If man starts to live on other planetary bodies e.g. mars or from far away where the earth will only be viewed like a star then,
1. As a muslim, where will one face if he is to pray and at what time will he pray if the daylight or night-time is constant.
2. Assuming a man has left earth to settle on another favourable planet which will take him say 50yrs to reach, how will he be able to perform hajj, will a child be sent to Mecca to perform hajj and not be able to come to his new home or what?
3. The Holy month of Ramadan is decided on the lunar calendar. Now if a muslim is on another planet (eg mars), which the day and night and the revolution of the planet differs from that of earth, how will he be able to know that it is the month of ramadan and if daylight is constant, how will he be able to distinguish dusk and dawn?

All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.

Your question is hypothetical, and a person should not be preoccupied with hypothetical issues which are far from becoming reality.

However, if we suppose that a person is living in such a planet, he still has to face the Earth where the Ka'bah is. If he could not do so, then he can pray in any direction.

Allah Says (what means): {And to Allah belongs the east and the west. So wherever you [might] turn, there is the Face of Allah. Indeed, Allah is all-Encompassing and Knowing.} [Quran 2:115]

That is of course when it is not possible to determine the direction of the Qiblah.

As regards the timing for the prayers, he has to estimate it. In this era, the means of estimation had become available, Praise be to Allah.

The evidence about this is the Hadeeth in which it is mentioned that the first day of the days of Dajjal is like a year, and the second day is like a month, and the third day is like a week. The companions asked the Prophet : “Is it possible for them to pray only one prayer.” The Prophet replied: “No, you have to estimate for it.”

With regard to Hajj, he has to come down to the planet Earth, if it is possible for him to do so. However, if he is unable to come on Earth, then it will not be obligatory on him. In this case, he will be considered like a person who leaves in a remote country which is far away from Makkah, and cannot come to it.

Allah Says (what means): {And [due] to Allah from the people is a pilgrimage to the House - for whoever is able to find thereto a way.} [Quran 3:97]

Therefore, if the life of this person is in danger when descending from that planet to Earth in order to perform Hajj, then it is not obligatory on him to perform Hajj.

In relation to the month of Ramadan, if it is not possible to detrmine it, (then in this case) he has to fast one month in every 12 months and this will suffice him.

Allah knows best.