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I've seen estimates varying by an order of magnitude, e.g. (New Scientist)

Having such a precise yardstick allowed Russian dynamicists Gregoriy A. Krasinsky and Victor A. Brumberg to calculate, in 2004, that the sun and Earth are gradually moving apart. It’s not much – just 15 cm per year – but since that’s 100 times greater than the measurement error, something must really be pushing Earth outward.

I double-checked the paper and there's no typo in New Scientist, as far as I can tell. Krasinsky and Brumberg give it as "15 ± 4 m/cy" (which is 15 cm/year; "cy" is almost certainly 100 years in that context.)

Whereas another astrophysicist, Ethan Siegel, writing in Forbes in 2019 claims it's only 1.5 cm/year.

This year, 2019, our perihelion was 1.5 centimeters farther away than it was last year, which was more distant than the year before, etc.

The same figure (1.5 cm) appears in an undated Cornell FAQ page. So, is there a consensus established in the meantime that the true rate is (close to) the latter 1.5 cm/year? What experiments/models/papers is the latter based on?

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    $\begingroup$ A "year" as a unit of time to astronomers is typically 365.25 days of 86400 seconds each. No leap years, no leap seconds. And yes, "cy" (short for century) almost certainly mean exactly 36525 days. $\endgroup$
    – David Hammen
    Commented Jul 20, 2022 at 20:29
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    $\begingroup$ Having read the latter FAQ page more closely, it does detail what the 1.5cm figure is based on: current Earth distance from the Sun and expected mass loss of the Sun (0.1%) over 10 billions year . It does seem like more of a quick estimate than the Krasinsky and Brumberg paper, but that one could also be not quite "mainstream". I'd be curious if the estimate based Sun mass loss appears e.g. in textbooks, because it definitely seems to be too simple for a standalone paper. $\endgroup$
    – got trolled too much this week
    Commented Jul 20, 2022 at 20:30
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    $\begingroup$ different but related and potentially helpful: How much mass does the Sun lose as light, neutrinos, and solar wind? and especially Sun constantly converts mass into energy, will this cause its gravity to decrease? $\endgroup$
    – uhoh
    Commented Jul 20, 2022 at 20:44
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    $\begingroup$ I see this was asked on physics too physics.stackexchange.com/questions/71652/… I'm not too convinced by the answer there as it seems to pick one (non-review) paper as the "obviously" correct number. (But at least it's a more recent paper.) $\endgroup$
    – got trolled too much this week
    Commented Jul 20, 2022 at 21:11
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    $\begingroup$ OTOH Petjeva's paper (which is the accepted answer there) simply says that Krasinsky & Brumberg got their calculation wrong, by ignoring the correlation between the change in AU and the change in its speed. Interestingly, Petjeva works at the same place as Krasinsky & Brumberg ; Petjeva's (4-page) paper appears to have been published only at a conference ui.adsabs.harvard.edu/abs/2012jsrs.conf...17P/abstract $\endgroup$
    – got trolled too much this week
    Commented Jul 20, 2022 at 21:21

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Having such a precise yardstick allowed Russian dynamicists Gregoriy A. Krasinsky and Victor A. Brumberg to calculate, in 2004, that the sun and Earth are gradually moving apart. It’s not much – just 15 cm per year – but since that’s 100 times greater than the measurement error, something must really be pushing Earth outward.

That's New Scientist, after all. Here's a better reference: Values of some astronomical parameters - AU, GM, M of the Sun, their possible variations from modern observations, and interrelations between them.

The author of that paper, Elena V. Pitjeva, worked closely with Krasinsky and Brumberg. She was one of Krasinsky's students and continued working with him at the prestigious Russian Academy of Sciences's Institute of Applied Astronomy (essentially the Russian equivalent of JPL with regard to ephemerides).

In that conference paper she describes what that paper by Krasinsky and Brumberg found. First off, they were writing about possible secular variations in the Astronomical Unit (au). That is not quite the mean (average) distance between the Sun and the Earth. It's close, but the semi-standard and widely used definition used at the time of the paper by Krasinsky and Brumberg was convoluted (and that's putting it nicely).

The key problems with the paper by Krasinsky and Brumberg were that

  • The definition of the au they were using was rather convoluted.
  • They used a 42 year span of time. the space era marks the onset of reliable, high quality data needed for ephemerides.
  • They tried to simultaneously estimate the value of the au and its rate of change (along with a whole lot of other parameters in their ephemeris generation).
  • The derived values of the au and its rate of change were very highly correlated; 98.5% per Pitjeva's paper.

Pitjeva's takeaway was that we simply don't have enough data (yet) to reliably estimate the rate at which the Earth is receding from the Sun. It should be receding to some extent as the Sun has to be losing mass. (I wrote "has to be" in scare quotes because while it is losing mass due to fusion and solar wind, it is also gaining mass due to infalling material. No sane solar scientist thinks the mass gain is anywhere close to the mass loss.)

However, an unmodeled 15 cm/year Earth recession rate would be more than enough to observationally interfere with JPL's ability to communicate with NASA's deep space probes. JPL does not currently model this. It doesn't even model the estimated mass loss rate of the Sun. It's below the observational threshold. 15 cm/year is not below the observational threshold.

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    $\begingroup$ Why would it "interfere with JPL's ability to communicate with NASA's deep space probes"? $\endgroup$
    – got trolled too much this week
    Commented Jul 20, 2022 at 21:47
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    $\begingroup$ I did find a paper that backs up your point that NASA says they can't measure that though, but only in the sense that they can't distinguish changes in the Sun's mass from changes in the gravitational constant adsabs.harvard.edu/full/2010IAUS..261..155F $\endgroup$
    – got trolled too much this week
    Commented Jul 20, 2022 at 22:21
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    $\begingroup$ @Fizz Because that big (15 cm/year) of a recession rate would affect the Earth's orbital position over time, which in turn would impact the aiming of NASA's Deep Space Network antennae, some of which have a very narrow bandwidth. $\endgroup$
    – David Hammen
    Commented Jul 20, 2022 at 23:25
  • $\begingroup$ It would most likely wreak even greater havoc with microarcsecond astronomy. The 15 cm/yr is not real. I doubt that even the 1.5 cm/yr cited (without reference) by Ethan Siegel is real. $\endgroup$
    – David Hammen
    Commented Jul 21, 2022 at 4:57
  • $\begingroup$ I'm having a hard time understanding the interference bit as well. These big radio telescopes used for communications are not pointed blindly in space and run through super-narrow notch filters, surely for the last fraction of a degree they use active pointing to maximize signal via conscan and digitize a wide frequency band looking for a narrow signal (1, 2, 3) $\endgroup$
    – uhoh
    Commented Jul 21, 2022 at 20:56

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