This **sidereal time calculator** is an **essential** tool in **astronomy** that helps determine the **position** of **celestial objects** relative to Earth’s **rotation**.

It calculates time based on Earth’s rotation concerning

distant stars, rather than theSun. This distinction iscrucialforastronomersandstargazerswho need toaccuratelylocate and trackcelestial bodies.

If you want to observe a particular star at its **highest point** in the sky (**culmination**), you would use our **local sidereal time calculator** to determine when this occurs. For instance, if the star **Vega** has a right ascension of **18h 36m 56.3s**, it will culminate when the **local sidereal time** matches this value.

## Sidereal Time Calculator

Date | Time (UT) | Location | Longitude | LST |
---|---|---|---|---|

2024-09-08 | 00:00 | London, UK | 0° | 23h 22m 46s |

2024-09-08 | 06:00 | Tokyo, Japan | 139.75°E | 11h 01m 31s |

2024-09-08 | 12:00 | New York, USA | 74°W | 6h 26m 57s |

2024-09-08 | 18:00 | Sydney, AU | 151.2°E | 5h 54m 12s |

2024-09-09 | 00:00 | Rio, Brazil | 43.2°W | 20h 20m 03s |

2024-09-08 | 03:00 | Cairo, Egypt | 31.25°E | 22h 15m 00s |

2024-09-08 | 09:00 | Moscow, Russia | 37.62°E | 14h 45m 30s |

2024-09-08 | 15:00 | Los Angeles, USA | 118.25°W | 3h 12m 45s |

2024-09-08 | 21:00 | New Delhi, India | 77.1°E | 17h 30m 15s |

2024-09-08 | 12:00 | Cape Town, South Africa | 18.42°E | 6h 50m 00s |

2024-09-08 | 18:00 | Beijing, China | 116.4°E | 11h 58m 30s |

2024-09-08 | 00:00 | Buenos Aires, Argentina | 58.42°W | 20h 10m 00s |

2024-09-08 | 06:00 | Bangkok, Thailand | 100.5°E | 11h 25m 30s |

2024-09-08 | 12:00 | Berlin, Germany | 13.41°E | 6h 45m 00s |

2024-09-08 | 18:00 | Mexico City, Mexico | 99.13°W | 4h 00m 15s |

## Sidereal Time Formula

The formula for calculating **sidereal time** is:

**LST = GST + λ**

Where:

LSTisLocal Sidereal TimeGSTisGreenwich Sidereal Timeλ(lambda) is the observer’slongitudein time units (positive for east, negative for west)

The **GST** is **14h 30m 00s** and you’re observing from a location with longitude **45° West** (which is **-3h** in time units), the **LST** would be:

`LST = 14h 30m 00s + (-3h) = `**11h 30m 00s**

## How do you calculate sidereal time?

**Determine the Julian Date**(JD) for the desired observation time.**Calculate the number of days since J2000.0**(JD –**2451545.0**).**Compute the Greenwich Mean Sidereal Time**(GMST) at**0h UT**: GMST =**18.697374558 + 24.06570982441908 * D**Where D is the number of days since J2000.0.**Apply the equation of the equinoxes**to get the**Greenwich Apparent Sidereal Time**(GAST).**Convert GAST to Local Sidereal Time**by adding the observer’s**longitude**.

Let’s calculate the **LST** for **January 1, 2024**, at **00:00 UT**, for an observer at **30° East** longitude:

- JD for
2024-01-01 00:00 UT=2460310.5- D =
2460310.5 – 2451545.0 = 8765.5 days- GMST =
18.697374558 + 24.06570982441908 * 8765.5 = 6.6456 hours- Assuming negligible equation of equinoxes, GAST ≈ GMST
- LST =
6.6456 + (30° / 15°/hour) = 8.6456 hoursor8h 38m 44s

## Local sidereal time formula

The formula for **Local Sidereal Time** (LST) can be expressed as:

**LST = GMST + λ + ΔT + ΔΨ cos(ε)**

Where:

GMSTisGreenwich Mean Sidereal Timeλis the observer’slongitude(positive east, negative west)ΔTis the difference betweenUT1andUTCΔΨis thenutationin longitudeεis thetrue obliquityof the ecliptic

Assuming **GMST = 15h 30m 00s**, **λ = 45°E**, and neglecting the small corrections (ΔT and nutation terms):

`LST = `**15h 30m 00s + (45° / 15°/hour) = 18h 30m 00s**

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