Question

Does gravity always include the Earth’s pull or can it be between other objects?

Answer 1

Well other planets have a gravitational pull that's what keep the planet's orbiting the sun. But the amount of gravity differs by mass.

Hope this helps :)

Answer 2

What a great question !

There is a pair of forces of gravity (one in each direction) between EVERY two specks of mass in all of creation.  

-- Between you and the Earth.

-- Between the Moon and the Earth.

-- Between the Moon and you.

-- Between you and your dog.

-- Between your dog and your goldfish.

-- Between every pair of corn flakes in your cereal bowl.

-- Between the lint in your pocket and every grain of sand on the beach on the far side of the farthest planet in orbit around the farthest star in the farthest galaxy on the other side of the Universe.  You don't feel it, and it's too small to measure, but its strength can be calculated.