Greetings from Palmia Observatory
Well here we are wondering, after having received our second vaccine dose, how this "new normal" will affect our decisions to travel and go out more? In the meantime we can report on the latest drama from the Starship SN10 test flight and look into possible launch viewing sites in Boca Chica and finish up with some discussion on three qubit quantum entanglement.
In this first photo we can see the Starship SN10 just after landing on the landing pad. It looks a little off to one side, but it made it down. You can also see how close the landing pad is to Highway 4, which goes down to the ocean and Boca Chica beach..
|SN10 lands after successful test hop (Source: GreatSpaceX)|
It initially looked like that the test flight of Starship SN10 was a complete success. It made it to the scheduled test hop altitude and the rocket engines started and stopped as required. But about 10 minutes after the successful landing, something went wrong and the SN10 exploded. Ok, SN10 was a success until it failed, but SN11 is coming out of the high bay and other prototypes will follow shortly.
|But 10 minutes after landing, SN10 explodes (Source: NASA.Spaceflight.com)|
It was just a year ago that we were in Boca Chica for the first time. Our plans to attend the Lunar and Planetary Society meeting in Houston were cancelled when the meeting itself was cancelled, but we chose to continue with a portion of our trip to visit Boca Chica. The virus was really taking off and with spring break going on at the same time we hoped our decision to travel would turn out ok. Here I am along state highway 4 in Boca Chica and we had an uneventful rest of the trip.
|Resident Astronomer visits Boca Chica, last year March 14, 2020 (Source: Palmia Observatory)|
Now that we feel a little safer about travelling to Boca Chica to observe some of the next launch tests, we need to revisit which of possible locations are the best.
We have an ongoing project to identify a good location from which to observe rocket launches. Areas close to the launch site, along state highway 4, will be blocked off during testing and there is not where to eat or stay while there. Many bloggers that follow SpaceX Starship activities seem to observe the launches from either South Padre Island or Port Isabel. Here is one example that seems likely to be somewhere in Port Isabel along the Brownsville Ship Channel.
|One possible viewing site along the Brownsville Ship Channel (Source: ValleyCentral.com)|
From that same location, the flight of the SN10 could be tracked. Here we see SN10 coming back down for a landing. This series of photographs are useful in finding out what kind of telephoto lens focal length is required to see the Starship.
The width of this image is 590 pixels and the Starship is 60 pixels tall. Unfortunately, I clipped the vertical height of the image while screen saving it, but we can still estimate the focal length used. My convention is to compare angular sizes in the vertical direction. If the aspect ratio of the photographers camera is the same as mine then we can get the field of view of the telephoto lens used.
|Observation site has pretty good view of launch/landing (Source: ValleyCentral.com)|
In this next photo, the photographer pulled the camera lens back to lower the focal length and we can see all of the other participants just enjoying the weather. You can see the smoke cloud from the SN10 explosion at the left hand side of the photo.
|Starship spectators found one possible viewing site (Source: ValleyCentral.com)|
Ok, so we don't really know where these photographs were taken but we surmise that the observing point was somewhere on South Padre Island or on Port Isabel. Check out this Google Earth image of the surrounding area near Boca Chica. The distance from either South Padre Island or Port Isabel to the SpaceX launch site is right around 5 miles. The distance from the launch site to areas in Port Isabel seems a bit closer, but that whole area around Port Isabel southward is occupied by commercial shipyards and other businesses.
Our previous trip to Boca Chica considered staying on South Padre Island as a pretty reasonable location, especially if you could get a high rise hotel room facing south toward to the launch site. Regardless, we are going to find ourselves about 5 miles from the launch site.
|Google Earth views of sites like Port Isabel or South Padre Island (Source: Palmia Observatory)|
Let' use these photographs to estimate the focal length requirement of the telephoto lenses used to get the images of the Starship. First let's calculate what the angular size of a Starship, here assumed to be nominal 160 feet tall, will be seen while viewing from 5 miles away. In the following sketch, we find that the angular size of the Starship is about 0.33 degrees.
|Starship would extend 0.33 degrees from 5 miles away (Source: Palmia Observatory)|
So, will we be able to get by with just a small 300mm telephoto lens or will we have to upgrade to a 600mm lens or more? It would be great if the 300mm lens can be used to get comparable images because that lens and associated flimsy camera tripod can be easily fit into a single carry-on suitcase, containing all the rest of my travel accessories. If the 600mm lens is required, that would almost call for a separate carry-on bag because the lens is much bigger and it needs the sturdier tripod which won't easily fit in the carry-on bag.
The field of view of the 300mm lens is 2.7 degrees in the vertical direction. This FOV means that a little more than 5 full moon images can be placed in the vertical direction. The estimated FOV for the Starship images is 0.33 * 598 * (14.9 / 22.3) / 60 = 2.3 degrees.
Hooray, it looks like we can get away with just a 300mm telephoto lens and flimsy tripod and can almost get as good of resolution as the other photographers images!
Whew, now with that task out of the way, let's finish up with some interesting quantum computing news, which ties in very nicely with our ongoing study of the nature of quantum entanglement. The article, "Deterministic multi-qubit entanglements in a quantum network", in the 25 Feb 2021 Nature magazine, by Youpeng Zhong, et al, describes a 3-qubit superconducting circuit that is tied together with another circuit over a superconducting cable. The neat thing is that the entanglement between the two networks is maintained. A copy of the circuit diagram and description from that article is presented below.
|Multi-qubit entanglement in a quantum network (Source: Y Zhong, et al, Nature, 28 Feb 2021)|
Now I can't comment about the importance of this new step forward in quantum computing, but the fact that three qubits can now be entangled in the laboratory brings us right back to the theoretical considerations of the so called GHZ or Greenberger-Horne-Zeilinger quantum state. Check out the simplest GHZ state shown in this Wikipedia article. The article shows the quantum gates used to create this superposition, but look at the case where all three bits can be all '0' or all '1'. This is a good example to show how we can immediately see that this state is entangled. Just like the easier case for two entangled qubits, here we see that any measurement on any one of the entangled bits in this superposition will immediately tell us what state the other bits must be in. The first measurement on this superposition determines which part of the superposition is selected and subsequently we know the state of the other qubits without needing to make a measurement. So, what started off as just a mathematical description of three entangled qubits now has been demonstrated in the quantum computer laboratory.
|GHZ 3-qubit entangled quantum state (Source: Wikipedia)|
Now, the GHZ state is easy to see that the superposition is entangled. Not that we understand how entanglement occurs or what the impact will be on our concepts of reality and locality, but that we can write down a mathematical statement that displays the entangled nature of these three qubits. But it turns out that there is one other entangled state between three qubits that is not easy at all to tell by inspection that the state is an entangled one. This state is called the W-state as illustrated in this Wikipedia article.
I can't immediately see that this equation represents an entangled state. For instance, if we measure the first qubit and find it is in a '0' state, we still don't know for sure what the other qubits condition is. Hmm, I'm going to have to think about this some more. How about you, do you see why this W-state is an entangled state? Maybe it has something to do with what is called "multipartite entanglement."?
|W-state with 3-qubit entanglement (Source: Wikipedia)|
Until next time, here from our burrow, stay safe, as we recover more of our freedom,
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