Examination December 2011
M.A. (Previous)
Mathematics
Sixth Paper
Elective-I: Spherical Astronomy
Time : 3 Hrs.M.M. : 70
Note:This Question Paper consists of 4 Sections. Read instructions carefully before attempting the Question.
Section–A
All Questions are Compulsory.101=10
1. Define Aberration.
2. What is the Physical Cause of Precession and nutation?
3. Define the dip of the horizon.
4. Define Planetary Aberration.
5. Define Diurnal Aberration.
6. Write down the Law of Refraction.
7. Write down the greatest number of eclipses possible in a year.
8. Define Solar Eclipse.
9. Write the equation of Effect of refraction on sunrise and sunset.
10. Write Bradley’s formula.
Section–B
Attempt any Ten Question from the following.102=20
11. Prove that if the declination of a star is unaffected by refraction at a given moment, the star culminates between the pole and the zenith and that the azimuth is then a maximum.
12. To find out the linear dimensions of the sun and the planets.
13. To find the Aberration in the Distance between two star.
14. Derived the formula for Planetary Aberration.
15. Find Aberration of a Star resolved in any Direction.
16. To show that apex is a point on the elliptic behind the sun.
17. To prove that Distance of the observer is .
18. To find the length of the Earth’s shadow.
19. Show that in latitude on 600N, on 21st of March, the setting sun is visible for about 69 secs. longer from the top than from the bottom of a tower 66ft., high taking the earth’s radius as 4000 miles.
20. Show that the parallax in declination of a planet observed from a place in latitude vanishes if
being the planets declination and hour angle respectively and the each being assumed spherical.
21. Find the formula for Planetary Aberration.
22. To find the angular radius of the earth’s shadow at the moon’s distance.
23. Find out the linear dimensions of the sun and the planets.
24. Two altitudes and of the sun are at an interval of time 2H, and then the positions are orthogonally.
Show that where is the sun’s declination.
25. The equatorial co-ordinates of a star on the ecliptic are and its longitude is . If and are the annual Precession in right ascension, declination and longitude respectively. Prove that
Section–C
Attempt any Two Question from the following.2×10=20
26. Show that the retardation due to parallax in the time of rising of an object of geocentric parallax P seconds of arc and of declination is seconds where being the latitude of the place.
27. To find the Parallactic equation of Ellipse.
28. If a and b are the equatorial and polar radius of the earth (assumed spherical). Show that the greatest value of the angle of vertical is
29. The angular distance between two stars which have the same latitude is , and the mean of their longitude is. Show that the increase in due to observation is where K is the constant of aberration and is the longitude of the sun.
30. Prove that
where
Section-D
Attempt any One Question from the following1×20=20
31. Obtain the differential equation for Refraction.
32. Owing to precession the interval between two consecutive transits of a star across a given meridian from a mean sidereal day. If, show that this difference vanishes if the stars longitude is given by where is the star’s latitude and is the obliquity of the ecliptic.