User:JonathanSun218/sandbox/astronomical algorithms

Astronomical algorithms are sets of formulas that can be used to calculate calendars, determine positions of objects in space, and improve technologies in the medical field. Used since the 16th century, astronomical algorithms are still used today and have slowly been developing. They are able to provide essential information that people use every day such as determining dates, which people can then use to plan their schedules ahead and maximize their efficiency. People also use devices like the GPS, which use astronomical algorithms to obtain coordinates and guide people to their destinations.

Trigonometric Functions

Astronomical calculations often contain large angles. For instance, a large angle can be written as the sine of 36 000 030 degrees, which simply results to 0.5. To make calculations easier, converting them to the range between 0 to 360 degrees is highly advised. Astronomical algorithms also deal with right ascensions, which are generally expressed in hours, minutes, and seconds of time. (One hour corresponds to 15 degrees).

Example:

Calculate tan α, where α = 9h 14m 55.8s. h = hours, m = minutes, s = seconds

First, convert α to hours and decimals. (There are 60 minutes in an hour and 3600 seconds in an hour).

9h 14m 55.8s = 9 + (14 / 60) + (55.8 / 3600) = 9.248833333 hours.

Then multiply by 15 because one hour corresponds to 15°.

9.248833333 * 15 = 138.73250°.

Dividing this value by (180 / pi) converts the answer from degrees to radians. 138.73250 / (180 / pi) = 57.295779513.

Ultimately, tan α results in -0.877517.

Gregorian Calendar

The Gregorian Calendar, the most commonly used calendar throughout many countries, is calculated through the use of astronomical algorithms. It is a reform of the Julian Calendar, which is the predominant calendar in the Roman world, most of Europe, and in European settlements in America. Introduced in 1582, the Gregorian Calendar implements leap years to maintain each year to be 365 days long. The solar day is the basic unit of all calendars because the alteration of day and night is repetitive and countable.

Resurrection of Easter

The Julian Calendar was slightly too long, which ultimately led to Easter drifting toward early March and away from its original time (usually the first Sunday after the first Full Moon occurring on or after the March equinox). Although the Gregorian Calendar was developed as an improvement of the Julian Calendar, it did not resolve the issue of Easter shifting away. Pope Pius V invented a system with adjustments and the introduction of leap years. Eventually, all it was settled that Easter would be celebrated one universal day. With that idea established, astronomical algorithms are implemented to calculate the dates of each Easter. A new a table of New Moons and Full Moons was also introduced to help determine the dates of Easter.

Astronomical Algorithm for Easter

This algorithm computes the date of Easter. It is important to note that all variables are integers, meaning that the remainders of all divisions are dropped from the answer. The input variable is the Gregorian year, Y. The output (final answer) is given by month, M, and day of the month, D.

C = Y / 100

N = Y - 19 * (Y / 19)

K = (C - 17) / 25

I = C - (C / 4) - ((C - K) / 3) + 19 * N + 15

I = I - 30 * (I / 30)

I = I - (I / 28) * (1 - (I / 28) * (29 / (I + 1)) * ((21 - N) / 11)

J = Y + (Y / 4) + I + 2 - C + (C / 4)

J = J - 7 * (J / 7)

L = I - J

M = 3 + (L + 40) / 44

D = L + 28 - 31 * (M / 4)

Pinpointing Locations

Astronomical algorithms are used to determine geocentric coordinates. They are coordinates that refer to a coordinate frame whose origin is at the center of mass of the Earth and whose fundamental planes are the equator. The frame also uses a system of rectangular coordinates (x, y, z) or of spherical coordinates (longitude, latitude, and radial distance). This is extremely valuable to organizations such as the military for developing strategies and locating enemy territories. To this day, those in the NATO military are required to learn and use the Military Grid Reference System to locate points on the earth, which are derived from using astronomical algorithms.

Longitude is measured positively east and usually set from ± 180°. Latitude is measured from the equator (0°) to ± 90°, positively to the north.

Astronomical Almanac

The military, specifically the US Navy, uses astronomical algorithms to update The Astronomical Almanac, which contains fundamental astronomical data supplied by many scientists from around the world. The Astronomical Almanac contains 10 sections regarding phenomena, sun, moon, and natural satellites.

Some topics include:

• Phenomena
  • seasons
  • configurations of planets
  • sunrise, sunset
  • moon rise/set times.
• Sun
  • positional information
  • geocentric rectangular coordinates.
• Moon
  • positional information
  • orbit and rotation
  • equatorial coordinates
• Natural Satellites
  • positional information on the satellites of Mars, Jupiter, Saturn (including the rings), Uranus, Neptune, and Pluto.

Breast Cancer

Astronomical algorithms also play a role in improving technology for breast cancer. They are able to create objective, reproducible, and continuous information. Because the data came in large volumes, astronomical algorithms are used for the images of breast cancer. According to the British Journal of Cancer, their method is a technique in which they divide the study population into “positive” and “negative” subgroups. Then they tested over 2000 breast tumors using the algorithms represented in tissue microarrays (TMAs).

Methods

0.6 mm tissue cores were used to represent tumors. They were then dewaxed in xylene and rehydrated through graded alcohols. Finally, the tissue cores were immunostained (detecting a specific protein in a sample) using a BondMax Autoimmunostainer.

Adaptations

The British Journal of Cancer converted stained TMA images into a format where they were compatible with the astronomy processing techniques. The flexible image transport system (FITS) was used because JPEG images come in Red Green Blue (RGB). The images are then extracted into three image planes and the intensities are inverted.

Risks

Although astronomical algorithms can come in handy for conditions such as breast cancer, there are some risks. Particular phenomena may be stain-specific, so making methodological adjustments will be advantageous. Also, the potential clinical utility to whole-tissue sections had not been evaluated.