Well, this week we were happy to see that the Starship, Serial Number 1 (SN1) was transported across the highway to the launch site in Boca Chica, TX.
Now SpaceX does not always give advance notice as to when major operations like this will occur so we rely on various Twitter feeds from volunteer who hang around the area and peer through the fences around the site. It also turns out that many folks are monitoring required disclosures to the state and local officials and the FAA, whose approval is often needed and this approval is publicly disclosed. In the case of the move across the state highway, some advance notice was available so that folks could set up their cameras. It is a little harder for the rest of us that need to schedule airline flights to get down there on such short notice.
|SpaceX temporary road closure to transport Starship SN1 to launch site (Source: Mary, @BocaChicaGal)|
Well, in addition to watching various twitter feeds for the latest news about activity there, we have been wanting to travel down to Boca Chica, TX, ourselves to check out the SpaceX manufacturing site and launch complex and with the supposedly upcoming test hop of the Starship rocket, we elected to piggy back on our air travel to the 51st Lunar and Planetary Society meeting in the Woodlands, TX, and just stop in Brownsville, TX on one of the legs of the flight there.
Well, just after we arranged our air tickets, we get the news that the Starship SN1 suffered some kind of "anomaly" during pressure testing. Hmm, this latest photo from @Bocachicagal explains that the anomaly was really more like an explosion during pressure testing. Darn! Well, as Elon says SpaceX team learns a lot from failures and is apparently moving full speed ahead with revised design and test plans. So, we still plan to spend the night in Brownsville and will reconnoiter the site and peer through the fence at some of the ongoing construction and other activities. Hopefully, then once we get a bit of advance notice when the scheduled test hop of, I assume SN2, is set, we will know where the best observing sites are!
|Starship SN1 suffers failure during pressure test (Source: Mary, @BocaChicaGal)|
Ok, so that was sad SpaceX news, but it was time to head out for an Association of Energy Engineers (AEE) tour of one of Southern California Edison's Technology Learning Centers. This facility in Pomona is used to test and evaluate energy storage systems including electric vehicles and charging systems. The site didn't allow any photos but we did get to see some of the energy storage systems and battery components under environmental testing. The also have an electrical microgrid where other distributed energy resources, like solar panel roofs, can be connected and tested. We also had a tour of the full sized vehicle chassis dynamometer where electric vehicles can be tested at full speed under simulated road load conditions such as going up and down hills and just normal accelerating and breaking as in normal city traffic. The outside of this building was the only place we were our tour group was allowed to take a photo.
|AEE tour group gets ready to visit SCE full-size vehicle chassis dynamometer (Source: Palmia Observatory|
So, all in all it was an interesting tour and I also learned about an upcoming IEEE conference on technologies for sustainability called SusTech 2020. This 7th annual conference will be held here locally in Santa Ana on April 23-25, 2020. I'm thinking about putting it on my calendar, especially since I spent many years working on new more sustainable forms of power generation, and as an IEEE Life Member, I can attend for just $75. But the real point is that we need technologies that are more sustainable in terms of resources and environment and we might learn about some of the emerging technologies. So if you want to learn more about this check it out and put it on your calendar!
|7th Annual IEEE SusTech 2020 is here locally in Santa Ana (Source: https://site.ieee.org/sustech/)|
In other space news, there was an interesting article on Terrain Relative Navigation (TRN) in the February 2020 edition of Air Space Magazine. Recall that we mentioned during the previous post of February 23, that future exploratory missions to Mars and the Moon are depending on landing craft much closer to the target than ever previously achieved. For some missions, like the Moon Diver mission, you want to land as close as you can to the "hole in the moon." This current article describes how TRN has evolved and developed.
|Terrain-relative navigation can shrink landing ellipse (Source: Kara Platoni, Airspacemag.com, Feb 2020)|
When the spacecraft is launched from Earth it is hard to predict exactly where it will enter orbit around Mars or the Moon. TRN uses advanced vision systems to identify from onboard photo imaging and processing how to adjust the entry approach to achieve a much tighter landing ellipse. The technique uses landmarks on the planet's surface to control the landing ellipse and reduces the error from kilometers to meters. Mars 2020 lander will use this new technique.
This week at the CSULB Physics Colloquium we had a great presentation by Dr. Jocelyn Read, CSUF. She spoke on how gravitational waves from merging neutron stars can tell us much more than just the masses of the binary pair. It turns out that the internal structure and equation of state of the neutron star affects some of the measurable aspects of the detected gravitational waves. This is a new method now available to learn much more about matter in the highly dense state in neutron stars. She showed several examples of gravitational waveforms where during the ring down time, which depends on how easily the two stars are disrupted by tidal gravitational forces, much can be learned about the equation of state of the highly dense neutron star. Recall that we previously described how NICER (Neutron Star Internal Composition Explorer), located on the ISS, was used to measure the radius and other properties of neutron stars. Using the radius measurement and mass estimate one cn calculate the density and compare it with various equation of state models. For more of those details check out this blog post of February 25, 2019. Anyway, it was a very interesting presentation. Thanks for that, Jocelyn!
|Professor Jocelyn Read, CSUF, uses gravitational waves to study structure of neutron stars (Source: Palmia Observatory)|
During our lunchtime discussion, I asked Jocelyn, what classes were being offered at CSUF. As a CSUF graduate myself, with an MBA rather than a physics degree, I thought CSUF might be a good school to learn more theory of general relativity. The Gravitational Wave Physics and Astronomy Center (GWPAC) at CSUF supports more than a dozen students doing research and was instrumental in doing many of thousands of inspiral simulations so that LIGO could more easily detect gravitational waves, and just recently the recipient of a $10 million grant from engineer and philanthropist, Nicolus Begovich. She said that their general relativity course is a 400 level course and that the students learn about gravitational waves more as independent study work. She said they are currently using Jim Hartle's classic textbook, "Gravity - An Intro to Einstein's General Relativity."
Hmm, I also already working my way through that textbook, so this might be a good time to switch topics a little bit and mention about one of the topics that I am trying to work my way through. So, Hartle has a whole chapter on gravitational waves, but my interest right now is just on how one calculates the orbit of some particle about ready to fall into a black hole. So, let's depart from general observational astronomy a moment and dive into some of the mathematics of general relativity and how modern software packages, like Mathematica, can help reduce some of the drudgery of going through all of the calculations by hand. In this framework, particles are described by a four-vector, with one component representing the time and three components representing the particle position in three dimensions. The coordinates used to describe the particles position in space and time can be any set of coordinates such as x,y, and z or spherical coordinates or what ever.
We know that in flat Euclidian space the motion of a particle is in a straight line as long as no forces are acting on the particle. This means we can say that the acceleration of the particle is zero. The acceleration is the 2nd time derivative of position, but in curved spacetime, that is in a gravitational field, the motion need not be in a straight line and the 2nd derivative of position need not be exactly zero.
So, for curved spacetime, the path of the particle, called the geodesic, has a much more complicated 2nd derivative as outlined below from the Hartle textbook. So be warned, we are going to dive more deeply into the mathematical structure of general relativity. The purpose is not to explain the principles but just to show how the use of new mathematical software can remove the hard work that used to have to be done by hand.
Part 1 of the problem is first to see how the equations of motion in general relativity differ from Newtonian equations of motion. If we say that gravity is a force then Newtonian force equations can be written as differential equations and those equations can be solved to predict the motion of a particle in the gravitational field. But these equations assume that space is flat and that the gravitational field is weak. When we make the transition to strong gravitational fields like that around stars and especially black holes, then space and time are not flat and they are both distorted by the strong field. To cover the motion of particles in this situation, the geodesic equation must be modified to include the curved nature of spacetime.
|Developing the geodesic equation for curved spacetime (Source: J. Hartle, "Gravity - An Intro to Einstein's GR)|
Now the geodesic equation (Equation 8.15 in the figure above) is written in standard tensor notation so all the indices (Greek alpha, beta and gamma) take on four values, typically identified as 0, 1, 2, and 3. So what looks like an ordinary differential equation really represents 4 x 4 x 4 = 64 separate equations because each of the three indices can take on four values. The capital gamma symbol, called the Christoffel symbol or connection symbol contains all of the information required to transform the acceleration as seen from flat Euclidian space to the curved spacetime associated with the accelerating particle. So this connection symbol really has 64 separate components and can take a lot of work to calculate what each of the those 64 values are.
So how to do all of these calculations? Well it is a lot of work if you try doing it by hand, so I reached out to Math Whiz Dave and asked him how the problem might be set up in Mathematica. Well, he very quickly sent me some solutions. Here you can see how he choose standard black hole type coordinates used in the Schwarzschild metric where, t represents time, r represents radial distance, and theta and phi represent the angular position around the black hole.
|Mathematica representation of the Schwarzschild metric (Source: Math Whiz Dave, Saguarosoft)|
With this Schwarzschild metric, we can then calculate the connection by the well defined method of differentiating the metric as outlined below. Here you can see the standard definition of the connection as the sum of three partial derivatives of the metric. It turns out that many of the derivatives will be zero because of the symmetry of the problem, which really helps for spherically symmetric objects like non-rotating planets or black holes. Check out just how many of the terms are actually zero.
Without going into the details you can see that many terms do indeed just go to zero because of symmetry. For example, with index definitions going not from 0 to 3, but with standard black hole coordinates, as defined above, many of the terms just drop out and go to zero. There is a lot of pre-definitions of variables that go into Mathematical that I am not showing here. Also, since Mathematica can solve equations symbolically, we don't at this stage have to assign numerical values to any of the variables. For instance, if we define a variable as the sine of theta, we don't have to assign any values to theta and if we were to call for the differentiation of the sine function, Mathematica would then just treat the result as cosine theta. So we will be able to follow all of the operations involved without ever talking about any specific numerical value. In the printout below, to make the list clearer, shortcut symbols like "C" and "S" represent cosine and sine functions. The main thing to note though is that the connection is equal to the sum of three derivatives of the metric. Whew, all of that helps! Thanks for all of that Dave!
|Using Mathematica to compute the connection for curved space time geodesic (Source: Math Whiz Dave, Saguarosoft)|
Ok, now I can sort of see what is happening with all of the 64 components of the connection. I still have to check them to make sure all is ok, but now I can sort of begin work out these and the other details. Now this is just Part 1 of calculating the trajectory of particles around a black hole. Part 2 is to now solved the geodesic equation (Equation 8.14) for the actual motion of the particle. Part 1 just got us ready to account for the effects of curved spacetime.
Ok, so we are not going on to work on Part 2 just now. There is still a lot of work to do and integrating Eqation 8.4 still will be a lot of work. But what I hope you can see is that with the help of Mathematica software we can more easily let the software do the grunt work while we are more free to work on understanding the physics without trying to account for all 64 equations of curved spacetime.
My explanation is probably not the clearest explanation but hopefully you can get a sense of how lucky we are to have access to Mathematica to take care of the drudgery. We are also lucky to know experts who actually do understand it all. By the way, you each can get your own copy of the home version of Mathematica at very low cost. Thanks for your help, Dave!
Finally, after being exhausted by trying to work in curved spacetime, we can take a break. With a few moments of free time, I saw this interesting Facebook post about wild wolves and how some of their kind were eventually domesticated to become our familiar dogs. The (unkonwn) author of this post considered the decision making of one of the early wild wolves, who elected to take a free meal around an early man campsite. Hmm, I guess there is some good and some bad in a free meal!
|Beware of free food? (Source: Facebook post)|
Well, I guess it hasn't been all bad for the descendants of the wild Wolf. For instance, Astronomer Assistant Ruby has proved valuable for all sorts of tasks around the observatory. Here we see her spotting some suspicious looking object in the gutter. It does seem to somewhat resemble a giant corona virus particle. Thanks for that Ruby; just don't bring it back to the observatory!
|Astronomer Assistant, Ruby, finds "corona virus" look alike (Source: Palmia Observatory)|
Until next time,