Reflective vs. Refractive Telescopes

Telescopes: Reflection vs. Refraction

• Reflective telescopes use the change in light direction upon reflection to focus light from space onto a focal spot.
• Refractive telescopes use the change in light direction when light moves from one medium to another to focus light from space onto a focal spot.
• Refractive telescopes use lenses to bend and focus light.
  • They are less common now due to engineering difficulties with large, heavy lenses that are difficult to support, potential image blurring from imperfections, the need for a long tube to reach the focal point, and chromatic aberration (where different colors refract differently).
• Reflective telescopes use mirrors to reflect and focus light.
  • They are more common now because mirrors do not require the same level of perfection as lenses, can be supported from behind, and can be designed with shorter focal lengths for more compact designs.

Advantages of Telescopes

• Telescopes gather more light than the naked eye.
• They provide higher resolution for finer detail.
• Telescopes magnify distant objects.
• They can collect light outside the visible range, increasing sensitivity.

Light Gathering Power

• Light gathering power is determined by the collecting area of the telescope's aperture.
• A larger aperture allows for collection of more light.
• Radio telescopes collect and focus radio waves, requiring very large reflectors due to the long wavelengths of radio waves.
• Large mirrors can be created using multiple smaller mirrors precisely aligned with lasers.

Telescope Resolution

• When light waves pass through a small opening, they diffract, spreading out the light from a small point.
• Resolution is the smallest angular separation at which two points of light can still appear separated.
  • A small angular separation represents high resolution.
• Angular separation (θ) = $2.5 * 10^5 *$ [wavelength (λ) / telescope diameter (D)].
• Atmospheric refraction of interstellar light limits resolution, causing stars to twinkle.
• High resolution in radio telescopes is achieved by using multiple smaller telescopes in tandem as one large telescope.

Capturing Images

• Photographic film, used from the 1850s, captured only 2% of incoming photons.
• Charge-coupled devices (CCDs) record digital images and capture 95-98% of incoming photons.
  • CCDs have pixels that accumulate electrons when struck by photons.
  • The amount of electric charge in each pixel is measured to produce the digital image.
• CCDs do not inherently detect color; they record the number of photons.
  • Color images are made by using filters that only allow certain wavelengths through.
  • Red, green, and blue filters are often used on alternating pixels to create color images.
• False-color images use artificial colors to represent different emissions, including those outside of the visible range.

Space Telescopes vs. Ground Telescopes

• Space telescopes offer sharper images by avoiding atmospheric refraction.
• They can observe parts of the electromagnetic spectrum that are absorbed by the atmosphere.

James Webb Space Telescope (JWST)

• It is an infrared reflecting telescope.
• It orbits the Sun along with Earth, with its own small orbit.
• The Earth blocks sun rays protecting the mirror from damage, and the solar panels are always facing the sun.
• A large sunshield keeps sunlight off the telescope to maintain a low temperature, preventing its own infrared glow from overwhelming observations.

Planetary Motion

• Planets orbit in nearly the same plane.
• Their orbits appear as concentric circles around the Sun, following the ecliptic.
• Planets move relative to background stars, sometimes exhibiting retrograde (backward) motion.

Kepler's Laws

• Planets orbit the Sun in ellipses, with the Sun at one focus.
• A planet moves faster when closer to the Sun and slower when farther away, sweeping out equal areas in equal times.
• Distant planets take longer to orbit the Sun, following the relationship: $P^2 = a^3$ (orbital period squared equals semi-major axis cubed).

Explaining Planetary Motion

• The heliocentric model places the Sun at the center, with planets in circular orbits.
  • It originally failed to explain retrograde motion.
• Kepler's Laws explain retrograde motion: Earth orbits the Sun faster than planets at larger distances, so when Earth passes Mars (or another outer planet), Mars appears to move backward briefly.

Newton's Laws

• Inertia: A body remains at rest or in uniform motion unless acted upon by a net force.
• Force = mass * acceleration: More force is required to accelerate a larger mass.
• Action-reaction: For every action, there is an equal and opposite reaction.

Conservation Laws

• Conservation of momentum: The total momentum of interacting objects remains constant unless acted upon by an external force.
• Conservation of angular momentum: The total angular momentum of a system remains constant unless acted upon by an external torque.
• Conservation of energy: Energy cannot be created or destroyed, only transformed.

Gravity

• Gravity holds Earth's atmosphere, causes planets to orbit the Sun, formed the solar system from a cloud of gas and dust, and binds stars into galaxies and galaxies to each other.

Newton's Universal Law of Gravity

• Every mass attracts every other mass.
• The force is directly proportional to the product of the masses and inversely proportional to the square of the distance between them.
• Larger masses and closer objects exert greater gravitational pulls.

Classifying Stars

• Classifying stars helps reveal underlying physical processes.

Key Properties of Stars to Know

• Distance: Measured using parallax, the apparent shift in a star's position when viewed from different points in Earth's orbit.
  • A longer baseline results in a bigger shift.
• Luminosity: Actual brightness of a star, distinguished from apparent brightness, which depends on distance.
• Surface temperature: Determined from the peak wavelength of a star's thermal-continuous spectrum and the absorption lines in the star's photosphere.

Hertzsprung-Russell (H-R) Diagram

• Stellar luminosity vs. temperature.
• Main sequence: Most stars (including the Sun) spend most of their lives fusing hydrogen into helium, with more massive stars being hotter and more luminous.
• Supergiants and giants: More luminous than main sequence stars of the same temperature, implying larger radii.
• White dwarfs: Less luminous than main sequence stars of the same temperature, implying smaller radii.

Binary Stars

• Gravity can be measured using masses.
• Binary stars orbit around their center of mass, which is closer to the more massive star.
• Visual binary: Individual stars are resolvable.
• Spectroscopic binaries: Orbital motion is revealed in the combined spectrum.
• Eclipsing binaries: Brightness changes occur when stars eclipse each other.
  • $𝛿=𝜋R_B^2/𝜋R_A^2$: This is the formula to calculate the decrease in brightness when the smaller star (B) eclipses the bigger star (A).
• Main sequence stars range in radius from 0.1 to 10 times the Sun's radius.
• Giant and supergiant stars range in mass from 1 to 100 times the Sun's mass but have radii up to 1000 times the Sun's radius.

Star Formation

• Stage 1: Molecular Clouds: Dense, cold interstellar clouds where dust blocks starlight, causing the temperature and pressure to drop as molecules emit photons.
• Stage 2: Cloud Collapse: The cloud collapses when gravity overpowers pressure.
  • Gravitational potential energy converts to kinetic energy, which then converts to radiative energy.
  • The cloud forms a thin, rotating disk as it collapses.
• Stage 3: Protostar and Protostellar Disk: The central part of the cloud becomes a protostar when it is dense enough that radiation can no longer escape easily.
  • Matter still flows onto the protostar through the protostellar disk.
  • Protostars maintain hydrostatic equilibrium.
  • The protostar shines by converting gravitational energy into thermal energy but is shrouded in gas and dust, visible in infrared light.
• Stage 4: Star: Fusion of hydrogen begins when the core temperature and pressure are high enough.
  • Fusion energy stops collapse.
  • Radiation blows away surrounding gas and dust, stopping accretion.
  • The star moves onto the main sequence.

Star's Mass and Evolution

• A star's mass determines its future evolution.
• Main sequence lifetime depends on the amount of fuel and the rate of fusion: lifetime = mass / luminosity.
• More mass means more rate of fusion and shorter lifetime.
• The star eventually runs out of Hydrogen.