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-------------------- 2565 - TELESCOPES - come in all shapes and sizes.
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- You probably do not recognize the telescope on your, or your neighbor’s, roof. But, every satellite dish is a radio telescope. The dish is collecting radio waves in a metallic mirror and focusing them on a detector.
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- The satellite is a stationary target because it is orbiting in just the right spot above the Earth to match the rotation of Earth. The satellite is above the equator and completes one orbit in one day.
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- To calculate the TV satellite’s orbit use Kepler’s formula that the period of the orbit squared = the radius of the orbit cubed.
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---------------- One day = 86,164 seconds
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---------------- Mass of the Earth = 5.976*10^24 kilograms
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---------------- Gravitational constant = 6.67*10^-11 meters^3 / Kg*sec^2
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-------------- Period^2 = 4*pi^2 * radius^3 / G * Mass
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------------- (8.6164*10^4)^2 = 4*pi^2 * radius^3 / 6.67*10^-11 meters^3 /
- Kg*sec^2 * 5.976*10^24 kilograms
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------------- Radius^3 = 74.96^10^21 meters^3
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------------ Radius of orbit = 42,157 kilometers.
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------------ Radius of Earth = 6,374 kilometers
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- The elevation of the satellite above Earth’s equator is 35,783 kilometers (22,235 miles).
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- The direct TV satellite dish is 0.5 meters in diameter. It works ok for a strong TV signal but how well would it really work as an astronomy radio telescope? All telescopes are rated in how well they resolve two objects. Can the telescope resolve them as separate objects or are the two blurred together? This is called angular resolution of the telescope.
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- For example the Hubble Space Telescope has an angular resolution of 0.05 arc seconds. This resolution ability is dependent of the wavelength of the light and the diameter of the light collecting lens, or mirror. The Hubble mirror is 2.4 meters diameter. The wavelength of blue-green light is 500 nanometers. The formula for the Diffraction Limit, as the angular resolution limit is called, is:
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------------- Arc seconds Limit = 250,000 * wavelength / diameter
------------- Hubble’s arc second limit = 250,000 * 500 * 10^-9 meters / 2.4 meters
------------- Hubble’s arc second limit = 0.05 arc seconds.
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- Let’s do this same calculation for your direct TV satellite dish: The wavelength used for radio astronomy is 21 centimeters. This is the radio emission of active hydrogen gas.
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------------- Arc seconds Limit = 250,000 * wavelength / diameter
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------------- Direct TV’s arc second limit = 250,000 * 0.21 meters / 0.5 meters
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------------- Direct TV’s arc second limit = 105,000 arc seconds
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- There are 3,600 arc seconds in a degree of arc so this corresponds to 29 degrees of arc. The Full Moon is ½ degree of arc, so this is 60 times the diameter of the Full Moon. That is the spot you have to hit in the sky in order to get your TV reception.
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- This would not be very good angular resolution for radio telescope astronomy. We need a much larger dish. The radio telescope in Puerto Rico is 1,000 feet ( 305 meters) in diameter.
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------------- Arc seconds Limit = 250,000 * wavelength / diameter
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------------- Radio Telescope’s arc second limit = 250,000 * 0.21 meters / 305 meters
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------------- Radio Telescope’s arc second limit = 170 arc seconds
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- Therefore the radio telescope in Puerto Rico can resolve two hydrogen gas clouds that are separated by 170 arc seconds in the sky, but the antenna has to be the length of 3 football fields in order to do that.
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- Infrared light from space gets absorbed by our atmosphere and does not reach the ground. Absorbing this energy is what keeps our atmosphere warm. That is also why high mountain tops that are closer to the Sun are colder, because the atmosphere is thinner up there.
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- It is also why high mountain tops and high flying telescopes are used to get some infrared images. Infrared wavelengths and thermal radiation are the same thing. Therefore, infrared telescopes need to be cooled with liquid helium to a few degrees above absolute zero in order to avoid thermal interference. Infrared satellites are also in orbit behind the Earth’s orbit around the Sun in order to stay in Earth’s shadow.
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- Most ultraviolet radiation from space does not reach the ground either. So ultraviolet telescopes also need to be satellites. Conventional light telescope’s lens and mirrors deflect the infrared and ultraviolet wavelengths well enough but different detectors need to be used to be sensitive to these longer and shorter wavelengths. Hubble has all three detectors and has done a great job collecting images in infrared, light, and ultraviolet wavelengths.
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- X-ray telescopes can not use the conventional light collecting methods of light telescopes. The wavelengths are too short and these photons travel right through visible light mirrors. Instead of reflective mirrors they use metal shields that are at graduated angles to gently deflect the X-ray photons to focus on a target detector.
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- Typically X-ray photons are only deflected 2 degrees so the telescopes have to be very long. A 4 meter diameter X-ray telescope would have a length of 2 meters times the sine of 2 degrees, a length of 57 meters.
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- Gamma ray photons have even shorter wavelengths and even grazing incidence mirrors will not work to focus them. In Gamma Ray telescopes the photons go directly into the detectors without focusing. As a consequence it is very hard to pin point the source of Gamma Ray emissions. What happens is the Gamma Ray telescope detects the radiation in a general location. Then, X-ray and visible light telescopes search for the afterglow and try to locate the source.
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- Neutrino telescopes are very unusual. Neutrinos are almost like photons. They are nearly massless and travel at nearly the speed of light, but they do not interact with matter the way photons do. They can pass right through the Earth and not be deflected at all.
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- Neutrino telescopes are built in the ice glaciers of the Antarctic with detectors buried deep in the ice. It takes a long time to collect only a few neutrino deflections as they pass through the Earth.
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- Cosmic Ray telescopes work on the same principles as the neutrino telescopes. In fact, astronomers have trouble separating a hit in their telescope as being caused by a neutrino, or a Cosmic Ray. The big difference is that Cosmic Rays are charged particles and can be influenced by a magnetic field. Neutrinos are neutral and are not influenced by magnetic or electric fields.
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- Gravity Wave telescopes are even more unusual. Gravity waves travel at the speed of photons and distort the shape of spacetime as they pass by. The distortions are very small. Even the biggest emissions of gravity waves coming from binary Black Holes would only distort these telescopes by the width of a proton.
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- The telescopes are laser beam interferometers that are several miles in length and perpendicular to each other. As a gravity wave passes one length would be stretched while the other length would be compressed only this slight amount. These telescopes have been built and their sensitivity has been continually improved. We are just beginning to discover gravity waves using these interferometers.
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- Interferometer techniques can also be used to improve the sensitivity of ordinary telescopes. Telescopes need to collect as much light as possible and to have the smallest angular resolution as possible.
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- Starting with radio telescopes multiple telescopes have been linked together using interferometry. In Socorro, New Mexico, there are 27 radio dishes linked together with interferometry making the array equivalent to a single telescope 40 kilometers in diameter.(25 miles).
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- Interferometry is more difficult at higher frequencies than radio, but it is starting to happen. This capability to use multiple telescopes will soon spread across the entire spectrum and even be launched into space.
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- As you can tell from the Diffraction Limit formula the angular resolution becomes smaller as the diameter of the telescope becomes larger. The Keck Telescopes in Hawaii are 10 meters in diameter. Using two Keck telescopes linked together with interferometry would have an equivalent diameter of 300 meters. Substituting these numbers into the formula would give an Arc Second limit of 0.000417 arc seconds. Amazing!
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- Hubble is 0.05 arc seconds limit and it can resolve two binary stars that are 20 light years away and only 200 million kilometers apart. The angular separation is 206,265 * physical separation / distance. 1 lightyear is 10^13 kilometers .
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- The calculation works out to be an angular separation of 0.20 arc seconds. So, the Hubble at 0.05 arc seconds could resolve these two stars. Jupiter is 778 million kilometers from the Sun. So, turning things around, if Hubble was orbiting these binary stars looking back at us it could resolve the planet Jupiter from the star, our Sun.
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- The human eye is a kind of telescope. A lens focuses photons on a mirror called the retina. When the dogs eyes glow in the headlights of your car you can see the mirror effects of the eye.
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- The diameter of the eye is 0.8 centimeters. Its Diffraction Limit is 15.6 arc seconds. However, you have two eyes and a brain that can do interferometry. The eyes are separated by 7 centimeters so you can get greater resolution power down to 1.8 arc seconds. The Hubble is still 36 times better.
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- The other thing that Hubble can do is take long time exposure into the CCD’s, charge coupled detectors. Your eye detects one photon at a time. The CCD’s can collect one photon after another to accumulate a charge over time. Some of the Hubble Deep Field time exposures have looked at the same spot for over 1,000,000 seconds.
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- I hope you learned some new things about telescopes. We have come a long way in the last 400 years and the rate of change is the greatest today.
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- December 26, 2019 2565 941
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--------------------- Thursday, December 26, 2019 --------------------
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