it difficult to appear as a fixed point against the background stars.