February 2023 M T W T F S S 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28
© Mark Biegert and Math Encounters, 2022. Publication of this material without express and written permission from this blog’s author and/or owner is strictly prohibited. Excerpts and links may be used, provided that full and clear credit is given to Mark Biegert and Math Encounters with appropriate and specific direction to the original content.
DisclaimerAll content provided on the mathscinotes.com blog is for informational purposes only. The owner of this blog makes no representations as to the accuracy or completeness of any information on this site or found by following any link on this site. The owner of mathscinotes.com will not be liable for any errors or omissions in this information nor for the availability of this information. The owner will not be liable for any losses, injuries, or damages from the display or use of this information.
Category Archives: Astronomy
I often see announcements of Near-Earth Objects (NEOs) in the scientific press. For asteroids, these announcements are usually accompanied by a size estimate of the asteroid. In this post, I will discuss a commonly used formula for the effective spherical diameter of an asteroid based on its normalized brightness (i.e. absolute magnitude). Continue reading
I have seen a number of articles in the popular scientific press about asteroid 1997 XF11 and the close approach it made to Earth back in June. The June approach was not that close – ~27 million kilometers. The closest approach is expected in 2028 and will be 980,000 km or 2.4 times the average Earth-Moon distance. Continue reading
I have always been interested in the fact that some planets have atmospheres and others do not. At the time of formation, planets have a primary atmosphere that consists largely of light elements (hydrogen and helium) – Earth has a secondary atmosphere formed outgassing from tectonic activity and comet impact residue. For small bodies, these low-molecular weight elements escape into space. I had never looked at how these gases escaped until I recently found a Wikipedia article about how gases escape from planetary atmospheres (e.g. Figure 1), and the math and physics involved were too enticing to pass up. Continue reading
I saw an article in the popular science press about a real rarity – an exoplanet that can be seen (Figure 1). I dug around the web and found the journal article on which most of the press articles were based. Given their measurement data, I wanted to see if I could duplicate some of their computed exoplanet characteristics. In this post, I will be using some of the techniques learned about while listening to The Search for Exoplanets: What Astronomers Know. Continue reading
Years ago, I read the book Parallax (Figure 1) and really enjoyed the tale of how 19th century astronomers measured the distance to the nearest stars. This measurement was critical to providing scientists some idea as to the scale of the universe.
The book Parallax describes how simple trigonometry, along with the introduction of large telescopes coupled to precision measurement gear, could be used to measure the angular parallax of a star as the Earth revolved around the Sun – a method called trigonometric or stellar parallax. During my recent perusing of the Wikipedia, I discovered that there was an alternative form of parallax measurement, called dynamical parallax, that allows one to estimate the distance to stars that are beyond the limits of trigonometric parallax. Continue reading
I was reading a Wikipedia article on the star Iota Apodis (Figure 1), which is a binary star, and noticed that three apparent visual magnitudes were listed for the two stars: 5.41 (5.90/6.46). The visual magnitudes listed represented the combined and individual brightness of the two components (in parentheses). I became curious as to how the magnitudes were summed. Continue reading
I have been interested in the possibility of their being habitable regions around stars that are smaller and dimmer than the Earth. I saw an article this week on a solar system about a star, Trappist-1, that is not much larger than Jupiter and that is quite cool for a star (2550K).
My plan here is to look at some measured data for Trappist-1 and see if I can derive some of the other parameters for this star and its system. I will use information available from the Wikipedia and the Open Exoplanet Catalog. Continue reading
I filter my news feed for anything related to astronomy, and I have been seeing a number of articles recently about large meteor explosions (called fireballs or bolides) in the atmosphere (example, example). These events are not occurring more frequently than before – we now have the technology to discover these explosions. The recent spate of bolide burst reports has caused me to become curious about how frequently these impacts are occurring. It turns out that NASA has an excellent set of web pages on this topic. There have been quite a few large meteor explosions, with the largest being the Chelyabinsk burst in 2013. As you can see in Figure 1, the cataloged meteor events are fairly even spread across the Earth. Continue reading
A reader mentioned to me that the Wikipedia has an good article on stellar luminosity versus stellar mass– the article is a good one. I thought I would compare the empirical relationship shown in the Wikipedia with a couple of different data sets that I found on the web. I was motivated to perform this analysis because: (1) I have been doing some reading on exoplanets, and luminosity is important when it comes to exoplanet temperature; and (2) I am presenting a seminar on Mathcad to our engineering staff, and this application provides me a nice demonstration on how to compute nonlinear piecewise functions. Continue reading