I continued testing Jared's understanding of the material we have covered until now. He has retained a lot of information! We covered the concept of the Big Bang, the evolution of stars, the classification of galaxies, and observational methods (how do we know what we know about the Universe). This was Jared's long lesson (one and a half hours), and we omitted to take a short break halfway through, yet he remained fully concentrated and engaged in our discussions. To finish off before Thanksgiving break, we started to watch a short documentary on special relativity, a subject Jared has shown an inordinate amount of interest in. I promised him that, in the future, from time to time, when he has worked really well and deserves a break, we would look at certain aspects of special relativity.
Assignment
A selection of calculations on special relativity
Session Minutes
90
Minutes Student Attended
90
Lesson Comments
As I mentioned in the Summary above, we completely forgot to take a five-minute break halfway through the long lesson, so as to stretch our legs, etc, yet Jared remained focused and concentrated. Instead of giving him a written test, which I was originally thinking of doing, I decided to quiz him orally - I don't think Jared knew he was being tested, as such, and I have to say he really knew his material. Sometimes he required a bit of prompting, but I think that had as much to do with self-confidence as anything else. Jared continues to show such interest in the topics we cover, and has even started talking about what he'd like to take in college (engineering-related subjects). I know we need to develop his writing skills, answering written tests. I'll work on that in the remaining weeks before the holidays.
I wanted to concentrate on Jared's understanding of the concept of the scientific method. All sciences, irrespective of discipline, rely on the scientific method to progress. Advances may be incremental, but ultimately they all contribute to the framework of scientific thought. Most scientists have the luxury of being able to control their experiments in terms of input parameters and setup. Astronomers have to rely on sporadic celestial events to occur, or advances in technology to access the dimmer objects. Ultimately, astronomers build their framework through multiple observations of similar objects, thereby producing a statistically significant sample. Jared appeared to understand these concepts very well, and was able to answer my questions, if not immediately then certainly after a bit of thought. Another hard lesson in which Jared performed extremely well.
Session Minutes
60
Minutes Student Attended
60
Lesson Comments
This was the first class in which I spent most of the lesson testing Jared's understanding of what we've covered thus far. I usually quiz him at the start of each class to see how much he has retained since the previous class. This was the first time he was subjected to my quizzing throughout the class - and he held up very well, despite being a bit tired. Jared's understanding, willingness to understand, and analytical skills are all very good. At times, though, I get the impression that he's reluctant to answer something in case he's wrong ... So I try to nudge him in the right direction, and then he gets the confidence to answer. His interest, even in going through drier topics such as the scientific method or reviewing the electromagnetic spectrum, remains high (he really wants to understand, even if he's a bit tired, and I can see him concentrating really hard).
Today we started with the Big Revision, going through everything that Jared has learned since we started class together. We reviewed some fundamental concepts regarding the Big Bang, and the evolution of the Universe from then until today - how galaxies formed, and how they're organized in structures called 'clusters' and 'superclusters'. Jared is fascinated with the concept of gravity, so we discussed the prevalence of the gravitational force in the Universe, and how it is one of the four fundamental forces to arise during the Big Bang, the other three being the strong and weak nuclear forces (that govern atomic nuclei and radioactive decay respectively) and the electromagnetic force (the governs interactions between atoms and electric charges). We had not yet discussed dark matter and dark energy and the fate of the Universe, but we touched upon it today in relation to Jared's questions about the gravity associated with our Galaxy.
Assignment
Prepare five more questions for tomorrow's session
Session Minutes
60
Minutes Student Attended
60
Lesson Comments
Another lesson during which Jared remained attentive throughout, posed many interesting questions, and was eager to show me what he had learned last night through his research on relativity - something he did completely on his own initiative ... He did have the five questions ready for me (the previous night's assignment) but he is absolutely riveted with the concepts of gravity and relativity. So I promised him that I'll dedicate part of tomorrow's second session to examining relativity with him, although I'm almost sure that by now he knows more about it than I do! We'll finish the revision tomorrow in the first class, during which I will test his understanding of what we've covered so far, before coming closer to home after Thanksgiving when we'll start studying the Solar System.
We reviewed Jared's assignment from the weekend, since I managed to see the movie 'Interstellar' yesterday. We discussed the physical properties of black holes as portrayed in the movie (very accurately, for the scientific consultant was Kip Thorne, a renowned cosmologist and theoretical physicist). Seeing as the (supermassive) black hole in the movie had an accretion disk, I showed Jared how accretion disks around both supermassive and stellar-mass black holes form. It is primarily via accretion disks that we can 'observe' black holes. In X-ray binaries, the accretion disks radiate in the X-rays, and with appropriate satellites we can detect this radiation.
Assignment
Write down five questions from the course to be discussed on Thursday
Session Minutes
60
Minutes Student Attended
60
Lesson Comments
Jared was thrilled that I had finally seen 'Interstellar' (and I must say, I was incredibly impressed with the portrayal of physics in the movie). He could not stop pondering on the behavior of physics and time in the proximity of the strong gravitational fields of black holes. He asked many relevant questions, most of which I was able to segue into the topic of the class - 'observing' black holes through their influence on their immediate environment (the companion star, the accretion disk). The next couple of classes will be spent on reviewing everything from September to this week, then we'll head for the Solar System after Thanksgiving.
We continued with black holes, and reviewed the concept that there are two main types of black holes in the Universe: Supermassive black holes at the centers of galaxies, and stellar-mass black holes that result from the evolution of a massive star. Since black holes do not emit radiation (the escape velocity from inside a black hole has to be faster than light, and since nothing travels faster than light, nothing can be emitted from a black hole, the question is how do we know they're there? For supermassive black holes, such as the one at the center of the Milky Way, we can follow the tracks of individual stars as they zip around the black hole, and - knowing the masses of the stars (through spectral classification) and using Kepler's equations, we can calculate the mass of the unseen object. In the case of stellar-mass black holes, we need to find one in a binary system with a 'normal' star, and through the motion of the normal star, we can deduce the mass of the unseen companion.
Assignment
None. Jared worked very hard in class today.
Session Minutes
60
Minutes Student Attended
60
Lesson Comments
Jared was again very attentive throughout the class, and asked all the right questions. His interest in the pure physics of the Universe appears to have grown exponentially over the past few weeks. He has completed his assignment from over the weekend, but we have not yet reviewed it (I still need to see the movie 'Interstellar' - it was the first question Jared asked me when I walked into class, but sadly my weekend was a bit too busy to go see it - I will go as soon as possible, Jared almost cannot contain his excitement regarding how much material in the movie was directly related to what we're covering in class). He had done a lot of independent research over the weekend regarding the Rosetta mission to the comet, the Higgs boson, and the meteorite shower of last night and tonight.
Escape velocities (Gravity and black holes cont.'d)
Lesson Outline
We revised escape velocities in today's class. We had already touched upon them in last Thursday's lesson, but I wanted to go into more depth, seeing as escape velocities are directly related to the mass (specifically, density) of a spherical object. They are a good benchmark for understanding gravity. I showed Jared again how to calculate the escape velocity for an object of mass, M, and radius, r. He then calculated the escape velocity for the Moon and Mars (we had calculated that of Earth last time), and together we looked at those of Jupiter, and a typical neutron star. We also looked at what the escape velocity would be if (IF! ... it will never happen!) the Earth were to become a black hole. Jared understood that in this case the escape velocity would have to be the speed of light, which is the defining feature of black holes.
Jared's math skills are very good - he has good intuition and understanding of the numbers themselves.
This class was an hour-and-a-half long, yet Jared remained focused and interested throughout. He was also eager to tell me that he had seen the movie 'Interstellar' twice since last Thursday, and understood the physics!
Assignment
An short essay on the physics of black holes as portrayed in the movie 'Interstellar'
Session Minutes
90
Minutes Student Attended
90
Lesson Comments
Today was a very good class. We had to repeat some concepts from last week, but that's because it had been a full week since we last met. Jared had not completed his assignment from last week, but we worked through it together today. We spent most of the time on calculations - first I showed Jared how to work his way through an equation on escape velocities, after which he performed some calculations himself. It was very gratifying to see how his understanding of the gravitational fields of celestial objects of differing masses and densities increased with each calculation he performed. At the end he understood perfectly that the escape velocity for a black hole is the speed of light (hence the term, 'black hole').
I would like to point out two things: First of all, Jared's handling of numbers is very good - he has an intuitive understanding of math that would be nice to see developed further! He handled operations on exponents with ease, and he understood that when working with large numbers it's convenient to round them and the final result is not so different than if we had used exact numbers - a useful skill in a subject such as astronomy! Secondly, he appeared very eager to tell me that he had seen the movie 'Interstellar' twice since last Thursday, and appeared to be quite proud of himself that he understood the physics involved due to our classes! (I have yet to see the movie, but I know Kip Thorne was the main science consultant, and he's probably the most reliable source around.)
Jared also expressed an interest in relativity (partly as a result of seeing the movie) and mentioned he would like to take it as a course at some point in the future (an incentive to do well at school and go on to college??).
After having talked about black holes for the past few lessons, it was time we examined gravity. So today we looked more closely at Newton's theory of gravitation, and dissected the equation that states that the gravitational force exerted by one body on another is directly proportional to their masses, and inversely proportional to the square of their separation. In other words, the more massive a body is, and the closer two objects are, the stronger the gravitational influence. We can then use the equations for kinetic and potential energy to calculate the escape velocity that an object requires to free itself from the gravitational influence, say, of the Earth. In class we calculated what that is for Earth, and compared this velocity to the maximum velocity attained by a car on a race track. Jared came to realize that even the fastest car would not be able to leave Earth forever! Hence, rockets.
Assignment
Calculate the escape velocity for the following celestial bodies: Earth, the Moon, Jupiter, a neutron star
Session Minutes
90
Minutes Student Attended
90
Lesson Comments
Even though today's lesson was much more centered on physics and math than most prior classes, I have to say Jared stayed focused and engaged in the calculations I was doing on the whiteboard. On top of it, it was a 90-minute session (with a 3-minute break). He appeared to be very intrigued in the concept of gravitation. I can genuinely say that I think we both had fun today, and all we did was dissect equations and plug in relevant numbers in an effort to understand the underlying physics better!
We finished the last few minutes of yesterday's documentary, during which Jared posed some excellent and very relevant questions. I then checked his understanding of the final evolutionary stages of stars (like our Sun and much more massive than our Sun) when reviewing his assignment from yesterday. We started to review some specific properties of black holes, mainly the fact that their sizes are linearly proportional to their masses. So, the more massive a black hole, the bigger it is, and vice versa.
Assignment
Calculate the size of the black hole the Sun would form IF it were to become a black hole; repeat for the Earth.
Session Minutes
60
Minutes Student Attended
60
Lesson Comments
I was happy to see that Jared had made an effort with his assignment. He hadn't fully completed it, but when we reviewed it together, it was obvious that he is on the right track with comprehension of the subject. He again remained attentive throughout the class, and was full of inquisitive questions.
