Question

Since we're dealing with exponents that are fractions, let's check the spreadsheet syntax for these before you

start using them in calculations. Enter the formula in spreadsheet syntax in the input box below each formula.
Assume that luminosity input values start in column A, row 2, and temperature values start in column B, row
2.
1/3.5
Ms = Ls
Rs =
¹/2
Ls
(T/5800)²

Answer 1

In spreadsheet syntax, the formula for calculating the mass from luminosity is =POWER(A2,1/3.5) and for radius given luminosity and temperature is =POWER(A2, 0.5)*POWER((B2/5800), 2); both are relative to the Sun's values.

When working with the luminosity and temperature of stars, we can express them in units relative to our Sun's mass (M/M Sun) and luminosity (L/L Sun). To find the mass of a star based on its luminosity, we use the mass-luminosity relation, which states the luminosity of a star is proportional to the mass to the power of approximately 3.9. In spreadsheet syntax, if you have luminosity values in column A starting from row 2, and temperature values in column B, also starting from row 2, the formulas would be expressed as follows:

For the mass-luminosity relationship (not considering the exponent 3.9 for simplicity), you’d use:

=POWER(A2,1/3.5) for the mass from luminosity.

For the radius-luminosity-temperature relationship, the formula in spreadsheet syntax would be:

=POWER(A2, 0.5)*POWER((B2/5800), 2) for the radius from luminosity and temperature.