Gravity

Gravity was a force of nature which caused all objects of mass to attract each other. Gravity caused the planets of star systems to stay in orbit.

4.6 billion years BC, rocks were pulled towards a Racnoss webstar, creating the Earth. (DW: The Runaway Bride)

Sir Isaac Newton developed the theory of gravity. The Fourth Doctor once claimed that he sat in Newton's tree dropping apples onto his head, then explained gravity to him over dinner. (DW: The Pirate Planet)

In the year 100,000,000,000,000 when all the stars had burned out, planets were found through a gravitional field navigational system. (DW: Utopia)

During a crisis in midflight, the TARDIS locked onto the nearest place of gravity and landed there. (DW: Voyage of the Damned) This statement seems a little inaccurate, as all objects produce gravity, and it should lock on to the Titanic instead.

Manipulating gravity
The Gravitron was installed in the moonbase in the year 2050. By using it to alter the Earth's tides, people were able to control the Earth's weather. In 2070, the Cybermen attempted to take over the Gravitron as part of their invasion of Earth. (DW: The Moonbase)

The Tractators could control gravity with their minds. This power could be amplified by tunnel systems built in a precise way. On Frontios, the Tractators used an excavation machine to create a series of tunnels with which to create a gravity motor. (DW: Frontios)

The Byzantium had artificial gravity. On Alfava Metraxis in the 51st century, the Eleventh Doctor shot a gravity globe floating above him and ordered his companions to jump. This caused them to land on the Byzantium above them. (DW: The Time of Angels / Flesh and Stone) The failure of this gravity caused the Weeping Angels pursuing the Doctor, Amy Pond and River Song to fall into a crack in the universe. (DW: Flesh and Stone)