4 ms·

The Hubble constant is 67.8 (km/s)/Mpc. That means that something one Mega-parsec (Mpc) away will appear to recede at about 70 km/s. Our galaxy is about 35 kp

by mturmon 13y ago

The Hubble constant is 67.8 (km/s)/Mpc. That means that something one Mega-parsec (Mpc) away will appear to recede at about 70 km/s. Our galaxy is about 35 kpc across. Voyager is currently 0.0006 parsecs from Earth, moving at 17 km/s. Given this distance, we find that the cosmological effect alters the apparent velocity of Voyager by 4.2x10^-8 km/s. This is only 1 part in 4x10^8, which is probably too small to measure. There may be general-relativistic corrections to the spacecraft clocks, however, and computation of its trajectory may involve general-relativistic dynamics. So some of the often-ignorable effects probably do add up. Of course, the surrounding volume is also expanding with the same rate, so from that point of view, there is no effect.

privong 13y ago
The expansion of the Universe is irrelevant in this case. Our galaxy is gravitationally bound, so things (stars, planets, etc) within it do not follow Hubble's law. So there will be no modification to Voyager's distance from earth as a result of the Universe's expansion. Even nearby galaxies don't obey Hubble's law. Andromeda, for example, is moving towards us, despite the overall expansion of the universe. In this case, it is due to the gravitational attraction between it and our galaxy.
- mturmon 13y ago
  You are offering a more sophisticated take on the matter. At non-cosmological scales, metric expansion (i.e., the Hubble law) is not occurring because of bulk gravitational attraction. The arithmetic I did is a tool illustrating the scale that is needed to make metric expansion operative. The arithmetic has the advantage of giving a quantitative idea how far away Earth-Voyager is from the necessary scale.
  - privong 13y ago
    > The arithmetic I did is a tool illustrating the scale that is needed to make metric expansion operative. You might revisit the wording then. As it's written it implies that with arbitrarily increased measurement precision, we could measure an effect of the Hubble Flow on Voyager's movement. But even with arbitrary precision we'd never measure an effect from the Hubble Flow on Voyager's motion because the expansion of the Universe isn't contributing to the relative motion between Earth and Voyager.
jerf 13y ago
"So some of the often-ignorable effects probably do add up." Oh, they certainly do: http://www.cosmosmagazine.com/news/pioneer-anomaly-solved/ http://www.cosmosmagazine.com/news/pioneer-anomaly-solved/ I don't think any other space mission has ever had a chance to worry about that level of detail.
- mturmon 13y ago
  Nice example. GPS is another case; to get the most out of the data requires very careful modeling, including tidal effects, Earth mass density, and GR corrections. (E.g., https://gipsy-oasis.jpl.nasa.gov/index.php?page=software https://gipsy-oasis.jpl.nasa.gov/index.php?page=software)

by mturmon 13y ago

privong 13y ago

The expansion of the Universe is irrelevant in this case. Our galaxy is gravitationally bound, so things (stars, planets, etc) within it do not follow Hubble's law. So there will be no modification to Voyager's distance from earth as a result of the Universe's expansion. Even nearby galaxies don't obey Hubble's law. Andromeda, for example, is moving towards us, despite the overall expansion of the universe. In this case, it is due to the gravitational attraction between it and our galaxy.

mturmon 13y ago
You are offering a more sophisticated take on the matter. At non-cosmological scales, metric expansion (i.e., the Hubble law) is not occurring because of bulk gravitational attraction. The arithmetic I did is a tool illustrating the scale that is needed to make metric expansion operative. The arithmetic has the advantage of giving a quantitative idea how far away Earth-Voyager is from the necessary scale.
- privong 13y ago
  > The arithmetic I did is a tool illustrating the scale that is needed to make metric expansion operative. You might revisit the wording then. As it's written it implies that with arbitrarily increased measurement precision, we could measure an effect of the Hubble Flow on Voyager's movement. But even with arbitrary precision we'd never measure an effect from the Hubble Flow on Voyager's motion because the expansion of the Universe isn't contributing to the relative motion between Earth and Voyager.

jerf 13y ago

"So some of the often-ignorable effects probably do add up." Oh, they certainly do: http://www.cosmosmagazine.com/news/pioneer-anomaly-solved/ http://www.cosmosmagazine.com/news/pioneer-anomaly-solved/ I don't think any other space mission has ever had a chance to worry about that level of detail.

mturmon 13y ago
Nice example. GPS is another case; to get the most out of the data requires very careful modeling, including tidal effects, Earth mass density, and GR corrections. (E.g., https://gipsy-oasis.jpl.nasa.gov/index.php?page=software https://gipsy-oasis.jpl.nasa.gov/index.php?page=software)