Lecture Notes: Apparent and Absolute Magnitudes

Key Concepts

Apparent Magnitude

• Describes how bright a star appears from Earth.
• Influenced by:
  • True Power (Luminosity) of the star.
  • Distance from the observer.
• Larger apparent magnitude values indicate dimmer stars.
• Apparent magnitude is denoted as m.

Absolute Magnitude

• A hypothetical measure of a star's brightness if it were 10 parsecs away.
• Not affected by distance.
• Reflects the true power (luminosity) of a star.
• Denoted as M.

Mathematical Concepts

Logarithms

• Log base 10 examples:
  • Log(10) = 1
  • Log(100) = 2
  • Log(1000) = 3
• Exponential representation:
  • 10 = 10^1
  • 100 = 10^2
  • 1000 = 10^3
• The exponent value is the logarithm of the number.

Problem Solving: Calculating Absolute Magnitude

Given:

• Apparent magnitude (m) = 5
• Distance (D) = 1000 parsecs

Formula to calculate absolute magnitude (M):

[ M = -5 \times \log(D) + 5 + m ]

Steps:

1. Substitute values:
   • Log(1000) = 3
   • m = 5
2. Calculation:
   • [ M = -5 \times 3 + 5 + 5 ]
   • [ M = -15 + 5 + 5 ]
   • [ M = -5 ]

Interpretation

• Absolute magnitude M = -5 indicates an incredibly bright star.
• Even at 1000 parsecs, a star with apparent magnitude 5 would still be visible to the naked eye if its absolute magnitude is -5.

Conclusion

• Absolute magnitude provides a measure of a star's true brightness or luminosity.
• A negative absolute magnitude implies a very bright star.

Example Confusion

• Misprint in the homework: Question 18 should reference the star from Question 17, not 11.
• The calculated distance of 1000 parsecs is crucial for solving the problem.