Skip to main content

#FaveAstroPlot : Binary pulsars and general relativity

Another interesting astronomical plot is one that ended up providing an indirect evidence of a prediction of general relativity, gravitational waves. General relativity, proposed by Albert Einstein, predicts that gravitational masses can radiate energy in the form of gravitational waves but in reality, these waves are so weak (because gravity itself is weakly interacting) that it is hard to detect them directly. There are experiments to detect them directly (eg : LIGO and LISA) and indirectly (Pulsar Timing Array) but it was indirectly proved by Hulse & Taylor in 1974 when they discovered a double pulsar PSR 1913+16. This peculiar double pulsar had the interesting property that it's period was decaying, instead of remaining constant. As you can see from this plot on twitter, the horizontal line is what is expected if we assume that there is zero orbital decay and the data points are observed time periods over the course of a couple of decades. What's happening behind the scenes is that the pulsars are losing energy in the form of outgoing gravitational waves and because their overall energy is decreasing, their orbital periods decrease.

There are another interesting predictions of general relativity that also has observational evidence but I haven't come across any tweet mentioning it. It's that light can be bent by gravity. This stems from the fact that spacetime itself is curved and the curvature of spacetime depends on the mass of the object in it's vicinity. What we perceive as curved lines are infact straight lines from the point of view of the photon (light ray) but explaining that gets a bit involved and needs a bit of general relativity so I shall not go there this time. Observationally, this was first proved during a solar eclipse when an astronomer showed that our Sun bends the light of stars visibly behind it by a small but not insignificant amount (more about which you can read here and here).

Personally, I don't like theory as much as experimental or simulation work but a course on general relativity was enlightening and it gave me pretty interesting insight into cosmology. So, if you're a student and if there's a course on general relativity being offered in your college, you should take it!

Popular posts from this blog

Animation using GNUPlot

Animation using GNUPlotI've been trying to create an animation depicting a quasar spectrum moving across the 5 SDSS pass bands with respect to redshift. It is important to visualise what emission lines are moving in and out of bands to be able to understand the color-redshift plots and the changes in it.
I've tried doing this using the animate function in matplotlib, python but i wasn't able to make it work - meaning i worked on it for a couple of days and then i gave up, not having found solutions for my problems on the internet.
And then i came across this site, where the gunn-peterson trough and the lyman alpha forest have been depicted - in a beautiful manner. And this got me interested in using js and d3 to do the animations and make it dynamic - using sliders etc.
In the meanwhile, i thought i'd look up and see if there was a way to create animations in gnuplot and whoopdedoo, what do i find but nirvana!

In the image, you see 5 static curves and one dynam…

Pandas download statistics, PyPI and Google BigQuery - Daily downloads and downloads by latest version

Inspired by this blog post : https://langui.sh/2016/12/09/data-driven-decisions/, I wanted to play around with Google BigQuery myself. And the blog post is pretty awesome because it has sample queries. I mix and matched the examples mentioned on the blog post, intent on answering two questions - 
1. How many people download the Pandas library on a daily basis? Actually, if you think about it, it's more of a question of how many times was the pandas library downloaded in a single day, because the same person could've downloaded multiple times. Or a bot could've.
This was just a fun first query/question.
2. What is the adoption rate of different versions of the Pandas library? You might have come across similar graphs which show the adoption rate of various versions of Windows.
Answering this question is actually important because the developers should have an idea of what the most popular versions are, see whether or not users are adopting new features/changes they provide…

Adaptive step size Runge-Kutta method

I am still trying to implement an adaptive step size RK routine. So far, I've been able to implement the step-halving method but not the RK-Fehlberg. I am not able to figure out how to increase the step size after reducing it initially.

To give some background on the topic, Runge-Kutta methods are used to solve ordinary differential equations, of any order. For example, in a first order differential equation, it uses the derivative of the function to predict what the function value at the next step should be. Euler's method is a rudimentary implementation of RK. Adaptive step size RK is changing the step size depending on how fastly or slowly the function is changing. If a function is rapidly rising or falling, it is in a region that we should sample carefully and therefore, we reduce the step size and if the rate of change of the function is small, we can increase the step size. I've been able to implement a way to reduce the step size depending on the rate of change of …