Photometry questions. 1. Star M has an apparent magnitude of -1.0 and an absolut
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Question
Photometry questions.
1. Star M has an apparent magnitude of -1.0 and an absolute magnitude of +2.0. If it were moved 10 times farther from Earth as it is now, which one of the following things would occur? a. absolute magnitude number would decrease (gets smaller) b. apparent magnitude number would decrease (gets smaller) c. apparent magnitude number would stay the same d. absolute magnitude number would increase (gets bigger) e. apparent magnitude number would increase (gets bigger) 2. Star N is 4 parsecs (about 13 light years) away. Its apparent magnitude is +3.0 What is most likelv its absolute magnitude? a. +5.0 b. +3.0 c. +0.30 Star Q star gives off the same amount of energy as Star R. But Star Qis much, much cooler than Star R star. Which star has the greater surface area? a. Thev have the same surface area b. Star c. Star R d. There is insufficient information to answer this question. 3.Explanation / Answer
If we want to know how bright a star or any other celestial body looks in space, we measure it by something known as Apparent Magnitude. This scale is "backwards" and logarithmic. Larger magnitudes correspond to fainter stars while a lower apparent magnitude implies bright objects and the dimmest objects that human eyes can see have an apparent magnitude of nearly about 6. Those objects with an apparent magnitude of higher than 6 are too dim for the humans eyes to see. The objects with an apparent magnitude of 1 are bright. Few objects, like the Sun are so bright they have a negative apparent magnitude. On the other hand, Absolute Magnitude helps us to understand how bright a star really is which means the absolute magnitude of an object, such as a star, equals how bright that object would look if it were 10 parsecs, or 32.6 light years away from the Earth.
Now, we know that from the inverse square law for light, the ratio of its brightness at 10 parsecs to its brightness at any known distance d (in parsecs) is given by : B10/Bd=(d/10)2.
And like the formula above its absolute magnitude is:
Mv = m - 2.5 log[ (d/10)2 ].
Stars farther than 10 pc have Mv more negative than m so there is a minus sign in the formula.
1) Now it is given that the apparent magnitude of Star M is -1.0 and its absolute magnitude is +2.0.
We know that how bright a star looks depends on two things: on how bright the star really is and it depends on how far away the star is. If the distance increases,stars become fainter because brightness of a star is inversely proportional to its distance. As the star is moved 10times further away, its distance increases so its apparent magnitude will decrease or beome smaller and its absolute magnitude number would also decrease or become smaller.
2) Here, Star N is at a distance of 4 Parsecs away. Its apparent magnitude is given as +3.0. We have to find out its absolute magnitude.
We can find it out by the formula:
d = (10 pc) x 10(m-Mv)/5 where, d is the distance, Mv is the absolute magnitude and m stands for apparent magnitude. Putting the values we get,
4 = 10pc x 10(3-Mv)/5
or, 4/10 = 10(3-Mv)/5
Taking log on both sides we get,
log(4/10) = log 10(3-Mv)/5
Now we know, log 10 base 10 = 1,
or-0.39794 = (3 - Mv)/5
or,-0.39794 * 5 = 3 - Mv
or, -1.9897 = 3 - Mv
or, Mv = 1.0103
3) The luminosity of a bigger star is larger than a smaller star at the same temperature. We can use this relation to get another important characteristic of a star that is if we measure the apparent brightness, temperature, and distance of a star, we can determine its size. The luminosity depends on:
(a) the size of the star : for a star with a certain surface temperature the bigger the star the more energy it gives out. A star with double the radius of another one will have an area four times as great and so have a luminosity four times greater than the first star
(b) the temperature of the star : for a star of a certain size the hotter the star the more energy it gives out and so the greater its luminosity. A star with a temperature of double another one will have a luminosity sixteen times greater.
Here, according to question, Star Q and Star R has the lame luminosity but the surface temperature of Star Q is less than that of Star R. As, the luminosity is directly proportional to both the surface area and the temperature of a Star, to maintain the same luminosity, Star Q should have a higher surface area than Star R because the surface temperature of Star R is more. So the correct option is (b) Star Q