Astrophysics

• What is the potential energy formula for two orbiting bodies?

  $E_{pot} =$$-\frac{G m_1 m_2}{r}$
• What is the kinetic energy formula for an orbiting body?

  $E_{kin} =$$\frac{1}{2} m v^2$
• Why is the total energy of a bound orbit always negative?

  Because the potential energy is greater than the kinetic energy
• What is the formula for angular momentum in an elliptical orbit?

  $L =$$r \times p$
• What happens to the velocity of a planet at aphelion in an elliptical orbit?

  It is at its minimum
• What is the escape velocity formula?

  $v_{es} =$$\sqrt{\frac{2 G M}{R}}$
• What is the SI unit of luminosity?

  Watts (W)
• What is the SI unit of flux density?

  W m$^{-2}$
• What does the apparent magnitude scale measure?

  The brightness of stars as seen from Earth
• If a star dims by 0.1 magnitudes, by what factor does its flux density change?

  Approximately 0.9
• What is the definition of a parsec?

  The distance at which the parallax angle is 1 arcsecond
• Calculate the distance in parsecs for a star with a parallax angle of 0.5 arcseconds.

  2 pc
• What is the absolute magnitude of a star?

  The magnitude it would have if viewed from 10 parsecs
• If a star has an apparent magnitude of 5 and an absolute magnitude of 2, what is its distance in parsecs?

  20 pc
• What is the formula for the distance modulus?

  $m - M =$$5 \log_{10}(d) - 5$
• What is the significance of the DART mission's impact on Dimorphos?

  It caused Dimorphos to brighten by 3 magnitudes
• If the radius of Didymos is 850 m and Dimorphos is 180 m, what is the ratio of their surface areas?

  Approximately 22.3
• What are the key differences between circular and elliptical orbits?

  • Circular orbits have constant velocity, while elliptical orbits have varying velocity
  • In circular orbits, velocity is always perpendicular to the radius, while in elliptical orbits, it is only perpendicular at perihelion and aphelion
  • Circular orbits have eccentricity e=0, while elliptical orbits have 0<e<1
• What are the key components of luminosity and flux density?

  • Luminosity (L): Total power output from an astronomical source (SI unit: W)
  • Flux density (f): Total received power per unit area at the telescope (SI unit: W m$^{-2}$)
  • Spectral flux density (S(ν)): Flux density per unit frequency interval (SI unit: W m$^{-2}$ Hz$^{-1}$)
• What are the steps to calculate the parallax angle?

  1. Measure the apparent angular shift of a star relative to a fixed background
  2. Divide the shift by 2 to get the parallax angle
  3. Use the formula $d(pc) =$$\frac{1(AU)}{p(arcsec)}$ to calculate the distance
• What are the key points about apparent and absolute magnitude?

  • Apparent magnitude (m): Brightness of a star as seen from Earth
  • Absolute magnitude (M): Brightness of a star if viewed from 10 parsecs
  • Distance modulus: $m - M =$$5 \log_{10}(d) - 5$, where d is the distance in parsecs
• What is the total energy formula for an elliptical orbit?

  $E =$$-\frac{G M m}{2a}$
• How does velocity change with distance in an elliptical orbit?

  Velocity increases as distance decreases
• What is the relationship between luminosity, flux density, and distance?

  $f =$$\frac{L}{4 \pi d^2}$
• Why is the apparent magnitude scale logarithmic?

  To match the human eye's response to brightness
• What is the conversion factor between parsecs and light years?

  1 parsec ≈ 3.26 light years
• What is the formula for absolute magnitude?

  $M =$$m - 5 \log_{10}(d) +$$5$
• What is the primary focus of the Stellarium software in the Practical Astronomy Workshops?

  To simulate the night sky and celestial objects
• What is the apparent magnitude of Comet C/2023 A3 when it was discovered at 18 AU?

  18 mag
• If Comet C/2023 A3 is now at 0.55 AU, what is its current apparent magnitude?

  6.5 mag
• Why does the calculated magnitude of Comet C/2023 A3 not match the observation that it is just under the brightness detectable to the human eye?

  Because the calculated magnitude is theoretical and does not account for atmospheric conditions or detector sensitivity
• What is the definition of a parsec?

  The distance at which the parallax angle is 1 arcsec
• Calculate the parallax angle for Proxima Centauri at a distance of 1.3 pc.

  $p =$$\frac{1}{1.3} \approx 0.77 \text{ arcsec}$
• Calculate the parallax angle for the Hyades cluster at a distance of 47 pc.

  $p =$$\frac{1}{47} \approx 0.021 \text{ arcsec}$
• Calculate the parallax angle for the Andromeda Galaxy at a distance of 875 kpc.

  $p =$$\frac{1}{875,000} \approx 1.14 \times 10^{-6} \text{ arcsec}$
• What is the absolute magnitude (M) of a star?

  The magnitude a star would appear to have if viewed from a standard distance of 10 pc
• What is the distance modulus formula?

  $m - M =$$5 \log_{10}(d) - 5$
• What are the primary colors used to create colors in TV and mobile images?

  Red, green, and blue
• What is the effect of red-green blindness on color perception?

  It is an issue with detector sensitivity, affecting the ability to distinguish between red and green
• What is the unit used to measure the solar spectrum?

  Angstrom (Å)