PHE-15 Solved Assignment January 2026 | ASTRONOMY AND ASTROPHYSICS | IGNOU BSC

Q: Answer the following questions:

Answer available — download the full PDF for complete details.

Q: Answer the following questions:

Answer available — download the full PDF for complete details.

Q1. Answer the following questions:

(a)) The distance of planet Jupiter from the Sun is 5 AU. Express this distance in light year and parsec. (200 words)
(b)) Calculate the ratio of the surface temperatures of the stars 1 and 2 from the following data: Star 1: Absolute magnitude 2, Radius (RO) 64; Star 2: Absolute magnitude 7, Radius (RO) 4. (200 words)

Key Points:

1 AU = 1.496 × 10⁸ km is the standard astronomical unit.
1 light year is the distance light travels in one year (approx. 9.468 × 10¹² km).
1 parsec = 3.26 light years, a larger unit for stellar distances.
Absolute magnitude difference relates to luminosity ratio: M₂ - M₁ = -2.5 log₁₀(L₂/L₁).

Answer: The following response addresses two fundamental questions in astronomy and astrophysics: converting astronomical distances between common units and calculating the ratio of stellar surface temperatures using absolute magnitudes and radii. Both tasks require the application of key astronomical formulas and constants, as typically covered in the PHE-15 course. Understanding these concepts is crucial for comprehending the vast scales and physical properties of celestial objects.

Q2. Answer the following questions:

(a)) Show the horizon coordinates of a star X on a celestial sphere for a location at latitude 30° N. Would these coordinates be the same at latitude 45° N? (200 words)
(b)) Why do X-ray telescopes need to be placed beyond the Earth's atmosphere? Which telescope, optical or X-ray, would have higher resolving power for the same aperture? Calculate the magnitude of the faintest object that a 10 m optical telescope can detect. (200 words)

Key Points:

Horizon coordinates (altitude, azimuth) are local to an observer's position and time.
Changing an observer's latitude directly alters an object's horizon coordinates.
Earth's atmosphere absorbs cosmic X-rays, requiring space-based X-ray telescopes.
Resolving power (angular resolution) is inversely proportional to wavelength.

Answer: The following answers address the properties of celestial coordinate systems, atmospheric effects on astronomical observations, and fundamental telescope characteristics like resolving power and limiting magnitude, as commonly covered in Astronomy and Astrophysics courses like PHE-15. These concepts are crucial for understanding how we observe and study the universe from different locations and across various electromagnetic spectra.

Q3. Answer the following questions:

(a)) A main sequence star has mass 2x10^31 kg and radius 3x10^9 m. Obtain an estimate of the average temperature throughout the star. Examine if Newton's theory would be adequate for the study of this star. (200 words)
(b)) Explain how sunspots survive for so long even though they are surrounded by hotter matter. (200 words)

Key Points:

Stellar average temperature estimated using Virial Theorem: T_avg = (G M μm_p) / (5 k R).
Main sequence star temperature is millions of Kelvin, primarily from nuclear fusion.
Newtonian gravity is adequate for main sequence stars; general relativity is minor correction.
Sunspots are cooler regions due to strong magnetic fields inhibiting convection.

Answer: As an expert IGNOU tutor, I will answer the questions regarding a main sequence star's temperature and the survival of sunspots, drawing upon fundamental concepts in astronomy and astrophysics as taught in the PHE-15 course. Each sub-question will adhere to its specific word limit and structural requirements. For the main sequence star, we will estimate its average temperature using the virial theorem, which links its gravitational potential energy to its internal kinetic (thermal) energy. We w...

Q4. Answer the following questions:

(a)) The mean distance of Mars from the Earth is 0.5 A.U. and its orbital period is 687 days. Calculate the orbital period of Jupiter given that its mean distance from the Earth is 4 A.U. (200 words)
(b)) A star has surface temperature of 25000 K. Which lines would be prominent in its spectrum and why? (200 words)

Key Points:

Kepler's Third Law (P² ∝ a³) relates orbital period to semi-major axis for orbiting bodies.
Jupiter's orbital period was calculated as approximately 15535.5 days using given data and Kepler's Law.
A star with a 25000 K surface temperature is classified as a B-type star.
Prominent spectral lines in B-type stars include neutral helium (He I) and singly ionized helium (He II).

Answer:

Q5. Answer the following questions:

(a)) Derive the following expression for the mean temperature in a star: <T> x M^2/3 <p>^1/3. Will this result apply to a star which is not in equilibrium? (200 words)
(b)) The mean free path of photons in stars is of the order of 0.2 cm. Show that the time taken for a photon to reach the surface of a star of radius 4 Re is of the order of one million year. (200 words)

Key Points:

Virial Theorem: 2K + Ω = 0 governs stars in hydrostatic equilibrium.
Mean stellar temperature <T> is proportional to M^(2/3) <ρ>^(1/3).
This temperature-mass-density relation applies only to stars in equilibrium.
Photons escape stars via a random walk due to continuous scattering.

Answer: This response addresses two fundamental aspects of stellar astrophysics: the derivation of the mean temperature within a star based on its mass and density, and the calculation of the photon diffusion time from a star's core to its surface. Both concepts are crucial for understanding stellar structure and energy transport. The first part employs the Virial Theorem and the ideal gas law, while the second part uses the random walk model for photon transport. Sub-question (a) delves into the theor...

Q6. Answer the following questions:

(a)) Describe the composition of the interstellar medium. Explain how it has been possible to map the HI clouds. (200 words)
(b)) 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 10^8 particles / m^3 if the collapse is adiabatic. (200 words)

Key Points:

ISM comprises 99% gas (H, He, trace elements) and 1% dust in various phases.
HI clouds are cold neutral hydrogen, crucial for galactic structure and star formation.
21 cm (1420 MHz) spin-flip transition radiation maps HI clouds across galaxies.
Doppler shift of 21 cm line reveals HI cloud velocities and spatial distribution.

Answer: The interstellar medium (ISM) is the matter and radiation that exists in the space between the star systems within a galaxy. It is a dynamic and complex environment, fundamental to star formation and galactic evolution. Understanding its composition and dynamics, such as the distribution of HI clouds, is crucial for astrophysical studies. Star formation is a direct consequence of the ISM's gravitational collapse, governed by conditions like the Jeans instability. The free-fall timescale provide...

Q7. Answer the following questions:

(a)) Explain the meaning of a degenerate gas. A white dwarf star has a mass of 10^30 kg. Its luminosity is 10^24 Js^-1. Calculate how long it can survive with its present luminosity if its internal temperature is 10^7 K. (200 words)
(b)) How long will a 5 M☉ star burn hydrogen as fuel, given that the Sun will do so for about 10^10 years? (200 words)

Key Points:

Degenerate gas: High-density matter where Pauli Exclusion Principle creates quantum degeneracy pressure, independent of temperature.
White dwarfs are supported by electron degeneracy pressure and cool by radiating internal thermal energy from non-degenerate ions.
White dwarf cooling time (survival): Calculated as total thermal energy (mainly ionic) divided by its luminosity.
Stellar main sequence lifetime (τ) is inversely proportional to its mass (M) raised to a power, typically τ ∝ M^(-2.5).

Answer: This response addresses the nature of degenerate gases and applies astrophysical principles to calculate stellar lifetimes, a core concept in stellar evolution. The calculations are based on standard astrophysical relations commonly covered in introductory astronomy and astrophysics courses like PHE-15. Detailed step-by-step solutions are provided for clarity. Each sub-question is answered within its specified word limit, using precise terminology and focusing on the essential concepts and cal...

Q8. Answer the following questions:

(a)) Obtain an expression for the radial velocity of objects in the galaxy as a function of their galactic longitude. (200 words)
(b)) Distinguish between an active galaxy and a normal galaxy. Describe the classification of active galaxies. (200 words)

Key Points:

Radial velocity due to differential galactic rotation depends on distance and galactic longitude.
Radial velocity (solar neighborhood) = A d sin(2l), where A is Oort's constant.
Normal galaxies are stellar-luminosity dominated; active galaxies have luminous non-stellar nuclei.
Active galaxies are powered by accretion onto a supermassive black hole.

Answer:

Q9. Answer the following questions:

(a)) Describe Hubble's Classification scheme for galaxies. How bright were the galaxies which were included in the classification scheme? (200 words)
(b)) An electron is moving with a speed of 0.9c in a magnetic field of strength 10^9 G. Calculate the peak frequency at which the electron will radiate. (200 words)

Key Points:

Hubble's scheme classifies galaxies morphologically into ellipticals (E0-E7), spirals (Sa-Sc, SBa-SBc), S0, and irregulars.
Elliptical galaxies are smooth, lack arms, and contain old stars; spirals have bulges and arms with active star formation.
Hubble's initial classification included relatively bright, large, and nearby galaxies visible with early telescopes.
Synchrotron radiation is emitted by relativistic electrons in magnetic fields.

Answer: The following response addresses Hubble's galaxy classification scheme, including the types of galaxies classified and their general brightness, and then proceeds to calculate the peak radiation frequency for a highly relativistic electron in a strong magnetic field, detailing the steps and relevant physical principles. Hubble's classification is a foundational scheme in extragalactic astronomy, categorizing galaxies based on their visual morphology. It provides a systematic way to study the st...

Q10. Answer the following questions:

(a)) What is cosmic background radiation? Explain why it is so important to the debate between and evolving and a steady-state universe. (200 words)
(b)) If the temperature of the background radiation today is 3 K, at what time after the birth of the universe was the temperature 10^15 K. Take the age of the universe as 15x10^9 years. (200 words)

Key Points:

Cosmic Microwave Background Radiation (CMBR) is relic radiation from the Big Bang.
CMBR formed during recombination (~380,000 years post-Big Bang) when the universe became transparent.
CMBR today is a near-perfect blackbody spectrum at ~2.725 K, with slight anisotropies.
CMBR discovery in 1964 decisively supported the Big Bang model over the Steady-State model.

Answer:

PHE-15 Solved Assignment — January 2026 / July 2026

ASTRONOMY AND ASTROPHYSICS | IGNOU foKku esa Lukrad mikf/k dk;ZØe (ch-,l-lh-) (BSC)

PHE-15—January 2026 / July 2026

ASTRONOMY AND ASTROPHYSICS

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