Maths/Physics tattoo

Is it sad that instantaneously knew this was the Maclaurin series for sine?


Note! the if you follow the link the guy says it's a Taylor series but its a Taylor series where that starting point is zero so it's a Maclaurin series

Economical Numbers

"There are 10^11 stars in the galaxy. That used to be a huge number. But it's only a hundred billion. It's less than the national deficit! We used to call them astronomical numbers. Now we should call them economical numbers."- Richard Feynman

Determining a central mass from observations of its satellites

This is based on an experiment Ben and I did in our first year at Keele. Its was a good experiment that produced some surprisingly accurate results.

Kepler's Third Law states

The plan of the experiment is to fill in each of the variables(Period P and Radius a).

First things first is you need to acquire images of the thing you wish to determine the mass of, about 10 spaced over an adequate timescale (would depend on system observed). In the case of the experiment Ben and I conducted we had 7 images of Uranus over a period of 240 days.

Next Use a program that allows you to "blink" between images (we used SAOImage) and Find the bodies which are moving in the images. This can be quite difficult as the central body is most likely moving also relative to the background, this is why it is good to have a couple of images closer together. As there will be only a small change in the background-the moon should change position in a much smaller period. Once the satellites have been identified mark their positions on each image.

Then using the imaging program find the (central) x,y co-ordinates for each body and the central mass in each image. The relative positions of the satellites from the central body. Using these values its just a case of using the Pythagorean theorem (a^2 + b^2 = c^2) to calculate the radius of the orbit in pixels. Convert the radius into Kilometers.

Going back to the relative positions and using an ATAN2 function to convert the x,y co-ordinates into a relative angle to the central mass. Then using n Pi (where n is an integer value) to adjust so an angle against time is a straight line graph - this is needed due to definition of the ATAN2 function . The gradient of such a graph is the angular frequency ω of orbit. From the angular frequency ω we can find the period P of the orbit using the relation below.

Once the period is known it is just a case of rearranging Kepler's third law for Mass M and you have the mass of the central body

New Radio Space Telescope in Orbit

The Construction of RadioAstron in Russia

The Russian Federal space agency has launched a new radio space telescope, RadioAstron, which will combine signals with ground-based telescopes to provide "incredibly high resolution - as if taken by a telescope with a dish as wide as the maximum distance between the antennas - from the Earth to the Moon".

The launch of the telescope on a Zenith-3M Rocket

It is expected to be operational in a few months, and will aim to confirm the existence of a black hole in one of our neighbouring galaxies and hopefully obtain "detailed data about pulsars, interstellar plasma and neutron stars in the Milky Way"

Click on the linked title for more info.

The Hubble Space Telescope and Beyond

In 1990 the space shuttle Discovery carried the Hubble Space Telescope (HST) into orbit and 21-years later (after many upgrades and rescue missions by Shuttle crews), it is set to provide us with awe-inspiring images and valuable data until at least 2014. Only time will tell what Hubble’s successor, the James Webb Space Telescope (JWST) due to launch in 2018, will reveal about the mysteries of the cosmos.

Hubble Space Telescope in Orbit

The HST has certainly played a major role in the world of astronomy and physics, with achievements in many different areas of these subjects. Successful missions include researching black holes at the centre of galaxies, observing the formation of planets around new stars, estimating the age of the Universe, detecting the first organic molecule in the atmosphere of a Jupiter-sized exo-planet and providing evidence for the existence of dark energy. I thought I would write a little more about the age of the Universe since this is an area of particular interest to me.

In the early 20^th century, Edwin Hubble discovered the expansion of the Universe and also a relationship between the distance d of an object and the velocity v in which it is receding; v=H₀d, where H₀ is the Hubble Constant. A value for this Hubble Constant can therefore be determined by accurately measuring the velocity and distance of an object such as a galaxy; the Hubble Constant is simply related to the age (Age=1/H₀).

The recessional velocity could be accurately measured using the red-shift of the light that it emits (the Doppler Effect on a cosmological scale), however the distance proved a little trickier to find. Certain stars, called Cephieds, pulsate and this pulsation is related to the absolute magnitude of the star which can be used to find the distance. The inaccuracy occurred due to ground-based telescopes not being able to “see” faint enough. Using the ground-based telescopes the age of the Universe was estimated at 7-20 billion years old. There is a lot of uncertainty in these results!

With the launch of HST, the Cepheids could now be observed much more accurately, free from atmospheric effects and light pollution. With this data the Hubble Constant was found to be 71 km s^-1 Mpc^-1 with a 10% uncertainty¹, which corresponds to an age of 9 to 14 billion years, which is much more accurate than previous results. With the use of other experiments this was pin-pointed to 13.7 billion years¹.

The HST has also played another important role, and that is in bringing the world of science to the general public, and seeing images from the HST is partly what first sparked my interest in science. I saw beautiful images of galaxies and nebulae and formations of interstellar gas and dust, such as the Pillars of Creation, and I immediately wanted to know what they were, where they came from and how they fit into the grander scale of the Universe.

Pillars of Creation- Image by HST

With the construction of the James Webb Space Telescope, things can only get better. The JWST will see further into the infra-red and hence will see further than Hubble (light from further objects is more red-shifted). The JWST also boasts a larger mirror, allowing it to collect more light and peer ever deeper into space. One disadvantage that I can see to JWST is that its orbit will be much further away from the Earth, it is in fact not going to orbit the earth at all, but the Sun! It orbits the Sun at the same rate as the Earth and so is stationary relative to us on Earth. Due to the immense distance astronauts will not be able repair or modify the JWST, as was possible with Hubble. The future however looks bright.

The orbits of HST and JWST

For more information on Hubble visit, www.nasa.gov/hubble

For more information on JWST visit, www.jwst.nasa.gov

1-Images and values from nasa.gov

New author

My friend Ben is going to start posting on here as well as me

What makes a good teacher/lecturer?

(In this when I refer to teachers I mean teachers and lecturers by the way)

This is something I've often wondered about being in my 13th or so year in education I've had fair few of them. Some I have thoroughly enjoyed being thought by, some I've not so much enjoyed but the where good none the less. However some have been appalling. Teaching isn't just knowing the subject! It's about bringing it to life, or at least showing how it relates to it so I can see how it's useful to know.

For instance in high school I HATED maths now I'm going out of my way to learn it! I guess it just depends on the teacher.

I'm not sure about that comment though because I've had teachers that have been fantastic teaching one subject then teaching another was woeful. So is it having the right teacher for the right subject? Or is it that I didn't like the subject so was unwilling to learn?

Anyway back to the main point. Does a teacher have to enjoy the subject there teaching? I've noticed that when a teacher is teaching subjects closer to there interests they are much better! Having said that though I've had fantastic teachers when teaching something so far away from there subject of interest as to be in a completely different universe.

Let me know what you guys think makes a good teacher/lecturer!

How about to day we have a ring galaxy?

Getting to mars

I heard the quote "Today's kids will not fly on the shuttle but they will walk on Mars" - Admin. Bolden

This got me thinking what are the problems facing a mission to Mars?

How long is a journey to mars? After some searching I found the value of 9 months just to get there, oh and the opportunity only comes around every 26 months! (source)

My next point of inquiry how long are astronauts on the ISS ? I found that it is about 6 months which is only a third of the time it takes just to get there and back!

So what are the heath risks of being in space? for this NASA where quite help full (source 1 ,source 2 )

Some of the most well known risks are muscle atrophy and spaceflight osteopenia (or bone-loss to you and me) these are both coursed by the micro-gravity in space! So we could use artificial gravity be a solution? Yes and it's easy enough to mimic gravity, use a centrifuge! However NASA says it's to expensive/complex to spin the entire space craft and suggest a bike in a loop- it would be a human powered centrifuge. This would also mean that the astronauts would be exercising too which is reported to help with these problems.

However in the experienced force would not be distributed evenly through the body which could make for interesting results.

Then there is the very serous problem of radiation! The main counter measure at the moment is limiting the time exposed not really much use for the trip to mars. Also inboard the ISS two thirds of the radiation is blocked by body of earth and it's magnetic field. In the Apollo missions the astronauts received three times the dose of astronauts on the ISS. But baring some devloping cataracts they where healthy. However for much longer trip to mars the radiation exposure is going to be much higher!

So what can be done about the radiation? according the NASA source above Hydrogen is the best element at absorbing high energy radiation! Hydrogen being a gas isn't much use as shield by it's self now is it! So finding a compound with high hydrogen content is the key to a good shield. Well my minor subject at uni is chemistry and I can tell you, as does the source, plastics such as polythene are very high in Hydrogen.

Problem sorted? Not quite as the structure of any spacecraft has to be strong and light, as well as providing adequate radiation shielding. At Marshall Space Flight Center they have developed a reinforced polyethylene that is 10 times stronger than the aluminum used in spacecraft today and it's lighter! Now all that needs to be done it to make it cheaply enough.

So it looks like NASA are well on there way to mars. However there still a lot more research to be done on the effects of micro-gravity and the radiation on the body, along with many other advisement that I haven't covered (you'd be here all day if I did) before any manned missions to mars can happen. I just hope that the US government give NASA the resources they need to meet there proposed target of today's children getting to mars and I hope I'm alive to see it!

Fireworks, Lightning and a Comet

Neptune fact file on it's first birthday

Named after the roman god of the sea.
Mass : 1.0243×10^26 kg
Orbital Period : 164.79 years
Discovered: 164.79 years ago (December 28, 1612) by Urbain Le Verrier bit of argument there though John Couch Adams claimed to have found it also!
Day: 15 hours, 57 minutes and 59 seconds (source)
Atmospheric components: 74% hydrogen, 25% helium, 1% methane
Number of moons: 13
Number of rings: 6
Looks like:

The people that inspire me to do physics Continued!

I thought I'd continue with adding more people who inspire me to do physics these two guys are actually connected as one inspired the other.

Neil deGrasse Tyson, I have seen him in documentaries, on youtube and I follow him on twitter. He has a great passion for astrophysics that you can't help to be caught up in.


The next guy is Carl Sagan! How can you not be inspired by him? I remember when a friend first showed me the pale blue dot video on youtube, it blew my mind!

How much would you pay for the universe?

Well I was going to write a post of the end of an era with the last shuttle fight of the Atlantis. But then I remembered this video I found a while ago and this says everything that needs to be said not that I'm American (as many of his points are based towards Americans and there pride as a nation) but it's still a sad day for space exploration none the less.

Sleeplessness and sticky notes

I have trouble sleeping! When I got to try to get to sleep my mind starts thinking about a million and one things. I just can't switch off! Anyway I read a tip somewhere to keep sticky notes by you bed when your trying to sleep, so you can jot down what your thinking of and drift off to sleep.

I thought it seemed reasonable enough. However when I get rid of one thought another one happily bounds in to replace it. So I end up with a load of sticky notes all over my wall and I still cant sleep!

Not only that, I shouldn't have got cheap ones they kept falling off my wall on to my head, or just generally making a noise which isn't something you want when your trying to sleep. Not only that my mind wont let me just forget about the idea after I've just written down, it wants to expand on it. Ironically this post is one of these ideas. So I was kept awake by thinking about how I'm going to write about being kept awake by the things that are supposed to be helping me to get to sleep.

Lies, damned lies and statistics

Interesting ted talk on making the optimum ted talk :)