Table 7.3 Useful Planetary Data Mean т? 10-19 13 Distance Mean Body Mass (kg) Radius (m) r from Sun (m) m Period (s) Mercury 3.18 X 1023 5.79 X 1010 1.08 X 1011 1.496 X 1011 2.28 X 1011 7.78 X 1011 1.43 X 1012 2.87 x 1012 4.50 x 1012 5.91 X 1012 2.97 7.60 X 106 1.94 X 107 2.43 X 106 6.06 X 106 Venus 4.88 X 1024 5.98 X 1024 6.42 X 1023 1.90 X 1027 5.68 X 1026 2.99 Earth 2.97 6.38 X 100 3.37 X 106 6.99 X 107 5.85 X 107 2.33 x 107 2.21 x 107 1.14 X 106 1.74 X 100 3.156 X 107 5.94 X 107 3.74 X 108 9.35 X 108 2.64 X 109 5.22 X 109 7.82 X 109 Mars 2.98 Jupiter 2.97 Saturn 2.99 Uranus 8.68 X 1025 1.03 x 1026 2.95 Neptune 2.99 Pluto2 1.27 X 1023 7.36 X 1022 1.991 X 1030 2.96 Мoon Sun 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.

A 230-kg object and a 530-kg object are separated by 3.90 m. (a) Find the magnitude of the net gravitational force exerted by these objects on a 65.0-kg object placed midway between them. N (b) At what position (other than an infinitely remote one) can the 65.0-kg object be placed so as to experience a net force of zero from the other two objects? m from the 530 kg mass toward the 230 kg mass

A coordinate system (in meters) is constructed on the surface of a pool table, and three objects are placed on the table as follows: a 5.0 kg object at the origin of the coordinate system, a 10.0 kg object at (0, 2.0), and a 11.0 kg object at (4.0, 0). Find the resultant gravitational force exerted by the other two objects on the object at the origin. magnitude direction

Mass M is divided into two parts xM and (1-x)M. For a given separation, the value of x for which the gravitational attraction between the two pieces becomes maximum. Find this maximum value of x.

At new moon, the Earth, Moon, and Sun are in a line. Find the direction and magnitude of the net gravitational force exerted on (a) the Earth, (b) the Moon, and (c) the Sun.?

space probe is launched from Earth headed for deep space. At a distance of 10,000 miles from Earth's center, the gravitational force on it is 929 lb. What is the size of the force when it is at each of the following distances from Earth's center? (a)    20,000 miles lb(b)    30,000 miles lb(c)    100,000 miles

A coordinate system (in meters) is constructed on the surface of a pool table, and three objects are placed on the table as follows: a m, = 1.9-kg object at the origin of the coordinate system, a m, = 3.3-kg object at (0, 2.0), and a m, = 5.3-kg object at (4.0, 0). Find the resultant gravitational force exerted by the other two objects on the object at the origin. magnitude Your response differs from the correct answer by more than 10%. Double check your calculations. N direction 68.12 o above the +x-axis

Newton's Law of Gravitation states that two bodies with masses M and N attract each other with a force MN F = G= where r is the distance between the bodies and G is the gravitational constant. Assume that Earth's mass is 5.98 × 1024 kg and is concentrated at its center. Moreover, take the radius of the Earth to be 6.37 x 10° m and G = 6.67 x 10-1" N · m²/kg. With this information, find the work required to propel a 1000-kg satellite out of Earth's gravitational field. Work =

(a) Calculate the magnitude of the gravitational force exerted on a 486-kg satellite that is a distance of 1.70 earth radii from the center of the earth. (b) What is the magnitude of the gravitational force exerted on the earth by the satellite? (c) Determine the magnitude of the satellite's acceleration. (d) What is the magnitude of the earth's acceleration? (a) Number i Units (b) Number i Units (c) Number Units (d) Number i Units

two spheres of mass m and a third sphere of mass M form an equilateral triangle, and a fourth sphere of mass m4 is at the center of the triangle. The net gravitational force on that central sphere from the three other spheres is zero. (a) What is M in terms of m? (b) If we double the value of m4, what then is the magnitude of the net gravitational force on the central sphere?