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What is the ratio of the light gathering power of Keck-I to the light-gathering power of HST?

What is the ratio of the light gathering power of Keck-I to the light-gathering power of HST?

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Keck-I has a 10m diameter mirror. HST  (Hubble Space Telescope) has a 2.4m mirror.

What is the ratio of the light gathering power of Keck-I to the light-gathering power of HST?

[Compute the ratio (light gathering power of Keck)/(light gathering power of HST) and express as a decimal. Do not use scientific notation when entering your answer. ]

[Hint: model the telescope mirrors as circular disks with the indicated diameters. What property of the telescope mirror shape determines how much light it collects?]

 

The question is number 5 and this is all the information I have.

HST orbits at an altitude of 559 km above the Earth's surface. Assume its orbit is circular. Compute its orbital period in hours. [Hint: one of Kepler's laws can help you here. Make sure you are using the correct form for that law. The orbital period depends on the distance from the satellite to the *center* of the object that is being orbited (in this case, the Earth). It also depends on the mass of the object being orbited. You will need to look up some numbers to solve this problem correctly. Keep careful track of units.] 1.598
Transcribed Image Text:HST orbits at an altitude of 559 km above the Earth's surface. Assume its orbit is circular. Compute its orbital period in hours. [Hint: one of Kepler's laws can help you here. Make sure you are using the correct form for that law. The orbital period depends on the distance from the satellite to the *center* of the object that is being orbited (in this case, the Earth). It also depends on the mass of the object being orbited. You will need to look up some numbers to solve this problem correctly. Keep careful track of units.] 1.598
While the HST is well known, there are actually many telescopes similar in size to HST. They look "down" at the Earth rather than the up at the stars. They are not controlled by NASA but by other government agencies (with acronyms like DOD, NRO, and CIA). If a satellite similar in size to Hubble was looking down at the Earth from the orbital altitude given in the previous problem, what is the smallest physical size (in cm) on the Earth's surface that it could resolve? [Hint: this problem is a slightly tricky. You will need to combine the distance/angular- size relation ( s Or ) with Rayleigh's criterion for resolvability ( 0 = 1.22). Pick a wavelength in the visible spectrum (e.g., pick a common color and look up it's wavelength. The diameter of an HST-sized mirror is given in a previous problem (above). Given the orbital altitude r, what does this imply for the smallest object size s that can be measured by an HST-like telescope.]
Transcribed Image Text:While the HST is well known, there are actually many telescopes similar in size to HST. They look "down" at the Earth rather than the up at the stars. They are not controlled by NASA but by other government agencies (with acronyms like DOD, NRO, and CIA). If a satellite similar in size to Hubble was looking down at the Earth from the orbital altitude given in the previous problem, what is the smallest physical size (in cm) on the Earth's surface that it could resolve? [Hint: this problem is a slightly tricky. You will need to combine the distance/angular- size relation ( s Or ) with Rayleigh's criterion for resolvability ( 0 = 1.22). Pick a wavelength in the visible spectrum (e.g., pick a common color and look up it's wavelength. The diameter of an HST-sized mirror is given in a previous problem (above). Given the orbital altitude r, what does this imply for the smallest object size s that can be measured by an HST-like telescope.]
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