In state of major ritual impurity, but cannot take a bath
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Sometimes on long journeys, some passengers go to sleep on their seats. One of them might have a wet dream, or may have boarded the plane having forgotten he was in a state of major ritual impurity (janaabah), or a woman may have completed her menses or post-partum bleeding as the time of Fajr enters. Bearing in mind the [time of] arrival at the destination is after the passing of the [prayer] time, and that the aircraft safety systems absolutely prohibit bathing in the toilet because it is not equipped for that, then what should one do?
Response: If it is possible for him to do tayammum [using the dust] on the floor of the aircraft, then he should do tayammum. And if it is not possible because it is dust free, then he should pray - even without having purified himself. And if he is able to purify himself afterwards, then he should purify himself.
Shaykh Ibn 'Uthaymeen
Fataawa Mu'aasirah - Page 32
I'laam al-Musaafireen bi-ba'dh Aadaab wa Ahkaam as-Safar wa maa yakhuss al-Malaaheen al-Jowwiyeen - Page 5