Question

Calculating Luminosity How should this formula be entered in a spreadsheet if the first luminosity input value is in column A, row 2 and the first distance value is in column B, row 2? F = L 4nd² Tips and Sample Calculation What is the flux for a planet orbiting at 4.5 au around a 8.4 Ls star? Convert 4.5 au to meters: 4.5 au x 1.496 x 10¹¹ m = 6.73 x 10¹¹ m Convert 8.4 Ls to watts: 8.4 Ls x 3.827 x 1026 W = 3.215 x 10²7 W Flux: 3.215 x 10²7 W/(4 x πx (6.73 x 10¹¹ m)²) = 564.9 W/m² Spreadsheet tips: • Place numbers and reference cell IDs in the same order in which they appear in the formula. These conversion formulas should already be in your spreadsheet so make use of them. Start the formula with= Use for multiplication. Use / for division. Enclose the entire denominator in (). • Use reference cell IDs for the location (column and first row) of the luminosity and distance input values. Spreadsheets do not have a symbol for pi, you have to spell it out. The spreadsheet will add () after the word pi so it will look like this: pi(). You don't need to enter anything between the (). Use^ to denote that the distance is squared. While the entire denominator should be in (), only distance is squared so nothing that comes before the ^2 should be grouped together in (). • Make sure your formula functions like you expect by plugging the input values from the sample calculation above into your spreadsheet. X

Answer 1

the flux (luminosity) for a planet orbiting at 4.5 au around an 8.4 Ls star is approximately 0.0332 W/m².

To calculate luminosity (F) using the formula F = L / (4 * π * d²), where L is luminosity and d is distance, and you want to enter this formula into a spreadsheet where the luminosity value is in cell A2 and the distance value is in cell B2, you can set it up as follows:

1. In the cell where you want to calculate the flux (luminosity), enter the following formula:

=F2 / (4 * PI() * B2^2)

Here's a breakdown of the formula components:

- `F2` refers to the luminosity value in cell A2.

- `B2` refers to the distance value in cell B2.

- `PI()` is used to represent the mathematical constant pi (π).

- `^2` denotes that the distance should be squared.

2. Press Enter to calculate the flux (luminosity) for the given values.

Now, you can use this formula for any other set of luminosity and distance values by replacing the cell references (F2 and B2) with the appropriate cells containing your data.

For the sample calculation you provided (planet orbiting at 4.5 au around an 8.4 Ls star):

- Luminosity (L) = 8.4 Ls

- Distance (d) = 4.5 au

Using the formula in your spreadsheet:

=F2 / (4 * PI() * B2^2)

=8.4 / (4 * PI() * 4.5^2)

Now, calculate this value to find the flux (luminosity) for this specific case:

=8.4 / (4 * PI() * 20.25)

=8.4 / (4 * 3.14159265359 * 20.25)

=8.4 / (253.598441104)

≈ 0.03316950992 W/m²

So, the flux (luminosity) for a planet orbiting at 4.5 au around an 8.4 Ls star is approximately 0.0332 W/m².