What do we know? Fg = 78.6 N Fg = mg = (8)(9.8) = 78.4 N 1. m1 = mass of the object = 8 kg m2 = mass of the earth = 5.98 × 1024 kg d = distance between the center of the earth and the center of the object = 6370 km G = 6.67 x 10-11 Nm2/kg2 Fg = 78.6 N REMEMBER g = 9.8 m/s2 is only valid for an object ON THE EARTH”S SURFACE This could have been solved in a much easier manner . . . . Fg = mg = (8)(9.8) = 78.4 N

What do we know? Fg = 3.74 x 1022 N 1 AU = 1.5 x 108 km 2. What do we know? Fg = 3.74 x 1022 N m1 = mass of Saturn = 5.69 x 1026 kg m2 = mass of the sun = 2.0 × 1030 kg d = distance between the center of Saturn and the center of the sun = 9.5 AU Fg = ?;T = ? s 1 AU = 1.5 x 108 km d = 1.425 x 1012 m This could have been solved in a much easier manner . . . . REMEMBER This equation is only valid for two objects ORBITING THE SAME CENTRAL BODY T =9.25 x 108 s 29.3 years 29.3 years

What do we know? m2 = 7.2 x 1022 kg T = 2.4 x 106 s = 28 days 3. Fg = force of attraction between earth and moon = 1.9 x 1020 N m1 = mass of the earth = 5.98 × 1024 kg d = distance between the center of earth and the center of the moon = 3.9 x 105 km G = 6.67 x 10-11 Nm2/kg2 m2 = 7.2 x 1022 kg T = 2.4 x 106 s = 28 days

Fg = 3.64 x 10-47 N m = 9.0 x 10-31 kg m1 = m2 (m)(m) = m2 4. m1 = 1.67 x 10-27 kg m2 = 9.11 × 10-31 kg d = 0.528 x 10-10 m G = 6.67 x 10-11 Nm2/kg2 5. Fg = 5.42 x 10-71 N d = 1.00 m m1 = m2 = ? Fg = 3.64 x 10-47 N m1 = m2 (m)(m) = m2 m = 9.0 x 10-31 kg

m = 7.3 kg Fg = 72 N EARTH SATURN Fg = 76 N Fg = 4.0 x 10-8 N 6. d = 0.30 m m1 = m2 = ? radius of Saturn =60,280 km 6. m = 7.3 kg Fg = 72 N EARTH SATURN Fg = 76 N

7. T = 23 hrs m1 = 5.69 × 1026 kg G = 6.67 x 10-11 Nm2/kg2 This is the radius of the moon’s orbit; we must subtract the planet’s radius to determine altitude above the planet R = 1.88 x 108 m - 60,268,000 m 1.27 x 108 m = 127,000 km