so here is the correct explanation( the preceding & succeeding verses have to be read in conjunction in general)
This verse is a challenge to Allah’s creatures. It is a challenge on the Day of Resurrection, since it is given after the verse mentioned by the op: “Soon shall We settle your affairs, O both you worlds!” [Sûrah al-Rahmân: 31]
Al-Tabarî explains that the two verses taken together mean:
Soon shall We settle your affairs, O both you worlds! And it will be said to you: “O assembly of Jinn and men! If you can pass beyond the zones of the heavens and the Earth, then pass! Not without authority shall you be able to pass!”
Al-Sa`dî explains in his commentary on the Qur’ân:
When Allah gathers them together at the place of standing on the Day of Resurrection, He will declare to them their weakness and helplessness, while affirming the fullness of His power and authority, and that His will shall be accomplished.
He will say to them: “If you can pass beyond the zones of the heavens and the Earth, then pass!”
This means: If you can find a way out of Allah’s dominion and power, then go ahead.
Then Allah will inform then: “Not without authority shall you be able to pass!”
This means: You will have no escape without power and authority that you surely do not possess.
On that Day, they will have no power to cause any benefit or harm. They will have no control over their life and death – nor over their own summons. In that assembly, no one will speak without Allah’s permission, and no voice will be heard above a murmur. Kings and subjects, princes and paupers – they will all be equal on that day.
Implications for Space Travel
Some people have tried to understand this verse as referring to the life of this world, ignoring its context. They have claimed that this verse refers to space travel. The people who have made this assumption are, in turn, divided into two diametrically opposed groups:
1. There are those who say that this verse is proof that space travel is humanly impossible. This group, understandably, has grown much smaller in the past few decades.
2. The other group takes the opposite position. They try to use this verse as proof that the Qur’ân predicts human space flight. They argue that the word “authority” in the verse should be understood to mean “knowledge”.
Ibn `Uthaymîn discusses the weakness of these interpretations in his book Regarding a Trip to the Moon. He discusses at length the problems associated with such interpretations. What follows owes a debt to his excellent work.
Anyone who reads the verse in the broader context of the entire chapter – Sûrah al-Rahmân – will understand clearly that the challenge takes place in the Hereafter. Allah begins the chapter by discussing the creation of humanity and the jinn. Then He tells us how He subjected to His servants the heavens and the Earth. Then He tells us how all the denizens of the Earth shall perish. It is at this point that He says: “Soon shall We settle your affairs, O both you worlds!” This is the Judgment. And at this point, the challenge is given. There will be no escaping from Allah’s judgment.
This is the danger of taking a sentence or a word out of context. A sentence or a word can mean many very different things, depending on the context in which it is used.
Even if we say that the verse could – taken in isolation – be understood to mean either a denial or prediction of space travel, neither of these ideas makes any sense in the context in which the verse is given.
If the verse were predictive as some people have recently alleged, and the word “authority” means knowledge, this would make the meaning of the verse: “O assembly of Jinn and men, you will not be able to pass beyond the zones of the heavens and the Earth without knowing how to do so!”
This is, to say the least, just stating the obvious. Nothing that any of us attempt to do can be achieved without knowledge of how to do it. Such a meaning is incongruous with the awe and majesty of the declaration. It makes no sense for something so banal to be declared right after such an ominous warning like: “Soon shall We settle your affairs, O both you worlds!”
It makes equally little sense for such a statement to come right before the equally ominous: “On you will be sent (O ye evil ones twain!) a flame of fire (to burn) and a smoke (to choke): no defense will you have.” [Sûrah al-Rahmân: 35]
Hence,There can be no doubt about what the verse means when it is taken in context.
( Ive copied the post from elsewhere for everyone's benefit & understanding. Even I stand corrected. See my 1st response above)