The moon that is so close in size to its planet that scientists consider it to be a binary planet is Pluto's moon Charon.

Here's why:

* Size Comparison: Charon is about half the size of Pluto, making it significantly larger than most moons in our solar system relative to their planets.

* Center of Mass: The center of mass of the Pluto-Charon system lies outside of Pluto itself, meaning that Charon's gravitational pull is strong enough to influence Pluto's orbit. This is a key characteristic of binary planets.

* Mutual Orbit: Pluto and Charon orbit around a common center of gravity, rather than Charon orbiting Pluto like a traditional moon.

While the term "binary planet" is still somewhat debated among scientists, the unique relationship between Pluto and Charon makes them a strong candidate for this classification.