Newton’s Universal Law of Gravitation

Factors Affecting the Gravitational Force mass distance

force varies directly with masses decrease mass  decreased force force varies directly with masses Fg α m1 m2

Distance r increase r  force decreased

Force varies inversely with distance squared Fg α 1/r2

Fg α m1m2 Fg α 1/r2 m1 m2 Fg α -------- r2 Fg slope = G m1 m2/r2

G = 6.67 x 10-11 N m2/kg2

A 1000 kg car and a 2000 kg truck are 0.50 m apart. Gravitational force: 5.3 x 10-4 N

Computing mass of Earth radius of Earth: 6.37 x 106 m 1.00 kg mass has a weight of 9.81 N mass of Earth: 5.97 x 1024 kg

2F 4F

¼ F 4F

F

“g” gravitational field – weight per mass wtg Fg g = ------ = ------ mass m G M = ------ r2 M = planet mass

Effect of changing variables GM g = ----- r2 if M doubles: if r doubles: if M & r doubles: if r becomes ½: 2g ¼ g ½ g 4g

radius: 53% radius of Earth gravitational field for Mars? mass: 11% mass of Earth radius: 53% radius of Earth gravitational field for Mars? 0.39 gE = 3.84 N/kg

Net gravitational force on bottom mass? √3 GM2/s2

G m1 m2 Fg = ---------- = weight r2 What would happen to your weight if: Earth had twice mass but the same radius: Twice weight Earth had twice radius but same mass: ¼ weight

What is “g” at top of Mt. Everest (8848 m elevation)? 9.77 N/kg = 9.77 m/s2