The Astronomy Learner

Scaling Relations In astronomy, indeed in science, there is a dizzying array of constants, equations, and units that all need to be kept straight if we want physics to work. While it is good to know Kepler's 3rd Law for a planetary system, \[ P^2 = \frac{4 \pi^2 a^3}{G\,M_\star} \] we can also use Kepler's original form, which was a scaling relationship, \[ P^2 \sim a^3 .\] The scaling form of Kepler's law works because it is specifically for the solar system in solar system units. It says that for a planet orbiting the sun we know that \(P^2\) scales with \(a^3\). Scaling must always be done with respect to something we know or by using ratios we know. e.g. If we know two objects have some intrinsic size ratio (say two hard spheres), we can determine their relative distance by checking their observed sizes. Notice that in the scaling version of Kepler's 3rd law the various physical/mathematical constants are no longer present. Both sides of the equation are dim...

Astrobites is an astro-ph digest developed by Harvard graduates students which now has an international author roll. What is astrobites ? In their own words, Astrobites is a daily astrophysical literature journal written by graduate students in astronomy. Our goal is to present one interesting paper per day in a brief format that is accessible to undergraduate students in the physical sciences who are interested in active research. Essentially, Astrobites takes new research in astronomy and astrophysics and digests it into something approachable. With posts written by graduate students from around the globe, it provides an excellent introduction to technical writing that is understandable for the lay person, yet still scientifically interesting to the expert. Check out some of the posts by the following authors: John Johnson Ben Cook Ben Montet Elisabeth Newton (co-founder) Chris Feasi (co-founder)