Praise be to Allah.
If we assume that he can not make ghusl on the airplane, then this is a case known to scholars of fiqh as the case of the one faqid al-tahoorain "missing the two purifications" (i.e. water for wudu' and soil for tayammum), and their sayings in this matter differ. Imam Ahmad and the majority of narrators say that the person should pray in his impurity, since this is what is within his capability and ability, and that Allah does not burden a soul more than it can bear. The evidence in this situation is what Imam Muslim narrated in his authentic collection of hadith that the Prophet (peace be upon him) sent some people to search for a necklace that Aa'isha had lost, during which the time for prayer had entered, so they prayed without wudu' (due to the absence of water). Afterwards they went to the Prophet (peace be upon him) and mentioned this situation to him. The verse allowing tayammum was then revealed.1 The Prophet (peace be upon him) did not disapprove their action and did not command them to repeat the prayer. A similar situation can happen to patients that cannot move their limbs completely (a paralyzed person who has no one to assist him) or prisoners in some cases of being tied-up or hung-up. The intention is one's prayer should performed and not delayed from its prescribed time depending on his situation and one is not required to repeat it. This is the most appropriate, as Allah did not burden us with religion.
From the book What Should You Do in the Following Situations... ?
1 Sahih Muslim 367