The Doctor was having a rather bad time of it. It wasn't every day that one lost one's companion to another universe, never to be seen again.
Of course, it was a little different for him, being the Time Lord that he was. People tended to come and go from his life with astounding frequency. Still, every once in a long while there was someone who he wished could be there forever. Rose was one of those people. She was a lovely girl; wore her heart on her sleeve, that one. Ah, but he missed her already, and it had only been a moment since he said goodbye. It took a long time for him to recover from their farewell, or it would have, if he had been given more time. But just as he'd turned away, someone appeared in the TARDIS, an impossible someone, in more than one definition of the word, and adventure was once again upon him. It was good this way; he'd managed to get through many a heartbreaking experience by busyness alone. After all, saving the world was a splendid distraction.
Then this horridly trying creature named Donna had the nerve to ask him what had happened to his last companion. As if she suspected that he himself had done away with her or some such thing. He would have given his own life to keep Rose alive and happy…indeed, he almost had many times. Ah, but such adventures they'd had.
Martha Jones appeared in his life just as suddenly as Rose had departed. The hospital was just a latest distraction for the Doctor. It was easy to smile and be witty for him. After all, such lovely floppy ears made one ever so aware that one mustn't take oneself seriously. He'd smiled at all of the interns, amused as they tried to diagnose him. He supposed he was suffering from a broken heart.
That was quite an adventure, and at the end of it, he'd found himself inviting Martha along for a trip in the TARDIS. It was her sense of delight in the impossible, he thought, that compelled him to do so, but he told her that it was in gratitude for her saving his life. The truth is, he was lonely, despite his claims to the contrary. One trip, he'd said, just one. She'd not replace Rose; he'd not give her enough time to try.