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Problem A.3 :
The stellar parallax of the star Arcturus in the constellation Boötes was measures with 0.0900
.
(a) Calculate the distance (in parsec) between Arcturus and the Earth.
(b) How long does it take to send a light message from Earth to Arcturus?

For a special mission to Mars you need to know the smallest distance between Earth and Mars.
However, you have lost your astronomy book and you could only find these values:
Distance Earth to Sun: 149.6 million km
Orbital period Earth: 1.00 years
Orbital period Mars: 1.88 years
By using these values and assuming that Mars and Earth move an circular orbits, calculate the
smallest possible distance between Earth and Mars.
Calculate the magnitude of the faintest object that can be detected by an optical telescope of diameter 5.0 m.
Calculate the half-width of a spectral line of wavelength λ = 550 nm when the
temperature of the gas is 6 × 105 K. Assume H atoms to be emitters.
The mass and radius of a neutron star is 2MΘ and 15 km, respectively. Calculate the
value of gravitational red shift for light of wavelength 6000
oA
at a distance of 2 m
from its surface.
Obtain an expression for the radial velocity of objects in the galaxy as a function of their
galactic longitude.
The mass and radius of a neutron star is 2MΘ and 15 km, respectively. Calculate the
value of gravitational red shift for light of wavelength 6000
oA
at a distance of 2 m
from its surface.
Write down the condition under which a large molecular cloud collapses to give rise
to new stars. Calculate the time of free fall of an HI cloud of density 106 particles/m3
What is the nature of radiation generated in the Sun’s interior? How does it differ
from the radiation we receive from the Sun?
Explain what you understand by the apparent magnitude of a star. How is it related
to the brightness of the star? An object A has an apparent magnitude of –5. Another
object B has an apparent magnitude of –10. Calculate the ratio of their brightness
Explain why we expect the gas in elliptical galaxies to be hot.
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