Newton’s Universal Law of Gravitation

Factors Affecting the Gravitational Force

mass

distance

Mass

m1 m2

force varies directly with masses

Fg α m1 m2

decrease mass forcedecreased

Distancer

increase r

forcedecreased

Force varies inversely with distance squared

Fg α 1/r2

m1 m2

Fg α -------- r2

Fg

m1 m2/r2

slope = G

Fg α m1m2

Fg α 1/r2

G = 6.67 x 10-11 N m2/kg2

A 1000 kg car and a 2000 kg truckare 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

Mars mass: 11% mass of Earthradius: 53% radius of Earth

gravitational field for Mars?

0.39 gE = 3.84 N/kg

M M

M

s

s s

Net gravitational force on bottom mass?

√3 GM2/s2

G m1 m2

Fg = ---------- r2

= weight

What would happen to your weight if:

Earth had twice mass but the same radius:

Earth had twice radiusbut same mass:

Twice weight

¼ weight

What is “g” at top of Mt. Everest(8848 m elevation)?

9.77 N/kg = 9.77 m/s2