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Galaxies move through space with velocities of the order of a several 100 km per second; small velocities for small groups (~100 km/s; e.g Carlberg et al. 2000) and large velocities for rich clusters (~1000 km/s; e.g Girardi et al. 1993).

In addition to this so-called "peculiar velocity", galaxies also also carried away from each other due to the expansion of the Universe, at a velocity proportional to the distance from each other (the "Hubble flow"). But this is not a motion through space; rather it is space itself that is expanding (and hence the velocity may exceed the speed of light for sufficiently large distances).

One may define a "global reference frame" with respect to which velocities are measured. Any reference is valid, but it makes sense to use the frame in which all galaxies are, on average, in rest (when the Hubble flow is subtracted)$^\dagger$. In this frame, the Local Group that the Milky Way is a part of moves with some $620\, \mathrm{km \, s}^{-1}$ (as noted in John Duffield's answer above), whereas the center of the Milky Way has a velocity$^\ddagger$ of $\mathbf{565 \pm 5 \, km \, s^{-1}}$ (Planck Collaboration et al. 2018).

What causes this movement of galaxies? Galaxies that are not too far from each (i.e. closer), "feel" each others mutual gravitational forces. A galaxy in a group or cluster moves around in the common gravitational field, but for galaxies that are farther away, the Hubble flow carries them away from each other too fast for them to attract each other.

This movement can be traced back to the tiny quantum mechanical fluctuations in the primordial soup of particles during cosmic inflation, i.e. less than $\sim10^{-32}\,\mathrm{s}$ after the Big Bang. As time went by, ever-so-slight overdensities grew in amplitude, until they collapsed to form the structure we see in the Universe today. During this collapse, matter grew turbulent, whirling clumps around that eventually became the galaxies that orbit each other.

$^\dagger$_{Formally, one uses the frame in which the cosmic microwave background is isotropic.}

$^\ddagger$_{Taking into account our motion around the Galactic center, our Sun (currently) moves through space at $369.82\pm0.11\,\mathrm{km\, s^{-1}}$.}

Galaxies move through space with velocities of the order of a several 100 km per second; small velocities for small groups (~100 km/s; e.g Carlberg et al. 2000) and large velocities for rich clusters (~1000 km/s; e.g Girardi et al. 1993).

In addition to this so-called "peculiar velocity", galaxies also also carried away from each other due to the expansion of the Universe, at a velocity proportional to the distance from each other (the "Hubble flow"). But this is not a motion through space; rather it is space itself that is expanding (and hence the velocity may exceed the speed of light for sufficiently large distances).

One may define a "global reference frame" with respect to which velocities are measured. Any reference is valid, but it makes sense to use the frame in which all galaxies are, on average, in rest (when the Hubble flow is subtracted)$^\dagger$. In this frame, the Local Group that the Milky Way is a part of moves with some $620\, \mathrm{km \, s}^{-1}$ (as noted in John Duffield's answer above), whereas the center of the Milky Way has a velocity$^\ddagger$ of $\mathbf{565 \pm 5 \, km \, s^{-1}}$ (Planck Collaboration et al. 2020).

What causes this movement of galaxies? Galaxies that are not too far from each (i.e. closer), "feel" each others mutual gravitational forces. A galaxy in a group or cluster moves around in the common gravitational field, but for galaxies that are farther away, the Hubble flow carries them away from each other too fast for them to attract each other.

This movement can be traced back to the tiny quantum mechanical fluctuations in the primordial soup of particles during cosmic inflation, i.e. less than $\sim10^{-32}\,\mathrm{s}$ after the Big Bang. As time went by, ever-so-slight overdensities grew in amplitude, until they collapsed to form the structure we see in the Universe today. During this collapse, matter grew turbulent, whirling clumps around that eventually became the galaxies that orbit each other.

$^\dagger$_{Formally, one uses the frame in which the cosmic microwave background is isotropic.}

$^\ddagger$_{Taking into account our motion around the Galactic center, our Sun (currently) moves through space at $369.82\pm0.11\,\mathrm{km\, s^{-1}}$.}

Galaxies move through space with velocities of the order of a several 100 km per second; small velocities for small groups (~100 km/s; e.g Carlberg et al. 2000) and large velocities for rich clusters (~1000 km/s; e.g Girardi et al. 1993).

In addition to this so-called "peculiar velocity", galaxies also also carried away from each other due to the expansion of the Universe, at a velocity proportional to the distance from each other (the "Hubble flow"). But this is not a motion through space; rather it is space itself that is expanding (and hence the velocity may exceed the speed of light for sufficiently large distances).

One may define a "global reference frame" with respect to which velocities are measured. Any reference is valid, but it makes sense to use the frame in which all galaxies are, on average, in rest (when the Hubble flow is subtracted)$^\dagger$. In this frame, the Local Group that the Milky Way is a part of moves with some $620\, \mathrm{km \, s}^{-1}$ (as noted in John Duffield's answer above), whereas the center of the Milky Way has a velocity of $\mathbf{565 \pm 5 \, km \, s^{-1}}$ (Planck Collaboration et al. 2018).

What causes this movement of galaxies? Galaxies that are not too far from each (i.e. closer), "feel" each others mutual gravitational forces. A galaxy in a group or cluster moves around in the common gravitational field, but for galaxies that are farther away, the Hubble flow carries them away from each other too fast for them to attract each other.

This movement can be traced back to the tiny quantum mechanical fluctuations in the primordial soup of particles during cosmic inflation, i.e. less than $\sim10^{-32}\,\mathrm{s}$ after the Big Bang. As time went by, ever-so-slight overdensities grew in amplitude, until they collapsed to form the structure we see in the Universe today. During this collapse, matter grew turbulent, whirling clumps around that eventually became the galaxies that orbit each other.

$^\dagger$_{Formally, one uses the frame in which the cosmic microwave background is isotropic.}

Galaxies move through space with velocities of the order of a several 100 km per second; small velocities for small groups (~100 km/s; e.g Carlberg et al. 2000) and large velocities for rich clusters (~1000 km/s; e.g Girardi et al. 1993).

In addition to this so-called "peculiar velocity", galaxies also also carried away from each other due to the expansion of the Universe, at a velocity proportional to the distance from each other (the "Hubble flow"). But this is not a motion through space; rather it is space itself that is expanding (and hence the velocity may exceed the speed of light for sufficiently large distances).

One may define a "global reference frame" with respect to which velocities are measured. Any reference is valid, but it makes sense to use the frame in which all galaxies are, on average, in rest (when the Hubble flow is subtracted)$^\dagger$. In this frame, the Local Group that the Milky Way is a part of moves with some $620\, \mathrm{km \, s}^{-1}$ (as noted in John Duffield's answer above), whereas the center of the Milky Way has a velocity$^\ddagger$ of $\mathbf{565 \pm 5 \, km \, s^{-1}}$ (Planck Collaboration et al. 2018).

What causes this movement of galaxies? Galaxies that are not too far from each (i.e. closer), "feel" each others mutual gravitational forces. A galaxy in a group or cluster moves around in the common gravitational field, but for galaxies that are farther away, the Hubble flow carries them away from each other too fast for them to attract each other.

This movement can be traced back to the tiny quantum mechanical fluctuations in the primordial soup of particles during cosmic inflation, i.e. less than $\sim10^{-32}\,\mathrm{s}$ after the Big Bang. As time went by, ever-so-slight overdensities grew in amplitude, until they collapsed to form the structure we see in the Universe today. During this collapse, matter grew turbulent, whirling clumps around that eventually became the galaxies that orbit each other.

$^\dagger$_{Formally, one uses the frame in which the cosmic microwave background is isotropic.}

$^\ddagger$_{Taking into account our motion around the Galactic center, our Sun (currently) moves through space at $369.82\pm0.11\,\mathrm{km\, s^{-1}}$.}

Due to their mutual gravitational attraction, galaxies move through space with velocities of the order of a several 100 km per second; small velocities for small groups (~100 km/s; e.g Carlberg et al. 2000) and large velocities for rich clusters (~1000 km/s; e.g Girardi et al. 1993).

In addition to this so-called "peculiar velocity", galaxies also also carried away from each other due to the expansion of the Universe, at a velocity proportional to the distance from each other (the "Hubble flow"). But this is not a motion through space; rather it is space itself that is expanding (and hence the velocity may exceed the speed of light for sufficiently large distances).

One may define a "global reference frame" with respect to which velocities are measured. Any reference is valid, but it makes sense to use the frame in which all galaxies are, on average, in rest (when the Hubble flow is subtracted)$^\dagger$. In this frame, the Local Group that the Milky Way is a part of moves with some $620\, \mathrm{km \, s}^{-1}$ (as noted in John Duffield's answer above), whereas the center of the Milky Way has a velocity of $\mathbf{565 \pm 5 \, km \, s^{-1}}$ (Planck Collaboration et al. 2018).

$^\dagger$_{Formally, one uses the frame in which the cosmic microwave background is isotropic.}

Galaxies move through space with velocities of the order of a several 100 km per second; small velocities for small groups (~100 km/s; e.g Carlberg et al. 2000) and large velocities for rich clusters (~1000 km/s; e.g Girardi et al. 1993).

In addition to this so-called "peculiar velocity", galaxies also also carried away from each other due to the expansion of the Universe, at a velocity proportional to the distance from each other (the "Hubble flow"). But this is not a motion through space; rather it is space itself that is expanding (and hence the velocity may exceed the speed of light for sufficiently large distances).

One may define a "global reference frame" with respect to which velocities are measured. Any reference is valid, but it makes sense to use the frame in which all galaxies are, on average, in rest (when the Hubble flow is subtracted)$^\dagger$. In this frame, the Local Group that the Milky Way is a part of moves with some $620\, \mathrm{km \, s}^{-1}$ (as noted in John Duffield's answer above), whereas the center of the Milky Way has a velocity of $\mathbf{565 \pm 5 \, km \, s^{-1}}$ (Planck Collaboration et al. 2018).

What causes this movement of galaxies? Galaxies that are not too far from each (i.e. closer), "feel" each others mutual gravitational forces. A galaxy in a group or cluster moves around in the common gravitational field, but for galaxies that are farther away, the Hubble flow carries them away from each other too fast for them to attract each other.

This movement can be traced back to the tiny quantum mechanical fluctuations in the primordial soup of particles during cosmic inflation, i.e. less than $\sim10^{-32}\,\mathrm{s}$ after the Big Bang. As time went by, ever-so-slight overdensities grew in amplitude, until they collapsed to form the structure we see in the Universe today. During this collapse, matter grew turbulent, whirling clumps around that eventually became the galaxies that orbit each other.

$^\dagger$_{Formally, one uses the frame in which the cosmic microwave background is isotropic.}