Question

How far from Pluto must a space probe be along a line toward the Sun so that the Sun's gravitational pull on the probe balances Pluto's pull?

If the forces must be equal and that the equation `F=GmM/r^2` is used

Answer 1

4.42 E+05 km, nearly, from Pluto.

Explanation:

The stationary point in-between Sun and Pluto is distant r1 from Sun and r2 from Pluto,
The average of r1 + r2 = the semi-minor axis of the planet's orbit = 5.123 E+09 km.
r1 / r2 = `sqrt` (ratio of the masses) = `sqrt`(1.98 E+30 kg / 1.46 E+22 kg) = 1.16 E+04.
Solving, r1 = 5.12 E+09 km and r2 = 4.42 E+05 km
Only 3 significant digit (sd) approximation war aimed.
For higher precision, all data used should carry more correct sd
Reference for data: NASA Pluto Fact Sheet