Introduction to Astro Physics

Trace the evolution of massive black holes from the early universe to their growth in galaxies, powering active galactic nuclei, accretion, radiative output, and dark matter in cosmic history.

Hawking argues black holes lack true horizons and preserve information. He proposes temporary horizons that entrap energy, reemerge as Hawking radiation, and carry entangled information rather than creating firewalls.

Explore the motion of black holes, including moving supermassive black holes and their velocities, accretion disks, and the methods used to measure motion amid binary systems and chaotic gravity.

Apply the power rule to differentiate functions of the form x^n, yielding n x^(n-1). Learn how differential calculus measures rate of change and handles constant terms.

Learn how to apply the product rule to differentiate functions of two parts, identify first and second functions, and compute derivatives with respect to x using explicit examples.

Apply the quotient rule to differentiate divided functions, using f(x)=u(x)/v(x) and f'(x)=(u'v - uv')/v^2, with worked examples.

Explore derivatives of trigonometric and inverse trig functions, plus hyperbolic derivatives, review key formulas, and relate high-level calculus to astronomical concepts.

Explore practical integration techniques through three examples, including the power rule for x^2, splitting rational expressions, and integrating 1/(1+x^2) via arctan.

Explore integration by substitution through three examples that transform complex functions into easier forms, using substitution and differentials, with applications in astronomy and cosmology.

Learn the integration by parts method, choose the first and second functions, and work through examples to apply the technique.

Explore the integration of rational functions by completing the square, using the example x divided by x^2+3x+4, and applying the related integration formula.

Explore the fundamental theorem of calculus and the difference between definite and indefinite integrals. Apply these techniques to astronomy and cosmology through practical examples and continuous-function considerations.

Differentiate astronomy from cosmology—astronomy studies celestial objects, while cosmology examines the universe's origin and evolution. See how the line element in spherical polar coordinates yields the cosmological metric and expansion.

Explain how redshift supports the expanding universe through Hubble's law, linking distance, redshift, and the Hubble constant. Derive the Hubble relation within Robertson–Walker cosmology.

Explore the solar system's nine planets orbiting the sun, including Mercury, Venus, Earth, Mars, Saturn, Uranus, Neptune, and Pluto, and how the sun's nuclear fusion powers heat and light.

Compare Venus and Earth by examining Venus's backward spin, Earth's 365.3-day orbit around the Sun, their 93 million mile distance, and how Earth's weather, temperature, and atmosphere support life.

Explore Mars, the fourth planet from the Sun, with polar ice caps, a dusty rocky surface, and a day of about 24 hours 30 minutes; Pluto is the dwarf planet.

Explore Jupiter, the solar system’s largest planet with a volume for about thirteen hundred planets, ten-hour days, and a twelve-year orbit, and note Neptune’s methane-blue atmosphere and Saturn’s giant status.