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Its probably small, but is there a theoretical gravitational attraction between all objects in the universe? Light can move pretty far, so does that mean gravity can as well, and is the gravity blocked by the same way light is blocked by an object?

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Yes

The gravitational field from an object does extend infinitely far out into space, if there is an infinite space for it to fill. There isn't any sort of limit to how far an object's gravitational influence can travel. However, there is a catch: Gravity travels at a finite speed (the speed of light). If gravity propagated infinitely fast, any two objects would be guaranteed to be affected by each other. However, because it is not infinitely fast, two objects that have never been less than 13.8 billion light-years apart (the universe is only 13.8 billion years old) could only now be feeling each other's influence. If the Sun were to suddenly explode, it might not feel the influence of an object 13.8 billion that has never been less than 13.8 billion light-years away.

Is the gravity blocked by the same way light is blocked by an object?

An gravitational field extending infinitely (eventually) in all directions means that one object should always have an influence on another. But the gravitational influence of one object can sort of be "blocked" by another object if its field in one spot is strong enough compared to the other. For example, we still feel the force of Mars' gravity, but, to us, it is largely overwhelmed by that of the Earth.

We can show this easily using Newtonian gravity. Newton's law of universal gravitation is formulated $$F=G\frac{m_1m_2}{r_{12}^2}$$ where $m_1$ and $m_2$ are the masses of the two objects - we'll say $m_1$ is the mass of a human, $m_h$, and $m_2$ is the mass of Earth, $m_E$. A human on Earth's surface is roughly $6,371 \text { km}$ from it's center, or $6,371,000 \text { meters}$. Mars, on the other hand, is, at its closest, $0.3814 \text { AU}$ from Earth - or roughly $57,210,000 \text { km}$, or $57,210,000,000 \text { meters}$. Care to do the math? Well, what with this distance being squared ($r^2$), you can tell at a glance that the force from Mars is many orders of magnitude less than the force from Earth.

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