We discuss recent laboratory experiments with rotating superconductors and show that three so far unexplained experimentally observed effects (anomalous acceleration signals, anomalous gyroscope signals, Cooper pair mass excess) can be physically explained in terms of a possible interaction of dark energy with Cooper pairs. Our approach is based on a Ginzburg-Landau-like model of electromagnetic dark energy, where gravitationally active photons obtain mass in the superconductor. We show that this model can account simultaneously for the anomalous acceleration and anomalous gravitomagnetic fields around rotating superconductors measured by Tajmar et al. and for the anomalous Cooper pair mass in superconductive Niobium, measured by Cabrera and Tate. It is argued that these three different physical effects are ultimately different experimental manifestations of the simultaneous spontaneous breaking of gauge invariance and of the principle of general covariance in superconductive materials.

Clovis Jacinto de Matos

Christian Beck

Possible Measurable Effects of Dark Energy in Rotating Superconductors

We present new analysis of the birth rate of AXPs and SGRS and their associated SNRs. Using
Kolmogorov-Smirnov statistics together with parametric fits based on a robust estimator, we find a birth rate of ~1/(1000 years) for AXPs/SGRs and their associated SNRs. These high rates suggest that all massive stars (greater
than ~(23–32)<svg style="vertical-align:-3.46715pt;width:25.0875px;" id="M1" height="15.4875" version="1.1" viewBox="0 0 25.0875 15.4875" width="25.0875" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg"><g transform="matrix(.017,-0,0,-.017,.062,11.112)"><path id="x1D440" d="M998 650l-8 -28q-71 -4 -86 -16t-22 -69l-50 -397q-3 -28 -4.5 -44t2 -29t6.5 -18.5t17 -10.5t24.5 -6.5t37.5 -3.5l-8 -28h-271l7 28q63 6 78 22t25 90l60 415h-2l-353 -552h-23l-130 536h-2l-70 -254q-44 -158 -47 -188q-5 -38 9 -51t71 -18l-6 -28h-241l8 28&#xA;q45 4 67 18.5t35 45.5q16 38 74 233l52 173q24 79 11.5 98t-89.5 26l6 28h177l136 -508l337 508h172z" /></g><g transform="matrix(.012,-0,0,-.012,17.412,15.187)"><path id="x2299" d="M573 255q0 -114 -81.5 -194.5t-197.5 -80.5t-197.5 80.5t-81.5 194.5t81.5 194.5t197.5 80.5t197.5 -80.5t81.5 -194.5zM521 255q0 96 -66.5 163.5t-160.5 67.5t-160.5 -67.5t-66.5 -163.5t66.5 -163.5t160.5 -67.5t160.5 67.5t66.5 163.5zM350 255q0 -26 -16 -42&#xA;t-40 -16t-40 16t-16 42q0 25 16 41.5t40 16.5t40 -16.5t16 -41.5z" /></g></svg>) give rise to remnants with magnetar-like fields. Observations indicate a limited fraction of
high magnetic fields in these progenitors; thus our study is suggestive of magnetic field amplification. Dynamo
mechanisms during the birth of the neutron stars require spin rates much faster than either observations or theory
indicate. We propose that massive stars produce neutron stars with normal (~<svg style="vertical-align:-0.1638pt;width:28.487499px;" id="M2" height="16.049999" version="1.1" viewBox="0 0 28.487499 16.049999" width="28.487499" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg"><g transform="matrix(.017,-0,0,-.017,.062,15.775)"><path id="x31" d="M384 0h-275v27q67 5 81.5 18.5t14.5 68.5v385q0 38 -7.5 47.5t-40.5 10.5l-48 2v24q85 15 178 52v-521q0 -55 14.5 -68.5t82.5 -18.5v-27z" /></g><g transform="matrix(.017,-0,0,-.017,8.222,15.775)"><path id="x30" d="M241 635q53 0 94 -28.5t63.5 -76t33.5 -102.5t11 -116q0 -58 -11 -112.5t-34 -103.5t-63.5 -78.5t-94.5 -29.5t-95 28t-64.5 75t-34.5 102.5t-11 118.5q0 58 11.5 112.5t34.5 103t64.5 78t95.5 29.5zM238 602q-32 0 -55.5 -25t-35.5 -68t-17.5 -91t-5.5 -105&#xA;q0 -76 10 -138.5t37 -107.5t69 -45q32 0 55.5 25t35.5 68.5t17.5 91.5t5.5 105t-5.5 105.5t-18 92t-36 68t-56.5 24.5z" /></g><g transform="matrix(.012,-0,0,-.012,16.375,7.613)"><use xlink:href="#x31" /></g><g transform="matrix(.012,-0,0,-.012,22.086,7.613)"><path id="x32" d="M412 140l28 -9q0 -2 -35 -131h-373v23q112 112 161 170q59 70 92 127t33 115q0 63 -31 98t-86 35q-75 0 -137 -93l-22 20l57 81q55 59 135 59q69 0 118.5 -46.5t49.5 -122.5q0 -62 -29.5 -114t-102.5 -130l-141 -149h186q42 0 58.5 10.5t38.5 56.5z" /></g></svg> G) magnetic fields, which are
then amplified to <svg style="vertical-align:-0.1638pt;width:28.487499px;" id="M3" height="16.049999" version="1.1" viewBox="0 0 28.487499 16.049999" width="28.487499" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg"><g transform="matrix(.017,-0,0,-.017,.062,15.775)"><use xlink:href="#x31" /></g><g transform="matrix(.017,-0,0,-.017,8.222,15.775)"><use xlink:href="#x30" /></g><g transform="matrix(.012,-0,0,-.012,16.375,7.613)"><use xlink:href="#x31" /></g><g transform="matrix(.012,-0,0,-.012,22.086,7.613)"><path id="x34" d="M456 178h-96v-72q0 -51 12.5 -62.5t72.5 -16.5v-27h-256v27q65 5 78 17t13 62v72h-260v28q182 271 300 426h40v-407h96v-47zM280 225v295h-2q-107 -148 -196 -295h198z" /></g></svg>-<svg style="vertical-align:-0.1638pt;width:28.487499px;" id="M4" height="16.049999" version="1.1" viewBox="0 0 28.487499 16.049999" width="28.487499" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg"><g transform="matrix(.017,-0,0,-.017,.062,15.775)"><use xlink:href="#x31" /></g><g transform="matrix(.017,-0,0,-.017,8.222,15.775)"><use xlink:href="#x30" /></g><g transform="matrix(.012,-0,0,-.012,16.375,7.613)"><use xlink:href="#x31" /></g><g transform="matrix(.012,-0,0,-.012,22.086,7.613)"><path id="x35" d="M153 550l-26 -186q79 31 111 31q90 0 141.5 -51t51.5 -119q0 -93 -89 -166q-85 -69 -173 -71q-32 0 -61.5 11.5t-41.5 23.5q-18 17 -17 34q2 16 22 33q14 9 26 -1q61 -50 124 -50q60 0 93 43.5t33 104.5q0 69 -41.5 110t-121.5 41q-53 0 -102 -20l38 305h286l6 -8&#xA;l-26 -65h-233z" /></g></svg> G after a delay of hundreds of years. The amplification is speculated to be a consequence
of color ferromagnetism and to occur with a delay after the neutron star core reaches quark deconfinement density
(i.e., the quark-nova scenario). The delayed amplification allows one to interpret simultaneously the high birth
rate and high magnetic fields of AXPs/SGRs and their link to massive stars.

Denis Leahy

Rachid Ouyed

SGRs and AXPs: Evidence for Delayed Amplification of Magnetic Field after Neutron Star Formation?

If a quark-nova occurs inside a collapsar, the interaction between the quark-nova ejecta (relativistic iron-rich chunks) and the collapsar envelope leads to features indicative of those observed in Gamma Ray Bursts. The quark-nova ejecta collides with the stellar envelope creating an outward moving cap (<svg style="vertical-align:-0.0pt;width:23.4375px;" id="M1" height="11.175" version="1.1" viewBox="0 0 23.4375 11.175" width="23.4375" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg"><g transform="matrix(.017,-0,0,-.017,.062,11.113)"><path id="x393" d="M485 501l-30 -4q-15 64 -35 90q-12 16 -33.5 22t-68.5 6h-74q-21 0 -26.5 -5t-5.5 -26v-458q0 -62 15.5 -78t83.5 -20v-28h-270v28q58 4 72 20t14 78v399q0 61 -13.5 77t-71.5 20v28h433q0 -51 10 -149z" /></g><g transform="matrix(.017,-0,0,-.017,13.39,11.113)"><path id="x223C" d="M548 311q-21 -57 -59 -94t-89 -37q-53 0 -128 52q-55 38 -84 38q-39 0 -70.5 -23t-45.5 -60l-32 12q21 57 59 94t89 37q53 0 128 -52q55 -38 84 -38q39 0 70.5 23t45.5 60z" /></g></svg> 1–10) above the polar funnel. Prompt gamma-ray burst emission from internal shocks in relativistic jets (following accretion onto the quark star) becomes visible after the cap becomes optically thin. Model features include (i) precursor activity (optical, X-ray, <svg style="vertical-align:-3.56265pt;width:8.6374998px;" id="M2" height="12.175" version="1.1" viewBox="0 0 8.6374998 12.175" width="8.6374998" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg"><g transform="matrix(.017,-0,0,-.017,.062,7.675)"><path id="x1D6FE" d="M478 372q0 -39 -31 -97t-61 -98t-78 -98q-45 -55 -73 -102q-13 -79 -13 -197q-11 -11 -43.5 -25.5t-53.5 -15.5l-15 17q5 35 26 101.5t47 123.5q8 72 -1.5 174.5t-37.5 178.5q-14 37 -29 37q-20 0 -67 -65l-25 21q37 60 73 90.5t63 30.5q47 0 72 -112q13 -56 17.5 -141.5&#xA;t0.5 -143.5h2q155 193 155 297q0 26 -12 47q-5 8 -5 15q0 16 12.5 27t29.5 11q21 0 34 -21t13 -55z" /></g></svg>-ray), (ii) prompt <svg style="vertical-align:-3.56265pt;width:8.6374998px;" id="M3" height="12.175" version="1.1" viewBox="0 0 8.6374998 12.175" width="8.6374998" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg"><g transform="matrix(.017,-0,0,-.017,.062,7.675)"><use xlink:href="#x1D6FE" /></g></svg>-ray emission, and (iii) afterglow emission. We discuss SN-less long duration GRBs, short hard GRBs (including association and nonassociation with star forming regions), dark GRBs, the energetic X-ray flares detected in Swift GRBs, and the near-simultaneous optical and <svg style="vertical-align:-3.56265pt;width:8.6374998px;" id="M4" height="12.175" version="1.1" viewBox="0 0 8.6374998 12.175" width="8.6374998" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg"><g transform="matrix(.017,-0,0,-.017,.062,7.675)"><use xlink:href="#x1D6FE" /></g></svg>-ray prompt emission observed in GRBs in the context of our model.

Jan Staff

Brian Niebergal

Quark-Nova Explosion inside a Collapsar: Application to Gamma Ray Bursts

we continue our study of the CMB temperature polarization (TE) cross-correlation as a source of
information about primordial gravitational waves (PGWs). In a previous paper, we considered two
methods for detecting PGWs using the TE cross-correlation. The first method is the zero multipole
method, where we find the multipole, <svg style="vertical-align:-3.3907pt;width:13.45px;" id="M1" height="15.5375" version="1.1" viewBox="0 0 13.45 15.5375" width="13.45" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg"><g transform="matrix(.017,-0,0,-.017,.062,11.25)"><path id="x2113" d="M363 114l21 -20q-62 -106 -161 -106q-61 0 -94 40t-33 138v56l-54 -40l-14 27l68 57v89q0 112 15.5 166t49.5 91q43 46 96 46q44 0 71 -32.5t27 -88.5q0 -41 -17.5 -81.5t-49.5 -76t-55.5 -57t-55.5 -46.5v-87q0 -138 81 -138q60 0 105 63zM177 421v-101q117 105 117 217&#xA;q0 38 -15 60.5t-41 22.5q-34 0 -47.5 -46.5t-13.5 -152.5z" /></g><g transform="matrix(.012,-0,0,-.012,7.05,15.325)"><path id="x30" d="M241 635q53 0 94 -28.5t63.5 -76t33.5 -102.5t11 -116q0 -58 -11 -112.5t-34 -103.5t-63.5 -78.5t-94.5 -29.5t-95 28t-64.5 75t-34.5 102.5t-11 118.5q0 58 11.5 112.5t34.5 103t64.5 78t95.5 29.5zM238 602q-32 0 -55.5 -25t-35.5 -68t-17.5 -91t-5.5 -105&#xA;q0 -76 10 -138.5t37 -107.5t69 -45q32 0 55.5 25t35.5 68.5t17.5 91.5t5.5 105t-5.5 105.5t-18 92t-36 68t-56.5 24.5z" /></g></svg>, where the TE cross-correlation power spectrum, <svg style="vertical-align:-3.3907pt;width:28.174999px;" id="M2" height="20.549999" version="1.1" viewBox="0 0 28.174999 20.549999" width="28.174999" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg"><g transform="matrix(.017,-0,0,-.017,.062,16.263)"><path id="x1D436" d="M682 629q-1 -16 -1.5 -72t-2.5 -86l-31 -4q-5 92 -51 129t-139 37q-100 0 -177 -49t-116 -125t-39 -162q0 -122 66 -201t182 -79q83 0 137 42.5t112 128.5l26 -15q-12 -31 -42.5 -88t-45.5 -75q-139 -27 -199 -27q-148 0 -243 81.5t-95 226.5q0 173 129.5 274.5&#xA;t325.5 101.5q114 0 204 -38z" /></g><g transform="matrix(.012,-0,0,-.012,12.05,20.35)"><use xlink:href="#x2113" /></g><g transform="matrix(.012,-0,0,-.012,12.05,8.1)"><path id="x1D447" d="M649 676l-22 -187l-33 -2q3 56 -12 94q-8 20 -31.5 26.5t-86.5 6.5h-74l-90 -491q-4 -23 -6 -36.5t1 -25t7 -16.5t18 -9t27 -5t41 -3l-6 -28h-286l4 28q68 5 84 18.5t28 76.5l94 491h-55q-74 0 -100.5 -6t-41.5 -23q-24 -29 -54 -98l-32 1q32 98 53 188h22q7 -18 15 -22&#xA;t37 -4h417q23 0 33.5 5t25.5 21h23z" /></g><g transform="matrix(.012,-0,0,-.012,19.975,8.1)"><path id="x1D438" d="M609 650l-19 -162l-30 -2q2 69 -14 94q-9 18 -28.5 26t-74.5 8h-88q-30 0 -37 -6.5t-12 -36.5l-41 -212h103q48 0 69 5.5t32 19t26 50.5h29l-40 -198h-30q2 58 -11.5 70.5t-85.5 12.5h-99l-30 -167q-17 -87 3 -101q18 -15 111 -15q59 0 89 7t54 27q8 7 15.5 16t16 21.5&#xA;l14 20.5t15 23.5t13.5 21.5l29 -10q-52 -129 -71 -163h-500l6 28q66 4 83 17.5t28 73.5l77 409q11 61 -0.5 75.5t-78.5 18.5l10 28h467z" /></g></svg>, first changes sign. The second method Wiener filters the CMB TE data to remove the density
perturbation contribution to the TE power spectrum. We then use statistical tests to determine
if there is a detection of negative residual TE correlation and hence a detection of primordial
gravitational waves, the only source of negative TE correlation at these superhorizon scales. In this
paper, we will apply these tests to the WMAP 5-year data. We find that the TE power spectrum
consistent with <svg style="vertical-align:-0.1638pt;width:7.3000002px;" id="M3" height="7.9499998" version="1.1" viewBox="0 0 7.3000002 7.9499998" width="7.3000002" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg"><g transform="matrix(.017,-0,0,-.017,.062,7.675)"><path id="x1D45F" d="M393 379q-9 -16 -28 -29q-15 -10 -23 -2q-19 19 -36 19q-21 0 -52 -38q-57 -72 -82 -126l-40 -197q-23 -3 -75 -18l-7 7q49 196 74 335q7 43 -2 43q-7 0 -30 -14.5t-47 -37.5l-16 23q37 42 82 73t67 31q41 0 15 -113l-11 -50h4q41 71 85 117t77 46q29 0 45 -26&#xA;q13 -21 0 -43z" /></g></svg> &lt; 2.0 at 95% confidence with no additional assumptions about the PGWs. If we
assume that the PGWs are generated by inflation, then we get <svg style="vertical-align:-0.1638pt;width:7.3000002px;" id="M4" height="7.9499998" version="1.1" viewBox="0 0 7.3000002 7.9499998" width="7.3000002" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg"><g transform="matrix(.017,-0,0,-.017,.062,7.675)"><use xlink:href="#x1D45F" /></g></svg> &lt; 1.0 at 95% confidence.

N. J. Miller

B. G. Keating

A. G. Polnarev

CMB Temperature Polarization Correlation and Primordial Gravitational Waves: WMAP5

Conventional equilibrium statistical mechanics of open gravitational systems is known to be problematical. We first recall that spherical stars/galaxies acquire unbounded radii, become infinitely massive, and evaporate away continuously if one uses the standard Maxwellian distribution <svg style="vertical-align:-3.56265pt;width:19px;" id="M1" height="20.450001" version="1.1" viewBox="0 0 19 20.450001" width="19" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg"><g transform="matrix(.017,-0,0,-.017,.062,15.95)"><path id="x1D453" d="M619 670q0 -13 -9 -26t-18 -19q-13 -10 -25 2q-36 38 -66 38q-31 0 -54.5 -50t-45.5 -185h120l-20 -31l-107 -12q-23 -138 -57 -293q-27 -122 -55 -184.5t-75 -109.5q-60 -61 -114 -61q-25 0 -47.5 15t-22.5 31q0 17 31 44q11 8 20 -1q10 -11 31 -19t35 -8q26 0 47 19&#xA;q34 34 71 253l54 315h-90l-3 12l31 30h70q28 138 90 204q35 37 75 57.5t70 20.5q26 0 45 -14t19 -28z" /></g><g transform="matrix(.012,-0,0,-.012,10.975,7.8)"><path id="x1D435" d="M594 511q0 -122 -171 -157l1 -2q158 -33 158 -159q0 -52 -34.5 -95t-90.5 -65q-76 -33 -217 -33h-223l8 28q63 5 79.5 19t26.5 72l83 426q9 48 -2.5 60t-77.5 17l6 28h259q195 0 195 -139zM499 509q0 59 -37 83t-91 24q-36 0 -51 -9q-17 -9 -22 -44l-35 -195h62&#xA;q82 0 128 37t46 104zM481 199q0 71 -48 102.5t-121 31.5h-56l-37 -201q-11 -58 7.5 -77t80.5 -19q76 0 125 44.5t49 118.5z" /></g></svg>  (which maximizes the usual Boltzmann-Shannon entropy and hence has a tail extending to infinity). Next, we show that these troubles disappear automatically if we employ the exact most probable distribution  <svg style="vertical-align:-3.56265pt;width:11.0375px;" id="M2" height="16.6625" version="1.1" viewBox="0 0 11.0375 16.6625" width="11.0375" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg"><g transform="matrix(.017,-0,0,-.017,.062,12.162)"><use xlink:href="#x1D453" /></g></svg>  (which maximizes the combinatorial entropy and hence possesses a sharp cutoff tail). Finally, if astronomical observation is carried out on a large galaxy, then the Poisson equation together with thermal de Broglie wavelength provides useful information about the cutoff radius <svg style="vertical-align:-3.27605pt;width:17.15px;" id="M3" height="11.825" version="1.1" viewBox="0 0 17.15 11.825" width="17.15" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg"><g transform="matrix(.017,-0,0,-.017,.062,7.675)"><path id="x1D45F" d="M393 379q-9 -16 -28 -29q-15 -10 -23 -2q-19 19 -36 19q-21 0 -52 -38q-57 -72 -82 -126l-40 -197q-23 -3 -75 -18l-7 7q49 196 74 335q7 43 -2 43q-7 0 -30 -14.5t-47 -37.5l-16 23q37 42 82 73t67 31q41 0 15 -113l-11 -50h4q41 71 85 117t77 46q29 0 45 -26&#xA;q13 -21 0 -43z" /></g><g transform="matrix(.012,-0,0,-.012,7.238,11.762)"><path id="x1D43E" d="M764 650l-7 -26q-61 -10 -91.5 -22.5t-76.5 -48.5l-235 -184q104 -152 208 -276q31 -37 54.5 -48.5t68.5 -16.5l-7 -28h-156q-138 170 -213 284q-19 29 -33.5 35t-33.5 -7l-29 -173q-15 -75 -5.5 -90.5t74.5 -20.5l-5 -28h-260l7 28q58 5 74 21.5t30 89.5l70 378&#xA;q12 68 2 83t-72 22l6 28h257l-7 -28q-62 -7 -76 -21.5t-27 -83.5l-32 -172q29 11 78 46q112 84 217 179q18 16 23.5 25.5t-1 14.5t-26.5 8l-30 4l5 28h249z" /></g></svg>, cutoff energy  <svg style="vertical-align:-3.27605pt;width:16.950001px;" id="M4" height="11.825" version="1.1" viewBox="0 0 16.950001 11.825" width="16.950001" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg"><g transform="matrix(.017,-0,0,-.017,.062,7.675)"><path id="x1D700" d="M387 375q0 -16 -17 -31t-29 -15q-9 0 -12 13q-13 74 -80 74q-36 0 -61 -24.5t-25 -56.5t24 -51.5t68 -19.5q33 0 47 2l2 -7l-32 -42q-20 2 -54 2q-45 0 -74 -21.5t-29 -60.5q0 -41 28 -65.5t73 -24.5q78 0 145 67l17 -23q-33 -47 -84.5 -75t-111.5 -28q-70 0 -114.5 35.5&#xA;t-44.5 92.5q0 46 38 78t95 45v2q-35 10 -54.5 33t-19.5 52q0 55 53 88.5t122 33.5q67 0 98.5 -23.5t31.5 -49.5z" /></g><g transform="matrix(.012,-0,0,-.012,7.037,11.762)"><use xlink:href="#x1D43E" /></g></svg>, and the huge quantum number <svg style="vertical-align:-0.0pt;width:13.3125px;" id="M5" height="11.175" version="1.1" viewBox="0 0 13.3125 11.175" width="13.3125" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg"><g transform="matrix(.017,-0,0,-.017,.062,11.113)"><use xlink:href="#x1D43E" /></g></svg> up to which the cluster exists. Thereby, a refinement over the empirical lowered isothermal King models, is achieved. Numerically, we find that the most probable distribution (MPD) prediction fits well the number density profile near the outer edge of globular clusters.

Ritesh Kumar Dubey

V. J. Menon

M. K. Pandey

D. N. Tripathi

Entropy Maximization, Cutoff Distribution, and Finite Stellar Masses

The effect of perturbations in Coriolis and cetrifugal forces on the nonlinear
stability of the equilibrium point of the Robe's (1977) restricted circular
three-body problem has been studied when the density parameter <span class="inline" id="M1" /> is zero. By applying Kolmogorov-Arnold-Moser (KAM) theory, it has been found
that the equilibrium point is stable for all mass ratios <span class="inline" id="M2" /> in the range of
linear stability <span class="inline" id="M3" />, where <span class="inline" id="M4" /> and <span class="inline" id="M5" /> are, respectively, the perturbations in Coriolis and centrifugal forces, except for five mass ratios
<span class="inline" id="M6" />, <span class="inline" id="M7" /><span class="inline" id="M8" />, <span class="inline" id="M9" /><span class="inline" id="M10" /><span class="inline" id="M11" />, <span class="inline" id="M12" /><span class="inline" id="M13" /> + 1.11684064<span class="inline" id="M14" />, <span class="inline" id="M15" /><span class="inline" id="M16" /> + 1.22385421<span class="inline" id="M17" />, where the theory is not applicable.

P. P. Hallan

Khundrakpam Binod Mangang

Effect of Perturbations in Coriolis and Centrifugal Forces on the Nonlinear Stability of Equilibrium Point in Robe's Restricted Circular Three-Body Problem

We use the corrections to the Newton-Einstein secular
precessions of the longitudes of perihelia <svg style="vertical-align:-0.13794pt;width:14.4375px;" id="M1" height="10.0125" version="1.1" viewBox="0 0 14.4375 10.0125" width="14.4375"  xmlns="http://www.w3.org/2000/svg">
	<g transform="matrix(1.25,0,0,-1.25,0,10.0125)">
		<g transform="translate(72,-63.99)">
			<text transform="matrix(1,0,0,-1,-63.35,64.17)">
				<tspan style="font-size: 12.50px; " x="0" y="0">̇</tspan>
				<tspan style="font-size: 12.50px; " x="-8.5895615" y="0">𝜛</tspan>
			</text>

		</g>
	</g>
</svg> of some planets (Mercury, Earth, Mars,
Jupiter, Saturn) of the Solar System, phenomenologically estimated
as solve-for parameters by the Russian astronomer E. V. Pitjeva in a
global fit of almost one century of data with the EPM2004 ephemerides,
in order to put on the test the expression for the perihelion precession
induced by a uniform cosmological constant <svg style="vertical-align:-0.0pt;width:11.1px;" id="M2" height="10.6625" version="1.1" viewBox="0 0 11.1 10.6625" width="11.1"  xmlns="http://www.w3.org/2000/svg">
	<g transform="matrix(1.25,0,0,-1.25,0,10.6625)">
		<g transform="translate(72,-63.47)">
			<text transform="matrix(1,0,0,-1,-71.95,63.52)">
				<tspan style="font-size: 12.50px; " x="0" y="0">Λ</tspan>
			</text>

		</g>
	</g>
</svg> in the framework of the
Schwarzschild-de Sitter (or Kottler) space-time. We compare such an
extra rate to the estimated corrections to the planetary perihelion precessions
by taking their ratio for different pairs of planets instead of using
one perihelion at a time for each planet separately, as done so far in
literature. The answer is  negative, even by further rescaling by
a factor 10 (and even 100 for Saturn) the errors in the estimated extra
precessions of the perihelia released by Pitjeva. Our conclusions hold
also for any other metric perturbation having the same dependence on
the spatial coordinates, as those induced by other general relativistic
cosmological scenarios and by many modified models of gravity. Currently
ongoing and planned interplanetary spacecraft-based missions
should improve our knowledge of the planets&#x27; orbits allowing for more
stringent constraints.

Lorenzo Iorio

Solar System Motions and the Cosmological Constant:<?layout cmd="newline"?> A New Approach

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<p><em>Advances in Astronomy</em> publishes in all areas of astronomy, astrophysics, and cosmology, and accepts observational and theoretical investigations into celestial objects and the wider universe.</p>


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<p>Chief Editor, Professor Trigo-Rodríguez (ICE, IEEC-CSIC), has a background in the formation of primitive solar system minor bodies, the study of their fragments in space and the analysis of their surviving rocks that arrived on the Earth.</p>


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Advances in Astronomy publishes in all areas of astronomy, astrophysics, and cosmology, and accepts observational and theoretical investigations into celestial objects and the wider universe.

Advances in Astronomy