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I have this code for calculating the number of days passed from a given year:

for (int currentYear = localDate.getYear() - 1; currentYear >= STARTING_YEAR; currentYear--){
            LocalDate date = LocalDate.of(currentYear,5,5); //an arbitrary day of year
            jdn += date.lengthOfYear();
        }
jdn += localDate.getDayOfYear();

This code is working as expected.

I am not comfortable with choosing an arbitrary day to only get the length of the year. Is there any better approach?

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Your code scales poorly if there are many years between STARTING_YEAR and localDate.

Worse, if localDate occurs before the STARTING_YEAR, then your code behaves as if STARTING_YEAR is the same year as localDate, which is weird behavior.

To calculate the number of days between two dates, use DAYS.between().

import java.time.LocalDate;
import static java.time.temporal.ChronoUnit.DAYS;

…    
long jdn = 1 + DAYS.between(LocalDate.ofYearDay(STARTING_YEAR, 1), localDate);

The 1 + is necessary because the convention when subtracting dates is inclusive-exclusive, whereas your code uses an inclusive-inclusive range.

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