A Closer Earth and the Faint Young Sun Paradox: Modification of the Laws of Gravitation or Sun/Earth Mass Losses?

Abstract

Given a solar luminosity LAr = 0.75L0 at the beginning of the Archean 3.8 Ga ago, where L0 is the present-day one, if the heliocentric distance, r, of the Earth was rAr = 0.956r0, the solar irradiance would have been as large as IAr = 0.82I0. It would have allowed for a liquid ocean on the terrestrial surface, which, otherwise, would have been frozen, contrary to the empirical evidence. By further assuming that some physical mechanism subsequently displaced the Earth towards its current distance in such a way that the irradiance stayed substantially constant over the entire Archean from 3.8 to 2.5 Ga ago, a relative recession per year as large as r˙/r ≈3.4 × 10−11 a−1 would have been required. Although such a figure is roughly of the same order of magnitude of the value of the Hubble parameter 3.8 Ga ago HAr = 1.192H0 = 8.2 × 10−11 a−1, standard general relativity rules out cosmological explanations for the hypothesized Earth’s recession rate. Instead, a class of modified theories of gravitation with nonminimal coupling between the matter and the metric naturally predicts a secular variation of the relative distance of a localized two-body system, thus yielding a potentially viable candidate to explain the putative recession of the Earth’s orbit. Another competing mechanism of classical origin that could, in principle, allow for the desired effect is the mass loss, which either the Sun or the Earth itself may have experienced during the Archean. On the one hand, this implies that our planet should have lost 2% of its present mass in the form of eroded/evaporated hydrosphere. On the other hand, it is widely believed that the Sun could have lost mass at an enhanced rate, due to a stronger solar wind in the past for not more than ≈ 0.2–0.3 Ga

Gravitational anomalies in the solar system?

“…In Ref. 183, after having ruled out a cosmological mechanism based on the currently accepted ΛCDM (Lambda Cold Dark Matter) scenario, the FYSP was viewed, for the first m Measured at the Earth's atmosphere, it is defined as the ratio of the Solar luminosity to the area of a sphere centered on the Sun with a radius equal to the Earth-Sun distance, r; in the following, we will assume a circular orbit for our planet. time, as a possible gravitational anomaly since the putative shift of the heliocentric distance of the Earth was attributed to a certain long-range modified model of gravity.…”

On a correlation among azimuthal velocities and the flyby anomaly sign

“…We have, for example: (a) possible anomalous advances of planetary perihelia (beyond the predictions of GR) as discussed in some studies (Iorio, 2009a; Pitjeva & Pitjev, 2013; Pitjev & Pitjeva, 2013), (b) the lingering unexplained secular increase of the eccentricity of the orbit of the Moon (Iorio, 2011a, 2011b, 2014a; Williams & Boggs, 2009; Williams, Boggs, & Folkner, 2008; Williams, Turyshev, & Boggs, 2014), (c) the so‐called “Faint Young Sun Paradox”, that is, the predictions from models of stellar evolution of a smaller energy output from the Sun in the Archean period than the one necessary to keep Earth's oceans in liquid state (Iorio, 2013; Sagan & Mullen, 1972), (d) the anomalous secular increase of the astronomical unit (Kaplan et al, 2015; Krasinsky & Brumberg, 2004; Standish, 2005), (e) a possible discrepancy between the predicted values of the Sun's angular momentum and its value constrained from planetary dynamics (Iorio, 2007a, 2012a), and (f) an anomalous Doppler blue shift for the Pioneer 10 and 11 spacecrafts corresponding to a constant acceleration a P =(8.74±1.33)×10 −8 cm s −2 , commonly known as the Pioneer anomaly (Anderson et al, 2002; Bertolami, Francisco, Gil, & Páramos, 2008, 2010; Fienga et al, 2010; Francisco, Bertolami, Gil, & Páramos, 2012; Iorio, 2007b, 2010, 2012b; Iorio & Giudice, 2006; Standish, 2008; Tangen, 2007; Turyshev & Toth, 2010; Turyshev et al, 2012).…”

Modified theories of gravity with nonminimal coupling and orbital particle dynamics

“…The units used in Figure 1 and the magnitude of the effect depicted in it are not to be considered indicative. Finally, we mention the fact that the variation of the distance of the two-body system implied by the rates of change of a and e may be used, at least in principle, to accommodate the required orbital recession of the Earth away from the Sun postulated in [14] to explain the so called Faint Young Sun Paradox [15] during the Archean eon.…”