Time Systems and Representations¶

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Astrodynamics is the study of motion in space, which is inextricably linked with the concept of time. You cannot have motion without time. The trajectory of an object is defined by how it's state (location) changes between different points in time. As one might therefore expect, accurate timekeeping and the ability to convert between different representations of time are crucial for calculations in orbital mechanics.

The time module provides functions for the handling of time. The package makes the distinction between the representation of a specific time and the conversion between different time scales. Precise specification of an instant in time requires the specification of both a time representation and time scale.

Time Representation¶

A single instance in time can be represented in multiple different formats. For examples The J2000 Epoch can be represented as a calendar date in terms of years, months, days, hours, minutes, and seconds as 2000-01-01T12:00:00. The same instant can also be represented in terms of Modified Julian Days as 51544.5. Both of these representations refer to the same instant in time.

Time Scales¶

In addition to representing time in different manners, there are also different time scales. A time scale is a standard to reckoning and resolving instances in time. Multimple time scales have been introduced due to the criticality of being able to correctly measure and understand when specific events occur in science and engineering.

Within a time scale it is possible to compare different instances in time to determine if one is before, after, or at the same time as another instant. It is also possible to compare between time scales, however you must know how to properly convert between them. It is assumed that all time scales use the same definition of the SI second, and therefore advance at the same rate.

Athough the calendar date representations of time 2000-01-01T12:00:00 UTC and 2000-01-01T12:00:00 GPS have the same values, they are actually different instances in time!. This is because while the calendar date representations are the same there are actually offsets between the different time scales.

The time scales currently supported by brahe are

Time Scale	Description
`GPS`	`GPS` stands for Global Positioning System time. It is specifically, the time scale used by the US GPS satellites. It is different from TAI and TT by constant, fixed offsets.
`TAI`	`TAI` is a French acronym for temps atomique international. It is an atomic time scale meant to track the proper time on the Earth's surface.
`UTC`	`UTC` stands for Universal Coordinated Time. `UTC` tracks the solar day, accounting for long term variations due to changes in Earth's rotation to within +/- 1 second. Tracking the solar day in this manner introduces an offset between `TAI` and `UTC` of a fixed number of leap seconds.
`UT1`	`UT1` stands for Universal Time 1. `UT1` represents the time as determined by the true solar day. Due to Earth's rotation rate constantly changing UT1 itself is constantly changing. The difference between `UT1` and `UTC` is empirically estimated on a daily basis as an Earth orientation parameter.
`TT`	`TT` is Terrestrial Time, a time scale used historically to model the motion of planets and other solar system bodies. These models are still in wide use.

Epoch¶

The Epoch type represents a specific instant in time, defined by both a time representation and a time scale. The Epoch type provides methods for converting between different time representations and time scales, as well as for performing arithmetic operations on time instances.

It is the core type used throughout the brahe package to represent time and provides many advandages as