Why soviet didn't bring back "laika" to earth & how re-entry logic works?

Laikas survival was never part of the plan. The dog was launched atop Sputnik 2, which lacked re-entry capability as this had not (yet) been developed. Even if the USSR had wanted, they couldn't return the dog safely to earth at the time.

Little was known about the impact of spaceflight on living creatures at the time of Laika's mission, and the technology to de-orbit had not yet been developed, so Laika's survival was never expected. Some scientists believed humans would be unable to survive the launch or the conditions of outer space, so engineers viewed flights by animals as a necessary precursor to human missions. The experiment aimed to prove that a living passenger could survive being launched into orbit and endure a micro-g environment, paving the way for human spaceflight and providing scientists with some of the first data on how living organisms react to spaceflight environments.

Despite Laikas demise, the flight proved that animals could survive the launch and the space environment, at least for a while.

Human spaceflight was developed in the USSR in the Vostok programme. But even the first Vostok spacecraft, called Vostok 1KP, was not designed for re-entry. It was successfully launched on May 15, 1960. The next six flights of the Vostok programme used the Vostok 1K capsule, designed for dogs and for re-entry. Belka & Strelka, the two dogs launched on Korabl-Sputnik 2 were the first animals ever to be returned to earth from space, on 20 August 1960. This was only the second object ever to be returned from space, after the US recovery of Discoverer 13. A major setback in this phase of the programme was the Nedelin catastrophe.

The first spacecraft designed by the USSR for human re-entry was Vostok 3KA. Before a human was put into these, there were two unmanned test flights to verify the capsule, Korabl-Sputnik 4 and Korabl-Sputnik 5. Those two flights both carried dogs that were successfully recovered.

This eventually lead to the Vostok 1 mission carrying Gargarin into space and returning him safely.

In summary, Laika was launched on Sputnik 2, which was a very small and simple satellite without re-entry capability, because the technology to re-enter did not exist yet. Vostok 1KP still could not re-enter, but was a pre-cursor to Vostok 1K, which was able to bring back animals safely, which lead to the Vostok 3KA capsule able to bring back humans safely after two unmanned test flights. At the point where Laika was launched, the tech to bring her back safely simply did not exist and the dog was seen as expendable.

Ressources

• Laika. In Wikipedia, The Free Encyclopedia.
• Vostok programme. In Wikipedia, The Free Encyclopedia.
• Vostok (spacecraft). In Wikipedia, The Free Encyclopedia.