Section I: What are Solar and Lunar Eclipses? The Ruling of the Eclipse Prayers And Other Prayers Offered Upon the Occurrence of Cosmic Phenomena

Firstly: What are the kusoof and khusoof prayers?
Literally: Kusoof means change. The sun is referred to having undergone kusoof when its illumination disappears and it becomes black. The moon is referred to having undergone kusoof when its light disappears and it changes to black.
It is said that kusoof refers to the sun while khusoof refers to the moon. It is also said that they are synonymous.
Legally: Kusoof (eclipse) prayer is a prayer that is offered in a particular manner when either the sun or moon, or part of either, goes dark.

Secondly: Ruling of the solar eclipse Prayer
The solar eclipse prayer is a confirmed sunnah by agreement of the four schools of jurisprudence.

Thirdly: Ruling of the lunar eclipse prayer
The lunar eclipse prayer is a confirmed sunnah. This is the position of the Shafi`i and Hanbali schools, some Malikis, and Ibn Baz.

Fourthly: Offering the solar eclipse prayer in congregation
It is sunnah to offer the solar eclipse prayer in congregation. This is by agreement of the four schools of jurisprudence.

Fifthly: Offering the solar eclipse prayer alone
It is permissible to offer the solar eclipse prayer alone by agreement of the four schools of jurisprudence.

Sixthly: Women offering the solar eclipse prayer
It is mustahabb for women to offer the eclipse prayer by agreement of the four schools of jurisprudence. 

Seventhly: Offering the lunar eclipse prayer in congregation
It is sunnah to offer the lunar eclipse prayer in congregation. This is the position of the Shafi`i and Hanbali schools and the majority of the scholars. It is the position of choice of Ibn Hazm, Ibn Baz, and Ibn `Uthaymin.

Eighthly: Repeating the solar eclipse prayer
Repeating the eclipse prayer is not legislated after it has been performed, even if the sun does not reappear normally. This is by agreement of the four schools of jurisprudence.

Ninthly: Making up the solar and lunar eclipse prayers
The eclipse prayer is one of the prayers that has a specific reason and is not repeated if it is missed. Consensus on this was related by al-Nawawi, Ibn Hajar, and al-Shawkani.

Tenthly: Are prayers offered during other cosmic phenomena?
No other cosmic phenomena entail offering a prayer in a manner similar to the eclipse prayer. This is the position of the Maliki and Shafi`i schools. It is the position of choice of Ibn Baz.