The comfortable roller coaster -- on the shape of tracks with constant normal force

A particle that moves along a smooth track in a vertical plane is influenced by two forces: gravity and normal force. The force experienced by roller coaster riders is the normal force, so a natural question to ask is: what shape of the track gives a normal force of constant magnitude? Here we solve this problem. It turns out that the solution is related to the Kepler problem; the trajectories in velocity space are conic sections.Comment: 10 pages, 4 figure

Associations between lamb survival and prion protein genotype: analysis of data for ten sheep breeds in Great Britain

BACKGROUND: Selective breeding programmes, based on prion protein (PrP) genotype, have been introduced throughout the European Union to reduce the risk of sheep transmissible spongiform encephalopathies (TSEs). These programmes could have negative consequences on other important traits, such as fitness and production traits, if the PrP gene has pleiotropic effects or is in linkage disequilibrium with genes affecting these traits. This paper presents the results of an investigation into associations between lamb survival and PrP genotype in ten mainstream sheep breeds in Great Britain (GB). In addition, the reasons for lamb deaths were examined in order to identify any associations between these and PrP genotype. RESULTS: Survival times from birth to weaning were analysed for over 38000 lambs (2427 dead and 36096 live lambs) from 128 flocks using Cox proportional hazard models for each breed, including additive animal genetic effects. No significant associations between PrP genotype and lamb survival were identified, except in the Charollais breed for which there was a higher risk of mortality in lambs of the ARR/VRQ genotype compared with those of the ARR/ARR genotype. Significant effects of birth weight, litter size, sex, age of dam and year of birth on survival were also identified. For all breeds the reasons for death changed significantly with age; however, no significant associations between reason for death and PrP genotype were found for any of the breeds. CONCLUSION: This study found no evidence to suggest that a selective breeding programme based on PrP genotype will have a detrimental effect on lamb survival. The only significant effect of PrP genotype identified was likely to be of little consequence because an increased risk of mortality was associated with a genotype that is selected against in current breeding strategies

K2 Optical Emission from OJ 287 and Other Gamma-Ray Blazars on Hours-to-Weeks Timescales from 2014-2018

We present second observations by K2 of OJ~287 and 7 other $\gamma$-ray AGNs obtained in 2017-2018, second and third observations of the lobe-dominated, steep spectrum quasar 3C~207, and observations of 9 additional blazars not previously observed with K2. The AGN were observed simultaneously with K2 and the Fermi Large Area Telescope for 51-81 days. Our full sample, observed in 2014-2018, contained 16 BL Lac objects (BL Lacs), 9 Flat Spectrum Radio Quasars (FSRQs), and 4 other $\gamma$-ray AGNs. Twelve BL Lacs and 7 FSRQs exhibited fast, jagged light curves while 4 BL Lacs and 2 FSRQs had slow, smooth light curves. Some objects changed their red-noise character significantly between repeated K2 observations. The optical characteristics of OJ~287 derived from the short-cadence K2 light curves changed between observations made before and after the predicted passage of the suspected secondary supermassive black hole through the accretion disk of the primary supermassive black hole. The average slopes of the periodogram power spectral densities of the BL Lacs' and FSRQs' light curves differed significantly, by $\approx 12$\%, with the BL Lac slopes being steeper, and a KS test with a $p$-value of 0.039 indicates that these samples probably come from different populations; however, this result is not as strongly supported by PSRESP analyses. Differences in the origin of the jets from the ergosphere or accretion disk in these two classes could produce such a disparity, as could different sizes or locations of emission regions within the jets.Comment: 35 pages, 8 figures. Accepted for publication in the Astrophysical Journa

The Evolution of Volatile Production in Comet C-2009 P1(Garradd) During its 2011-2012 Apparition

We report observations at millimeter and submillimeter wavelengths of comet C/2009 P1 (Garradd) from 2011 December 28 to 2012 April 24, using the Arizona Radio Observatory submillimeter telescope (SMT) and the James Clerk Maxwell Telescope (JCMT). Garradd is a dynamically young long-period comet from the Oort Cloud, with a periodicity of 127,000 years, that reached perihelion on 2011 December 23 (at Heliocentric distance (Rh) = 1.55 Astronomical Units and delta = 20.1 Astronomical Units ) and made its closest approach to the Earth on 2012 March 05 (at Heliocentric distance (Rh) = 1.84 Astronomical Units and delta = 1.26 Astronomical Units). We obtained gas production rates, and molecular abundances relative to water for HCN, ortho-H2CO, CS, CO and CH3OH. A rotational temperature, T (sub rot) approximately equal to 50 degrees Kelvin, was determined by observing multiple methanol lines with the JCMT. By averaging the abundance ratio relative to water from the SMT and the JCMT we derive: CO: 7.03 plus or minus 1.84 percent, HCN: 0.04 plus or minus 0.01 percent, ortho H2CO: 0.14 plus or minus 0.03 percent as a parent molecule (and 0.28 plus or minus 0.06 percent as an extended source), CS: 0.03 plus or minus 0.01 percent and CH3OH: 3.11 for a range from plus 1:86 to minus 0.51 percent. We concluded that Garradd is normal in CH3OH, depleted in HCN, ortho-H2CO and CS and slightly enriched in CO with respect to typically observed cometary mixing ratios. We also studied the temporal evolution of HCN and CO and find that the production of HCN has a trend similar to water (but with short-term variation), with a decrease after perihelion, while that of CO shows contrary behavior: remaining constant or increasing after perihelion

Measuring Mars Atmospheric Winds from Orbit

Wind is the process that connects Mars’ climate system. Measurements of Mars atmospheric winds from orbit would dramatically advance our understanding of Mars and help prepare for human exploration. Multiple instruments in development will be ready for flight in the next decade. We urge the Decadal Survey to make these measurements a priority