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Earth-Luna is a binary planet
because
score: 6
It meets the IAU definition of a planet
because
score: 3
It orbits the Sun, as shown by:
because
score: 1
It's orbit around the Sun is always convex. To see a graphical representation of what I mean, see page 5 of my source.
because
score: 1
The Sun has ~2x the gravitational influence on it, compared to the Earth. In other words, it has twice the pull.
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because
score: 1
It would eventually clear its orbit, according to the IAU's formula:
because
score: 1
It has sufficient mass for its self-gravity to overcome rigid body forces so that it assumes a hydrostatic equilibrium (nearly round) shape
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because
score: 1
The two objects were formed from the same proto-planet
because
score: 0
The ESA says so
but
score: 0
The Earth-Luna barycenter is still inside the Earth's surface
but
score: 1
This would no longer be true near the end of the solar life. At it's current rate of retreat, Luna will reach an Earth-relative SMA of 525,079km (the point at which the barycenter will be outside Earth) in ~3.7 billion years.
however
score: 1
There is reason to believe the rate of retreat is accelerating. Mainly because if you extrapolate backwards, Luna would only be ~2 billion years old.
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