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  • a) How many astronomical units (AU) make 1 parsec? c) Mars has approximately half of the earth’s diameter. When it is closer to the earth it is at about ½ AU from the earth. Calculate at what size it will disappear when seen through the same telescope.

a) How many astronomical units (AU) make 1 parsec?

b) Consider the sun like a star at a distance of 2 parsec. When it is seen through a telescope with 100 magnification, what should be the angular size of the star? Sun appears to be (1/2) degree from the earth. Due to atmospheric fluctuations, eye cannot resolve objects smaller than 1 arc minute.

c) Mars has approximately half of the earth’s diameter. When it is closer to the earth it is at about ½ AU from the earth. Calculate at what size it will disappear when seen through the same telescope.

Answers (1)

(a)1 A.U. long arc subtends the angle of 1s or 1 arc sec at distance of 1 parsec.

Thus, angle 1 sec = \frac{1 A.U.}{1} parsec

Thus, 1 parsec = \frac{1 A.U.}{1} arc sec

Thus, 1 parsec= \frac{630(3600)}{11}

                              =206182.8

                              =2\times10^{5}A.U.

(b)Angle of the sun’s diameter \left ( \frac{1}{2} \right )^{o} is subtended by 1 A.U. since the distance from the sun increases angle subtended in the same ratio.

Now,

2\times10^{5}A.U. will form an angle of \theta =\left ( \frac{1}{4\times10^{5}} \right )^{o}, since the diameter is the same angle subtended on earth by 1 parsec will be same.

If the sunlike star is at 2 parsec the angle becomes half = (1.25 \times 10^{-6})^{o}

Thus, angle = 75 \times 10^{-6} min

When it is seen with a telescope that has a magnification of 100, the angle formed will be 7.5 \times 10^{-3} min, viz., less than a minute.

Hence, it can’t be observed by a telescope.

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infoexpert22

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