Phys 1403Stellar Magnitudes and ParallaxRev53. Suppose star A is barely visible through a 15-cm telescope and star B is barely visible through a60-cm telescope.a.Which star is brighter and by how much?b. What is the approximate difference in magnitudes of the two stars?c. What is the limiting visual apparent magnitude of a 60-cm telescope?d. What is the limiting visual apparent magnitude of a 15-cm telescope?Note that the difference in limiting magnitudes of the two telescopes is approximately thesame as the difference between the magnitudes of the dimmest stars that can be seen by them.4. The apparent magnitude of the Sun is -26.7 and that of Sirius is -1.4. How many stars as brightas Sirius would be required to supply as much light as the Sun?4. 3.Rev5Phys 1403Stellar Magnitudes and ParallaxSince the minimum brightness visible will be inversely proportional the LGP we can then write:LGP(D) D L(7) -(2.512)LGP(1)(m)7as long as m 7. ThenD =(2.512)*Take the logarithm of both sides of this equation:2 log D 0.4( m- 7)Solve this equation for m:m =7+5 log D(3)This equation represents the limiting magnitude (dimmest star) visible by a telescope of diameter D.ExampleFor a 100-cm telescope, the limiting visual apparent magnitude ism =7+5log(100) =7+5(2) =17Problems1. Photometric comparison shows that the star Mizar, magnitude 2.4, is 4.37 times a bright as itscompanion Alcor. What is the magnitude of Alcor?2. The variable star Algol declines from a magnitude of 2.2 at a maximum to a magnitude of 3.4 at aminimum. What is the ratio of the brightness at maximum to that at minimum?

Question

Phys 1403Stellar Magnitudes and ParallaxRev53. Suppose star A is barely visible through a 15-cm telescope and star B is barely visible through a60-cm telescope.a.Which star is brighter and by how much?b. What is the approximate difference in magnitudes of the two stars?c. What is the limiting visual apparent magnitude of a 60-cm telescope?d. What is the limiting visual apparent magnitude of a 15-cm telescope?Note that the difference in limiting magnitudes of the two telescopes is approximately thesame as the difference between the magnitudes of the dimmest stars that can be seen by them.4. The apparent magnitude of the Sun is -26.7 and that of Sirius is -1.4. How many stars as brightas Sirius would be required to supply as much light as the Sun?4. 3.Rev5Phys 1403Stellar Magnitudes and ParallaxSince the minimum brightness visible will be inversely proportional the LGP we can then write:LGP(D) D L(7) -(2.512)LGP(1)(m)7as long as m> 7. ThenD =(2.512)*Take the logarithm of both sides of this equation:2 log D 0.4( m- 7)Solve this equation for m:m =7+5 log D(3)This equation represents the limiting magnitude (dimmest star) visible by a telescope of diameter D.ExampleFor a 100-cm telescope, the limiting visual apparent magnitude ism =7+5log(100) =7+5(2) =17Problems1. Photometric comparison shows that the star Mizar, magnitude 2.4, is 4.37 times a bright as itscompanion Alcor. What is the magnitude of Alcor?2. The variable star Algol declines from a magnitude of 2.2 at a maximum to a magnitude of 3.4 at aminimum. What is the ratio of the brightness at maximum to that at minimum?

Accepted Answer

(1)
Given:
The magnitude of Mizor is 2.4.
The brightness of Mizor in companion to Alcor is 4.37…