The formula to calculate the Brightness Ratio (R) is:
\[ R = 10^{\frac{m2 - m1}{2.5}} \]
Where:
Let's say the apparent magnitude of the first object (m1) is 1 and the apparent magnitude of the second object (m2) is 3. Using the formula:
\[ R = 10^{\frac{3 - 1}{2.5}} = 6.31 \]
So, the Brightness Ratio (R) is 6.31.
Definition: Apparent magnitude is a measure of the brightness of a celestial object as seen from Earth.
Formula: \( m = -2.5 \log_{10}(I) \)
Example: \( m = -2.5 \log_{10}(0.8) \)
Definition: The magnitude ratio is the ratio of the brightness of two celestial objects.
Formula: \( \frac{I_1}{I_2} = 10^{0.4(m_2 - m_1)} \)
Example: \( \frac{I_1}{I_2} = 10^{0.4(5 - 3)} \)
Definition: The absolute magnitude is the apparent magnitude of a celestial object as it would be seen at a standard distance of 10 parsecs.
Formula: \( M = m - 5 \log_{10}(d) + 5 \)
Example: \( M = 4 - 5 \log_{10}(10) + 5 \)
Definition: Apparent visual magnitude is the apparent magnitude of a celestial object in the visible spectrum.
Formula: \( m_v = -2.5 \log_{10}(I_v) \)
Example: \( m_v = -2.5 \log_{10}(0.6) \)
