Question

What is pluto minimum distance from earth?

Answer 1

With due consideration of the high inclination `17.2^o` of Pluto's orbital plane to our ecliptic, the least lower bound for the minimum Earth-Pluto distance is 4.29 B km = 2.66 B miles, nearly.

Explanation:

I have used NASA Planetary Fact Sheet data.

Pluto : Perihelion = 4.436 billion (B) km and orbital inclination to Earth's orbital plane = `17.2^o`.
Earth : Aphelion: 0.1521 B km.

For least possible Earth-Pluto distance,,in the Earth (E) - Sun (S) - Pluto (P) `triangleESP`,
SE = Earth aphelion, SP = Pluto perihelion and `angleESP= max 17.2^o`

So, least `EP = sqrt(SP^2+SE^2-2XSEXSPXcosangleESP)`. ,
This simplifies to 4.29 B km