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

Question

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

______m from the center of Earth


Useful Planetary Data (T2 / r3) 10-19 (s2/m3)
Mean
Mean Distance
Body Mass (kg) Radius (m) Period (s) from Still (m)
Mecury 3.18 X 1023 2.43 X 106 7.60 X 106 5.79 X 1010 2.97
Venus 4.88 X 1024 6.06 X 106 1.94 X 107 1.08 X 1011 2.99
Earth 5.98 X 1024 6.38 X 106 3.156 X 107 1.496 X 1011 2.97
Mars 6.42 X 1023 3.37 X 106 5.94 X 107 2.28 X 1011 2.98
Jupiter 1.90 X 1027 6.99 X 107 3.74 X 108 7.78 X 1011 2.97
Saturn 5.68 X 1026 5.85 X 107 9.35 X 108 1.43 X 1012 2.99
Uranus 8.68 X 1025 2.33 X 107 2.64 X 109 2.87 X 1012 2.95
Neptune 1.03 X 1026 2.21 X 107 5.22 X 109 4.50 X 1012 2.99
Pluto 1.27 X 1023 1.14 X 106 7.82 X 109 5.91 X 1012 2.96
Moon 7.36 X 1022 1.74 X 106 - - -
Sun 1.991 X 1030 6.96 X 108 - - -

In August 2006. the International Astronomical Union adopted a definition of a planet that separates Pluto from the other eight planets. Pluto is now defined as a 'dwarf planet' like the asteroid Ceres.

Explanation / Answer

The gravitational force between two masses m1 and m2 seperated by distance d is given by F = Gm1m2/d2 Where G = 6.67*10-11 Nm2/kg2 is the universal gravitational constant The mass of the earth ia Me = 5.98*1024 kg The mass of the sun is Ms = 1.991*1030 kg distance between the earth and sun is d = 1.496*1011 m Radius of the earth Re = 6.38*106 m Radius of the sun is Rs = 6.96*108 m Let at a distance x from the earth the mass m is placed so that there is no net gravitational force acts on it i.e. the gravitational force due to earth is compensated by the gravitational force due to the sun GMe*m/x2 = GMs*m/d'2
Where d' = Re+Rs+d - x = 1.503*1011 m -x Me/x2 = Ms/(1.503*1011 m -x)2
(1.503*1011 m -x)2 / x2 = Ms/Me (1.503*1011 m -x)2 / x2 = 3.329*105 (1.503*1011 m -x)/x = 5.769*102 1.503*1011 m / x = 577.9 x = 2.6*108 m Therefore the object will experience zero gravitational force due to earth and eun at a distance 2.6*108 m from the center of the earth 1.503*1011 m / x = 577.9 x = 2.6*108 m Therefore the object will experience zero gravitational force due to earth and eun at a distance 2.6*108 m from the center of the earth

Related Questions

Navigate

• Browse (All)
• Browse U
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.