Use the data of this table to find the point between Pluto and the Sun at which

Question

Use the data of this table to find the point between Pluto and the Sun at which an object can be placed so that the net gravitational force exerted by Pluto and Sun on that object is zero.

Useful Planetary Data Mean Radius (m) 243 × 106 6.06 × 10° 6.38 × 10° 3.37 × 106 6.99×107 5.85 × 10' 2.33 × 107 221 × 107 1.14 × 10° 1.74 × 10° 696 × 108 Period (s) 7.60 × 106 1.94 × 107 3.156 × 10, 5.94 × 10' 3.74 × 108 9.35 × 108 2.64 × 109 5.22 × 109 782 × 109 Mean Distance from Sun (m) 579 × 100 1.08 × 1011 1.496 × 1011 2.28 × 1011 7.78 × 1011 1.43 × 1012 2.87 × 1012 4.50× 1012 5.91 × 1012 Body Mercury Venus Earth Mars Jupiter Saturn Uranus Neptune Plutoa Moon Sun In August 2006, the International Astronomical Union adopted a definition of a planet that separates Pluto from the other eight Mass (kg) 3.18 × 1023 4.88 × 1024 5.98 × 1024 6.42 × 1023 1.90× 10 5.68 × 1026 8.68 × 1025 1.03 × 1026 1.27 × 1023 7.36 x 1022 1.991 × 1030 2.97 2.99 2.97 2.98 2.97 2.99 2.95 2.99 2.96 27 planets. Pluto is now defined as a "dwarf planet" like the asteroid Ceres.

Explanation / Answer

if the distance of this point from ploto is r,

G*Mp*m / r^2 = G*Ms*m / ( d - r ) ^2 ,

where 'd' is the distacne of ploto from Sun.

After simplifications

r = d / [sqrt(Ms/Mp) + 1 ]

r = 5.91 x10^12 / [ sqrt ((1.991 x 10^30)/(1.27 x 10^23)) + 1 ]

r = 1.492 x10^9 m.

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