Fabio Falchi

I describe a simple method to calculate Earth dimensions using only local measurements and observations. I used modern technology (a digital photo camera and Google Earth) but the exact same method can be used without any aid, with naked eye observations and distances measured by walking, and so it was perfectly accessible to Ancient Greek science.

Read more at https://arxiv.org/abs/2007.02111

# Category Archives: ASTRONOMY

# Pi from the sky

**A null test of general relativity from a population of gravitational wave observations**

**Carl-Johan Haster**

Our understanding of observed Gravitational Waves (GWs) comes from matching data to known signal models describing General Relativity (GR). These models, expressed in the post-Newtonian formalism, contain the mathematical constant π. Allowing π to vary thus enables a strong, universal and generalisable null test of GR. From a population of 22 GW observations, we make an astrophysical measurement of π=3.115^{+0.048}_{−0.088}, and prefer GR as the correct theory of gravity with a Bayes factor of 321. We find the variable π test robust against simulated beyond-GR effects.

Read more at https://arxiv.org/abs/2005.05472

# Profiles of James Peebles, Michel Mayor, and Didier Queloz: 2019 Nobel Laureates in Physics

**Neta Bahcall, Adam Burrows**

Published in PNAS, 117, 2, 799 – 801 (January 2020)

Mankind has long been fascinated by the mysteries of our Universe: How old and how big is the

Universe? How did the Universe begin and how is it evolving? What is the composition of the

Universe and the nature of its dark-matter and dark-energy? What is our Earth’s place in the cosmos

and are there other planets (and life) around other stars?

The 2019 Nobel Prize in Physics honors three pioneering scientists for their fundamental contributions to basic cosmic questions – Professor James Peebles (Princeton University), Michel Mayor (University of Geneva), and Didier Queloz (University of Geneva and the University of Cambridge) – “for contributions to our understanding of the evolution of the universe and Earth’s place in the cosmos,” with one half to James Peebles “for theoretical discoveries in physical cosmology,” and the other half jointly to Michel Mayor and Didier Queloz “for the discovery of an exoplanet orbiting a solar-type star.” We summarize the historical and scientific backdrop to this year’s Physics Nobel.

Read more at https://arxiv.org/ftp/arxiv/papers/2001/2001.08511.pdf

# The “Terrascope”

**On the Possibility of Using the Earth as an Atmospheric Lens**

**David Kipping**

Distant starlight passing through the Earth’s atmosphere is refracted by an angle of just over one degree near the surface. This focuses light onto a focal line starting at an inner (and chromatic)boundary out to infinity – offering an opportunity for pronounced lensing. It is shown here that the focal line commences at ∼85% of the Earth-Moon separation, and thus placing an orbiting detector between here and one Hill radius could exploit this refractive lens. Analytic estimates are derived for a source directly behind the Earth (i.e. on-axis) showing that starlight is lensed into a thin circular ring of thickness W H∆/R, yielding an amplification of 8H∆/W, where H∆ is the Earth’s refractive scale height, R is its geopotential radius and W is the detector diameter. These estimates are verified through numerical ray-tracing experiments from optical to 30 µm light with standard atmospheric models. The numerical experiments are extended to include extinction from both a clear atmosphere and one with clouds. It is found that a detector at one Hill radius is least affected by extinction since lensed rays travel no deeper than 13.7 km, within the statosphere and above most clouds. Including extinction, a 1 metre Hill radius “terrascope” is calculated to produce an amplification of ∼45, 000 for a lensing timescale of ∼20 hours. In practice, the amplification is likely halved in order to avoid daylight scattering i.e. 22, 500 (∆mag=10.9) for W =1 m, or equivalent to a 150 m optical/infrared telescope.

Read more at https://arxiv.org/pdf/1908.00490.pdf

**Using Earth to See Across the Universe: The Terrascope with Dr. David Kipping:**

Read also: “**The Terrascope – Using Earth As A Lens**“

# Estimating the Moon to Earth radius ratio with a smartphone, a telescope and an eclipse

**Hugo Caerols, Felipe A. Asenjo**

On January 20th, 2019, a total lunar eclipse was possible to be observed in Santiago, Chile. Using a smartphone attached to a telescope, photographs of the phenomenon were taken. With Earth’s shadow on those images, and using textbook geometry, a simple open-source software and analytical procedures, we were allowed to calculate the ratio between the radii of the Moon and the Earth. The results are in very good agreement with the correct value for such ratio. This shows the strength of the smartphone technology to get powerful astronomical results in a very simple way and in a very short amount of time.

Read more at https://arxiv.org/pdf/1907.08339.pdf

# Weighing the Sun with five photographs

**Hugo Caerols, Felipe A. Asenjo**

With only five photographs of the Sun at different dates we show that the mass of Sun can be calculated by using a telescope, a camera, and the third Kepler’s law. With the photographs we are able to calculate the distance from Sun to Earth at different dates along four months. These distances allow us to obtain the correct elliptical orbit of Earth, proving the first Kepler’s law. The analysis of the data extracted from photographs is performed by using an analitical optimization approach that allow us to find the parameters of the elliptical orbit. Also, it is shown that the five data points fit an ellipse using an geometrical scheme. The obtained parameters are in very good agreement with the ones for Earth’s orbit, allowing us to foresee the future positions of Earth along its trajectory. The parameters for the orbit are used to calculate the Sun’s mass by applying the third Kepler’s law. This method gives a result wich is in excellent agreement with the correct value for the Sun’s mass. Thus, in a span of time of four months, any student is capable to calculate the mass of the sun with only five photographs, a telescope and a camera.

Read more https://arxiv.org/pdf/1906.12272.pdf

# Exploring Gravitational Lensing

**Tilman Sauer, Tobias Schütz**

In this article, we discuss the idea of gravitational lensing, from a systematic, historical and didactic point of view. We show how the basic lensing equation together with the concepts of geometrical optics opens a space of implications that can be explored along different dimensions. We argue that Einstein explored the idea along different pathways in this space of implication, and that these explorations are documented by different calculational manuscripts. The conceptualization of the idea of gravitational lensing as a space of exploration also shows the feasibility of discussing the idea in the classroom using some of Einstein’s manuscripts.

Read more https://arxiv.org/pdf/1905.07174.pdf

# THAT Black Hole picture

Mike Merrifield, Omar Almaini and Meghan Gray react to the much-anticipated black hole photo from the Event Horizon Telescope Collaboration.