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Earth moves in a few different ways through the universe. Earth orbits the Sun (plus the orbit precesses), the Sun moves through the Milky Way, and the Milky Way moves through the universe.

Compared to my position exactly one Earth revolution around the sun, approximately how far have I actually moved relative to my starting point? Or more specifically, what is my displacement relative to my position when Earth was last in the same position within its orbital path around the Sun?

The movement of the solar system and/or the galaxy might be negligible over the course of a year, but negligible on those scales would presumably still translate to big distances relative to the scale of a person. Though I imagine the margin of error might make such a calculation impractical.

Another way to think about it is if I was able to jump forward in time one year, would I wind up floating in space or would I still be on the surface of Earth?

If the answer is insignificant or not determinable, how many years would you need to consider for the displacement to be significant / determinable?

Can assume that a year ago and right now I am at the exact same geographic coordinates on the surface of Earth.

shim
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    Your displacement in which frame? – ACuriousMind Jan 04 '24 at 17:01
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    In my frame? What are the possible frames? Are you asking because of relativistic effects? – shim Jan 04 '24 at 17:02
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    It's all relative. And really easy to look up the speed of the milky way relative to the local group. – Karl Jan 04 '24 at 17:04
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    In your frame, you are at 0,0,0 all the time. The rest of the world moves. – Karl Jan 04 '24 at 17:05
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    How about the CMB frame? https://physics.stackexchange.com/q/25928/123208 https://physics.stackexchange.com/a/411082/123208 – PM 2Ring Jan 04 '24 at 17:12
  • How about the centre of the Milky Way? Or maybe the centre of a neighbouring galaxy? If you framed the question as wanting to take off from the Earth in a ship, travel in as straight a line as possible, and land back on Earth a year later in the same spot, would that clear up which frame to should use? – shim Jan 04 '24 at 21:37
  • The frame of the center of the Milky Way is constantly changing. – WillO Jan 04 '24 at 21:44
  • Pick some suitably distant star? Surely there's some objectively appropriate frame here, no? – shim Jan 04 '24 at 22:41
  • "Surely there's some objectively appropriate frame here, no?" No. There is not an "objectively appropriate frame." It is a basic premise that physics works the same in any inertial frame... So, if you want to work in some specific frame, it is up to you to arbitrarily pick which one... and none have any primacy over any other... – hft Jan 05 '24 at 00:04
  • Ok, but I've suggested several – shim Jan 05 '24 at 05:31

4 Answers4

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I all depends on the frame of reference you choose, and the larger it is, the higher are the relative velocities observed.

Earth surface (at the equator) moves at .5 km/s relative to the center.

The earth moves around the sun at 30 km/s. After 12 h, you are not circa one, but approximately 100 earth diameters from the place you were.

The solar system moves with ~230 km/s around the milky way.

The milky way has about 550 km/s relative to the cosmic microwave background.

(Current speed of Voyager I: 17 km/s.)

If you chose the CMB as a reference, your displacement after a year would in fact be 78 astronomical units, far outside of Pluto.

Karl
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    As it’s currently written, your answer is unclear. Please [edit] to add additional details that will help others understand how this addresses the question asked. You can find more information on how to write good answers in the help center. – Community Jan 04 '24 at 17:23
  • 78 AU / 365 * 24 h is 1.3 million km/h. Is that not a bit high? Don't really know; maybe that's perfectly reasonable. – shim Jan 05 '24 at 15:23
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    @shim that's the value directly derived vom CMB measurements like WMAP and Plank, 371 km/s. https://physics.stackexchange.com/questions/206100/velocity-of-solar-system-relative-to-cmb On extragalactical length scales, that's not really fast. About 20 billion years to cover the distance to the andromeda galaxy. 0.1 % of light speed. – Karl Jan 05 '24 at 16:35
  • ok, pretty interesting stuff really – shim Jan 05 '24 at 17:11
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If we consider position relative to the fixed stars (more specifically, the Sun) and disregard the slow galactic rotation, one year's duration of orbit roughly moves you back to your initial position.

The most important remaining motion, is the combination of the Earth's annual extra quarter-day (roughly) rotation, and the offset of the Earth-Moon barycenter (about 3000 miles) times the progression of the Earth-moon direction vector.

The quarter-day of Earth rotation amounts to a displacement of circa 6000 ground miles (if you start at the equator) or less, and would leave you still at a comparable altitude (probably you could breathe).

It is only the Earth-moon barycenter that really follows a simple orbit, not either the Earth or Luna individually, though, so at a synodic month period of 29.53 days, one year mismatches a repeat by 0.37 of a revolution; straight-line distance, that's a couple of thousand miles. So, probably NOT within atmosphere, though it would be roughly in the ecliptic; direction depends on the phase of the moon.

Whit3rd
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  • How slow is slow though? On the scale of the galaxy the rotation might be slow but on the scale of a human maybe it's significant? – shim Jan 05 '24 at 16:08
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Displacement is a vector quantity, i.e. the difference between two points. In the rest frame of the sun an exact solar year would put you right back where you started, ignoring effects like Earth's orbital precession, wobble about axis of rotation, etc. In the rest frame of the center of mass of the Milky way, however, there would be a net non-zero displacement.

Albertus Magnus
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Spatial distances without reference system of rest are undefined in special, the more so in general relativity.

The spatial distance between two events $(t1,x1),(t2,x2)$ , one year apart in time, perhaps an astronomical unit or 6 light minutes in space, eg measured in the milky way system of reference, is microscopic small with respect to time distance of 1 year. So it depends mainly on the system of reference. Its zero for an observer moving on a straight line between the two events with constant velocity.

Roland F
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