Does Master Chief return to Earth at the end of Halo 3?

Question

In legendary mode you can see the half of the UNSC ship moving towards a blue planet.

Do you know which planet Master Chief is moving towards?

Is this Earth?

Answer 1

From Halopedia:

The planetoid is littered with blue-glowing symbols and geometric patterns - clearly Forerunner in origin. At least two of the symbols are clearly recognizable. This could mean that the planet is the Forerunner homeworld.

A Marathon symbol can also be observed on the surface. It is known to be a common Forerunner symbol, used in multiple Forerunner constructs, and also used to refer to a Reclaimer.

Theories about what the planet could be:

Shield World

Given the Legendary planet's clearly artificial appearance, it could be one of the many Shield Worlds constructed by the Forerunners as safe havens to protect them from the Flood and the activation of the Halo Array.

One theory suggests that the common Forerunner symbol seen on the surface solely represents a Shield World, relying on the fact that the cover of Ghosts of Onyx bears this symbol and the book prominently features a Forerunner Shield World, which leads to some believing that the planet is the planet that Catherine Elizabeth Halsey, Franklin Mendez, Blue Team and the remaining SPARTAN-IIIs and SPARTAN-IIs were transported to. However, the common symbol on the cover may simply reference to the fact that the story of the novel puts strong emphasis to the Forerunners. Furthermore, if the symbol only represented a Shield World, its common appearances on the Halo installations and the Ark would be unexplained. Also, all Shield Worlds seen so far are disguised as natural planets, whereas the Legendary Planet bears clear evidence of artificial Forerunner construction.

Forerunner colony

Yet another theory is that it could be an abandoned Forerunner colony or planetoid-class ship, similar to High Charity. Throughout the Halo franchise, there have been a few mentions of the Forerunner colonies prior to the discovery and subsequent war with the Flood, notably in the Halo 3 Terminals. This theory provides an alternative to the Shield World theory, as well as explaining the planetoid, the Forerunner symbols, and providing an opening for sequels; however, if the Forerunners had indeed been living on this planet-like object, they would have been killed when the Halo array was fired (unless, like the Ark, the planet is not located in the Milky Way Galaxy, placing it outside of the effective range of the Halo Array).

Another point supporting the theory is that there appear to be cities on the surface.

Reading the Terminals, an interesting phrase appears on Legendary, that Mendicant Bias, a Forerunner AI who defected to the Gravemind and was later defeated by Offensive Bias, says directly to Chief, stating:

"Atonement. 
And so here at the end of my life, I do once again betray a former master. The path ahead is fraught with peril. But I will do all I can to keep it stable - keep you safe. I'm not so foolish to think this will absolve me of my sins. One life hardly balances billions. 
But I would have my masters know that I have changed. 
And you shall be my example." - Mendicant Bias 

The last line has caused fans to believe that Mendicant Bias had an intention of showing the Forerunners an example of his "atonement" who is the Master Chief. Knowing this many believe that the AI protected the Master Chief, and prevented a number of unseen events on the Ark and Installation 04B from affecting the Chief and his missions. Some have also theorized that he deviated the portal's course at the last moment before he was destroyed. Though no information supports this and it has been neither stated nor implied, it can be supported logically in that the Ark's Portal might have several possible entrance/exit points throughout space; the Forerunners adapted to the Flood with extensive redundancy in all systems and escape mechanisms, so it is possible that the Forerunners on the Ark established themselves at a different Portal destination, possibly one of many, and Mendicant Bias shifted to this destination when the Forward Unto Dawn was halfway through, thus severing the ship and dropping the Master Chief's half near the colony.

Forerunner homeworld

Another possible identity is that the planet is the Forerunner homeworld, since the Forerunners would doubtlessly have wanted one of their ships to get to the homeworld safely if something similar happened to a Forerunner vessel as did Cortana and the Chief.

It strongly suggested in the Halo Legends episode "Origins" that the Unidentified Forerunner Planet, a Forerunner colony, is indeed the Legendary Planet. Hints include what looks like the Forward Unto Dawn drifting towards the planet, and Installation 00 orbiting a rocky, brown moon, which in turn is orbiting the planet in question.

Answer 2

No, this is not Earth. It has sometimes been referred to as the Marathon world because the Marathon symbol can be seen on the plant if you freeze frame.

However, no one knows for sure what planet he is moving towards or what it holds for the Chief.