Free Astronomy Magazine May-June 2021

33 MAY-JUNE 2021 ASTRO PUBLISHING seconds; total exposure of 3,600 sec- onds (1 hour). After enjoying the jet as seen in these images, we asked ourselves: “What if we used them to measure the size of the jet? Would we get measurements similar to the ac- cepted ones?” Taking as known the distance to M87 (53 million light-years) and by being able to calculate the apparent size of the jet in arcseconds from our exposures, we calculated the jet size by applying basic trigonometry. We know that, using the tangent formula, we can relate the angle and the two catheti, which is just what we needed in our case: Because the angle is so small, the tangent can be approximated as the angle itself: And by transforming the angle from radians to arcseconds we get: With D known − 5×10 23 m (53 mil- lion light-years converted into me- ters) − we simply had to calculate how many arcseconds the jet occu- pies in the sky. To do this, we first needed to know the resolution of our camera/tele- scope set, which is given by the fol- lowing formula: In our case: Now we just had to measure how many pixels the jet occupied in our image, from the center of the gal- axy to the edge of the jet, using the “Slice” tool of the IRIS program. This gave us 16 ± 1 pixels. By multiplying our R by 16, we get about 17.8 arcseconds, which we then substitute in the formula dis- cussed above to get d : which is: Even taking 3 ± 1 pixels for the width of the jet: we get the value: The accepted value for the jet is about 5,000 light-years, or about 20 arcseconds, placing our calculation within reasonable margins. Conclusions Jets are structures that exhibit very interesting properties and exist in amazing conditions due to their ex- treme nature and properties. Knowing more about them yields a greater understanding about quasars, radio galaxies, active galax- ies and black holes. In the case of the M87 jet, whose spatial dimen- sions we have studied, we believe we have obtained results compara- ble with official data using far more modest equipment. Our calculations show a plasma jet length of approximately 4,542 light-years, compared to the approximately 5,000 light-years calcu- lated by observatories with greater resolving power or located out- side of the Earth’s at- mosphere. Similarly, we obtained the value of 855.6 light-years for the width of the jet, 4,542 ± 285 light-years (1,392.6 ± 87.4 pcs) of length. 855.6 ± 285 light-years (262.3 ± 87.4 pcs) wide. arcseconds R (arcseconds per pixel) 206 × size of the pixel ( µ ) focal length (mm) . . .