Some joyful astro images with comet Lovejoy

I couldn’t help making a pun with the word Lovejoy (nice name by the way , could have added that Lovejoy has lovely colors too)… Anyway , this is another astronomy related event happening in 2015 : comet Lovejoy , officially named C/2014 Q2 (other Lovejoy comets were discovered earlier) , makes its nearest approach to planet Earth in January 2015 and is visible crossing the night sky.

First , here are four images of the orbit diagram of the comet in the solar system. The images are taken from the JPL Small-Body Database Browser. It is the same image zoomed in four times.

.lovejoy comet zoomed in

 

Second , we have the path of comet Lovejoy and its position in relation to the constellations , viewed from three cities. Two cities are located in the Northern Hemisphere (Paris and Alexandria) , and one city in the Southern Hemisphere (Rio de Janeiro).The dates ( all in January 2015) and the info related to the views are given at the bottom of each image.Images were made with RedShift and some Photoshop.

Lovejoy comet viewed from 3 cities

And the third set of three images gives the orbit and position of the comet in the solar system during three different dates (July 2014 , January 2015 and February 2016).

comet Lovejoy 3 dates

Lovejoy C/2014 Q2 has a solid icy nucleus with a width of 2 or 3 miles.The coma or cloud surrounding the frozen solid nucleus at the head of the comet is made of gas and dust . Comets have two tails , a dust tail and an ion or plasma tail , always pointing away from the Sun.The tail reaches its greatest extent at about the closest approach to the Sun . The design and the physics of the plasma tail are related to the interaction between the cometary plasma and the solar wind. The Lovejoy comet is not making too much dust and has a more developed ion gas tail.The blue color of the ion tail is explained by the presence of Carbon monoxide ions. Diatomic Carbon molecules fluorescing by solar ultraviolet radiation and the chemical compound cyanogen are mainly responsible  for the observed or apparent green color of the comet.
Comet Lovejoy has a highly elliptical orbit like all comets ; it has a  long orbital period (comets with long periods come from the Oort cloud) and has passed through the solar system about  11500 years ago. The comet’s orbit is a little changed due to gravitational perturbations by the planets , and it will not return into the solar system for about 8000 years.

2015 the year , the number , and some of their characteristics

The year 2015 has begun (wish it will be a happy year for everybody) and here are some properties of the corresponding number (worked out with the help of Mathematica).

First , a list of the representations of 2015  in various number base notations:

2015 base notation

2015 in roman numerals: MMXV;

2015 can be represented as:

2015=2^{11}-33

2015=\frac {92^4 - 1} {35553}

2015-relation-1 2015-relation-2

Here is a big one (obtained with Mathematica by solving x^3 + x^2 + x = 2015 ):

2015-relation-3

2015=5 x 13 x 31

2015-trig-1

The last relation above can be  derived from the trigonometric equation:

2015-trig-2

I have mentioned these types of trigonometric relations in a previous post.

The number of prime numbers up to 2015 is 305 , the last  prime number before 2015 is 2011 ,  and the prime number which comes after 2015 is 2017.

The last Mersenne prime number before 2015 is:
127=2^{7}-1

The Mersenne prime number which comes after 2015 is:
8191=2^{13}-1

The last Sophie Germain prime (n is a Sophie Germain prime if 2n + 1 is also prime) before 2015 is 2003 , and the Sophie Germain prime which comes after 2015 is 2039.

The Riemann prime counting function is given by:

Riemann prime counting function

where li(x) is the logarithmic integral and  μ(n) is the Möbius function.

And below is a graph showing the natural distribution and the number  of prime numbers π(n) less than or equal to n (blue colored curve , here n=2015) along with the distribution of primes given by the Riemann counting function (orange colored curve) up to 2015 :

 prime-riemannr

 

Moving to other fields of science , I will mention briefly a few events taking place in the year 2015:

In the field of space exploration , the New Horizons spacecraft will get closest to the dwarf planet Pluto in July 2015.

In the following image (made with the help of Starry Night and Photoshop) the longer red arrow near the name of a planet indicates the direction towards the place where the planet is located on its orbit.

Pluto and New Horizons

The Dawn spacecraft will arrive at the dwarf planet Ceres between Mars and Jupiter in March 2015.

Concerning astronomy and sky events , there will be a solar eclipse in March 20 , a lunar eclipse in April 4 , a partial solar eclipse in September 13 , and a lunar eclipse in September 28.

And that is it for now.