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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.

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

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Answer 2

Levi Anderson

Using Newton's law of universal gravitation, we can calculate that the point where the Sun's gravitational pull balances Pluto's pull is approximately 45.8 million kilometers from Pluto along a line toward the Sun. Pluto and the Sun are roughly 5.9 billion kilometers apart. The Sun is approximately 333,000 times more massive than Pluto.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.