Predicting Lunar Eclipses

How do we model lunar eclipses?

First we look at dates that lunar eclipses have been seen. Next we find a pattern in these dates.

For example what is the pattern in these dates?

7/24/93 9:00

That was easy. They are one year apart or 365.25 days apart.
They are very important to me. They are some of my birthdays.
The 9:00am is the time we had my birthday party.

Next we create an algorithm of our pattern. First I will state it in English.

Algorithm I
To find the next birthday party, start with a birthday that you know. Add 365.25 days to that and you find the next one.

Algorithm II
To find the next birthday party, start with a birthday that you know. Add one year (365 days) and 6 hours to that and you will find the next one.

Now I will state the algorithm in math terms.
Next birthday = birthday + 365.25 days
or Nb = b + 365.25
or Nb = b + 1 year + 6 hours

If I put this algorithm into a spreadsheet the computer will predict all of my birthdays.

Practice creating this simple model. Be sure to format the cells to time. The hours are fractional parts of a day.

12 hours is .5 days.
6 hours is .25 days.
3 hours is .125 days.
You get the picture.

You can use cell references to make your algorithm more useful. First put a birthday in a cell. For example, put 7/24/93 9:00 in cell B3. We want cell B4 to predict the next party. First we need to tell the computer that the cell has a formula in it. Formula cells have to start with =. Next we want the cell to remember the date in cell B3. We reference that information by entering =B3 in cell B4. If you put =B3+7 in cell B4 it will display 7/31/93 9:00.

After your model correctly predicts the next birthday, copy the predicting cell so it will predict the next 20 parties. Now you can celebrate with me!!!

Lunar eclipses also have a pattern. The eclipse pattern is a little more of a challenge. The table below shows the lunar eclipses for the years 1901-1903. Do you see any patterns?

Explain your pattern.

Make a formula to predict an eclipse using your pattern. .

Construct a spreadsheet using your formula. .

Use your spreadsheet to predict the lunar eclipses for the years 1904 - 1909. .

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4. model2