# What is pluto minimum distance from earth?

Mar 30, 2016

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) $\triangle E S P$,
SE = Earth aphelion, SP = Pluto perihelion and $\angle E S P = \max {17.2}^{o}$

So, least $E P = \sqrt{S {P}^{2} + S {E}^{2} - 2 X S E X S P X \cos \angle E S P}$. ,
This simplifies to 4.29 B km