Astronomy 112 Homework 4 - Chapter 6

How does this compare to the diffraction limit of a 10-meter telescope? Express your answer using two significant figures.

Øeye / Øtelescope = 1300

The stars in our sky twinkle in brightness and color because of __________.

turbulence in the Earth's atmosphere

Consider two future observatories in space: Observatory A consists of a single 50-meter telescope. Observatory B is an interferometer consisting of five 10-meter telescopes, spread out over a region 100 meters across. Which observatory can detect dimmer stars, and which one can see more detail in its images? (Assume all else is equal, such as quality of optics, types of instruments, and so on.)

Observatory A can detect dimmer stars, and Observatory B reveals more detail in images.

What do we mean by the diffraction limit of a telescope?

It is the angular resolution the telescope could achieve if nothing besides the size of its light-collecting area affected the quality of its images.

Shown following are six different types of light that travel to Earth from sources in space. Rank these types of light from left to right based on the altitude in the atmosphere where they are completely absorbed, from highest to lowest (Earth's surface). If two (or more) of the choices reach the same altitude or the surface, rank them as equal by dragging one on top of the other(s).

-----> HIGHEST ALTITUDE: X-rays most ultraviolet light most infrared light green visible light & most radio waves (stacked on top of each other) <--- LOWEST ALTITUDE

Large telescopes often have small fields of view. For example, the Hubble Space Telescope's (HST's) advanced camera has a field of view that is roughly square and about 0.06 degree on a side. Calculate the angular area of the HST's field of view in square degrees.

0.0036 square degrees

How much more light does an 8-meter telescope gather than a 2-meter telescope?

16 times as much

Suppose astronomers built a 130-meter telescope. How much greater would its light-collecting area be than that of the 10-meter Keck telescope? Express your answer using two significant figures.

170

How much greater is the light-collecting area of one of the 10-meter Keck telescopes than that of the 5-meter Hale telescope?

4

How do the angular resolutions you found in parts A and B compare to the angular resolution of the Hubble Space Telescope? Comment on the challenge of making images of planets around other stars.

Both planets could be distinguished from the Sun in means of angular resolution. However, the light from planets could be lost in the glare of the Sun.

Shown following are five different colors of visible light that travel to Earth from the Sun. Rank these colors of visible light from left to right based on the altitude in the atmosphere where they are completely absorbed, from highest to lowest (Earth's surface). If two (or more) of the choices reach the surface, rank them as equal by dragging one on top of the other(s).

EVERY DIAGRAM IS STACKED ON TOP OF EACH OTHER; THEY ARE ALL EQUAL

Which of the following best describes why radio telescopes are generally much larger in size than telescopes designed to collect visible light?

Getting an image of the same angular resolution requires a much larger telescope for radio waves than for visible light.

The angular area of the entire sky is about 41,250 square degrees. How many pictures would the HST have to take with its camera to obtain a complete picture of the entire sky? Express your answer as a number of pictures to two significant figures.

N = 1.2 * 10^7 pictures

Suppose that two stars are separated in the sky by 0.1 arcsecond. Choose the correct statement describing, what will you see if you look at them with a telescope that has an angular resolution of 0.5 arcsecond.

One point of light that is the blurred image of both stars.

refers to telescopic observations in which we separate an object's light so we can measure its intensity at different wavelengths.

Spectroscopy

Compare this to the diffraction limit of the Hubble Space Telescope for visible light. Why, to be useful, radio telescopes must be much larger than optical telescopes?

The angular resolution of the radio telescope is much poorer than such of HST. Radio telescopes are much larger than optical telescopes because the wavelengths of radio waves are much larger than such of visible light.

What does angular resolution measure?

The angular size of the smallest features that the telescope can see.

Suppose that two stars are separated in the sky by 0.01 arcsecond, and you observe them with a telescope that has an angular resolution of 1 arcsecond. What will you see?

The light from the two stars will be blended together so that they look like one star.

Suppose you have two small photographs of the Moon. Although both look the same at small size, when you blow them up to poster size one of them still looks sharp, while the other one becomes fuzzy (grainy) looking. Which of the following statements is true?

The one that still looks sharp at large size has better (smaller) angular resolution than the one that looks fuzzy.

The first telescopic photo shows what appears to be a single star. The second photo shows the same object, now revealed to be two distinct stars. What is the difference between the two photos?

The second photo has better (smaller) angular resolution than the first photo.

Which of the following is not a reason why telescopes tend to be built on mountaintops that are relatively far from cities and are in regions with dry climates?

The thin air on mountaintops makes the glass in telescope mirrors less susceptible to warping.

What is the primary reason that we launch X-ray telescopes into space rather than building them on the ground?

X-rays from space do not reach the ground.

Suppose you have a camera attached to a telescope, and you want to record an image of a faint galaxy. Which of the following will help the most?

a lot of pixels and a long exposure time

Interferometry uses two or more telescopes to achieve:

an angular resolution equivalent to that of a much larger telescope.

What are the two most important properties of a telescope? Select exactly two responses.

angular resolution light-collecting area

The familiar twinkling of the stars is caused by, which also blurs telescopic images.

atmospheric turbulence

How much greater is the light-collecting area of a 6-meter telescope than a 3-meter telescope?

four times

A camera is an example of an instrument used for observations.

imaging

If you see the color red in an X-ray image from the Chandra X-Ray Observatory, it means:

it depends: the colors are chosen arbitrarily to represent something about the X rays recorded by the telescope.

Human civilization is responsible for what astronomers call .

light pollution

When your eye forms an image, the _____ plays a role analogous to the detector in a camera.

retina

If we want to confirm that a star's brightness alternately dims and brightens, we need observations of the star.

time monitoring

Technological advances are now making it possible to link visible-light telescopes so that they can achieve the same angular resolution as a single telescope over 300 meters in size. What is the angular resolution (diffraction limit) of such a system of telescopes for observations at a wavelength of 500 nanometers? Express your answer in arcseconds to two significant figures.

Ø = 4.2 * 10^-4 arcsecond

What is the diffraction limit of a 130-meter radio telescope observing radio waves with a wavelength of 21 centimeters? Express your answer in arcseconds to two significant figures.

Ø = 400 ^n

Now remember that humans have two eyes that are approximately 7 centimeters apart. Estimate the diffraction limit for human vision, assuming that your "optical interferometer" is just as good as one eyeball as large as the separation of two regular eyeballs. Express your answer in arcseconds to two significant figures.

Ø2-eyes = 1.8^n

What angular resolution would you need to see the Sun and Earth as distinct points of light? Express your answer in arcseconds to two significant figures.

ØEarth = 0.27 ^n

Suppose you were looking at our own solar system from a distance of 12 light-years. What angular resolution would you need to see the Sun and Jupiter as distinct points of light? Express your answer in arcseconds to two significant figures.

ØJupiter = 1.4^n

Calculate the diffraction limit of the human eye, assuming a wide-open pupil so that your eye acts like a lens with diameter 0.8 centimeter, for visible light of 500-nanometer wavelength. Express your answer in arcseconds to two significant figures.

Øeye = 16 ^n