Astronomy | Astrophysics Answers

Two stars of declinations 56◦ 30` 10`` and 56◦ 30` 50`` are used for observation with a
zenith tube. After observation of the first star, the instrument is rotated through 180◦ and in order to
observe the transit of the second star, the micrometer needs to be turned by 0·4 of a thread in a direction moving the wire away from the zenith. If the plate scale of the telescope is 30 seconds of arc per mm and the pitch of the thread 1 turn per mm, what is the latitude of the observing station?

A lens suffers from spherical aberration. Its diameter is 200mm and it has focal lengths of 990 mm for rays incident at the edge of the lens and 1000 mm for rays 50 mm away from the optic axis.
(i) What is the position of the plane which contains the circle of least confusion?
(ii) What is the size of the image in this plane?

A 400 cm diameter lens has focal lengths in the blue and red regions of the spectrum given by: FB = 2995 mm, FR = 3000 mm.
(i) What is the value of the focal length corresponding to the position of the circle of least
confusion?
(ii) What is the linear size of the image of a star at its focal position?

At 6300 ˚A (630 nm) the flux from a source is 10−18 W m−2 ˚A−1. Determine the photon rate passing through a telescope aperture with D = 2·2 m over a wavelength interval of 100 A˚ . Calculate the best possible S/N ratio of a measurement with an integration time of 30 s.

At an observing site the brightness of the night sky background per `` is equivalent to a 21st magnitude star. In the search for a faint object a telescope scans the sky with a field of view limited to 200 ``. Calculate the equivalentmagnitude of the star matching the total effective brightness of the sky background.

When a telescope is pointed to two stars in turn, the received power is 5·3 × 10−14 W and 3·9 × 10−14 W. What is the difference in apparent magnitude of these stars?

Two stars are recorded as having a magnitude difference of 5. What is the ratio of their
brightnesses?

The artificial satellite Vanguard 1 was found to have a period of revolution of 134 minutes. It approached the Earth to distance of 660 km and receded to a distance of 4023 km. Calculate the mass of the Earth with respect to the Sun’s mass if the semi-major axis of the Earth’s orbit is 149·5 × 106 km, the radius of the Earth is 6372 km and the year contains 365·25 mean solar days.

The synodic period of Venus was found to be 583·9 days. If the length of the year is 365·25 days, calculate the sidereal period of Venus.

Calculate the Sun’s hour angle for an observer in longitude 103◦ 40` W, keeping the mean solar time of zone +7, who has made an observation of the Sun at approximate zone time 16h 30m, June 1st. The chronometer time was 23h 31m 20s, the chronometer error being 1m 10s slow on GMT. The ephemeris transit of the Sun for June 1st was 11h 57m 41s (taken from The Astronomical Almanac).