Rotation Curve Fitting Model

One key piece of evidence for dark matter is the flat rotation curve problem: the disagreement between measured galactic rotation curves and their luminous mass. A novel solution to this problem is presented here. A model of relativistic frame effects on Doppler shifts due to the slightly curved frames of an emitting galaxy and the Milky Way is derived. This model predicts observed Doppler shifted spectra (in excess of the luminous mass) based only on the observed luminous matter profile and one free model parameter. Fits to the 175 galaxies reported in the SPARC database of galactic rotation profiles and accurate photometry measurements are compared between this novel model and dark matter and MOND (RAR) models. We find on the SPARC sample of 175 galaxies; that MOND-RAR has an average reduced chisquare of $\chi^2_r = 4.22$ for 175 galaxies fitted, the isothermal dark matter model has $\chi^2_r = 1.90$ for 165 galaxies fitted, and the new model we present has $\chi^2_r = 2.39$ for 172 galaxies fitted. Implications of this model are discussed.Comment: 27 pages, 9 figure

Diminishing benefits of urban living for children and adolescents’ growth and development

Optimal growth and development in childhood and adolescence is crucial for lifelong health and well-being1–6. Here we used data from 2,325 population-based studies, with measurements of height and weight from 71 million participants, to report the height and body-mass index (BMI) of children and adolescents aged 5–19 years on the basis of rural and urban place of residence in 200 countries and territories from 1990 to 2020. In 1990, children and adolescents residing in cities were taller than their rural counterparts in all but a few high-income countries. By 2020, the urban height advantage became smaller in most countries, and in many high-income western countries it reversed into a small urban-based disadvantage. The exception was for boys in most countries in sub-Saharan Africa and in some countries in Oceania, south Asia and the region of central Asia, Middle East and north Africa. In these countries, successive cohorts of boys from rural places either did not gain height or possibly became shorter, and hence fell further behind their urban peers. The difference between the age-standardized mean BMI of children in urban and rural areas was <1.1 kg m–2 in the vast majority of countries. Within this small range, BMI increased slightly more in cities than in rural areas, except in south Asia, sub-Saharan Africa and some countries in central and eastern Europe. Our results show that in much of the world, the growth and developmental advantages of living in cities have diminished in the twenty-first century, whereas in much of sub-Saharan Africa they have amplified