The Projectile inside the Loop

In this paper we describe an alternative use of the loop-the-loop apparatus, which can be used to study an interesting case of projectile motion. We also present an effective way to perform and analyze these experiments, by using video capture software together with a digital video camera. These experiments can be integrated into classroom demonstrations for general physics courses, or become part of laboratory activities.Comment: 7 pages, including 2 figure

Astrophysical Tests of Kinematical Conformal Cosmology in Fourth-Order Conformal Weyl Gravity

In this work we analyze kinematical conformal cosmology (KCC), an alternative cosmological model based on conformal Weyl gravity (CG), and test it against current type Ia supernova (SNIa) luminosity data and other astrophysical observations. Expanding upon previous work on the subject, we revise the analysis of SNIa data, confirming that KCC can explain the evidence for an accelerating expansion of the Universe without using dark energy or other exotic components. We obtain an independent evaluation of the Hubble constant, H_{0} = 67.53 km/s Mpc, very close to the current best estimates. The main KCC and CG parameters are re-evaluated and their revised values are found to be close to previous estimates. We also show that available data for the Hubble parameter as a function of redshift can be fitted using KCC and that this model does not suffer from any apparent age problem. Overall, KCC remains a viable alternative cosmological model, worthy of further investigation.Comment: 31 pages, including 5 figures and 2 tables. Minor changes and references added. Final version published in Galaxies, Special Issue: Beyond Standard Gravity and Cosmolog

Conformal Cosmology and the Pioneer Anomaly

We review the fundamental results of a new cosmological model, based on conformal gravity, and apply them to the analysis of the early data of the Pioneer anomaly. We show that our conformal cosmology can naturally explain the anomalous acceleration of the Pioneer 10 and 11 spacecraft, in terms of a local blueshift region extending around the solar system and therefore affecting the frequencies of the navigational radio signals exchanged between Earth and the spacecraft. On the contrary, conformal gravity corrections alone would not be able to account for dynamical effects of such magnitude to be capable of producing the observed Pioneer acceleration. By using our model, we explain the numerical coincidence between the value of the anomalous acceleration and the Hubble constant at the present epoch and also confirm our previous determination of the cosmological parameters gamma ~ 10^(-28) cm^(-1) and delta ~ 10^(-4) - 10^(-5). New Pioneer data are expected to be publicly available in the near future, which might enable more precise evaluations of these parameters.Comment: 24 pages, including 3 figure

Kerr Metric, Geodesic Motion, and Flyby Anomaly in Fourth-Order Conformal Gravity

In this paper we analyze the Kerr geometry in the context of Conformal Gravity, an alternative theory of gravitation, which is a direct extension of General Relativity. Following previous studies in the literature, we introduce an explicit expression of the Kerr metric in Conformal Gravity, which naturally reduces to the standard General Relativity Kerr geometry in the absence of Conformal Gravity effects. As in the standard case, we show that the Hamilton-Jacobi equation governing geodesic motion in a space-time based on this geometry is indeed separable and that a fourth constant of motion-similar to Carter's constant-can also be introduced in Conformal Gravity. Consequently, we derive the fundamental equations of geodesic motion and show that the problem of solving these equations can be reduced to one of quadratures. In particular, we study the resulting time-like geodesics in Conformal Gravity Kerr geometry by numerically integrating the equations of motion for Earth flyby trajectories of spacecraft. We then compare our results with the existing data of the Flyby Anomaly in order to ascertain whether Conformal Gravity corrections are possibly the origin of this gravitational anomaly. Although Conformal Gravity slightly affects the trajectories of geodesic motion around a rotating spherical object, we show that these corrections are minimal and are not expected to be the origin of the Flyby Anomaly, unless conformal parameters are drastically different from current estimates. Therefore, our results confirm previous analyses, showing that modifications due to Conformal Gravity are not likely to be detected at the Solar System level, but might affect gravity at the galactic or cosmological scale.Comment: Revised version: improved notation, added references, comments, and one equation. 31 pages, including 2 figures. Accepted for publication in General Relativity and Gravitatio

Applications of Fractional Calculus to Newtonian Mechanics

We investigate some basic applications of Fractional Calculus (FC) to Newtonian mechanics. After a brief review of FC, we consider a possible generalization of Newton's second law of motion and apply it to the case of a body subject to a constant force. In our second application of FC to Newtonian gravity, we consider a generalized fractional gravitational potential and derive the related circular orbital velocities. This analysis might be used as a tool to model galactic rotation curves, in view of the dark matter problem. Both applications have a pedagogical value in connecting fractional calculus to standard mechanics and can be used as a starting point for a more advanced treatment of fractional mechanics.Comment: 14 pages, including 3 figure

Conformal Gravity and the Alcubierre Warp Drive Metric

We present an analysis of the classic Alcubierre metric based on conformal gravity, rather than standard general relativity. The main characteristics of the resulting warp drive remain the same as in the original study by Alcubierre, namely that effective super-luminal motion is a viable outcome of the metric. We show that for particular choices of the shaping function, the Alcubierre metric in the context of conformal gravity does not violate the weak energy condition, as was the case of the original solution. In particular, the resulting warp drive does not require the use of exotic matter. Therefore, if conformal gravity is a correct extension of general relativity, super-luminal motion via an Alcubierre metric might be a realistic solution, thus allowing faster-than-light interstellar travel.Comment: 24 pages, including 6 figure