Gravity

Newton’s Universal Law of Gravitation

Newton’s conceptual leap in understandinggravity was his realizationthat the same force governs the motion of a falling objecton Earth & the motion of the

Moon in its orbit around the Earth.

Universal Law of Gravitation

• Every mass attracts every other mass through gravity.

• The force of attraction between any 2 objects is directly proportional to the product of their masses.

• Doubling the mass of 1object doubles Fg between the 2 objects.

Inverse Square

• Doubling distance between two objects weakens force of gravity by a factor of 22 (or 4).

• Fg drops off by ¼.

NEWTON’S UNIVERSALLAW OF GRAVITATION

Fg =GMm

r2

G is universal gravitation constant.

G = 6.67 x 10-11 N m2. kg2.

m1 m2 are mass of objects in kg.

r is distance between ctrs m.

Gravity and Weight• Definition: The weight of an object is a measure

of the Fg one object feels in the presence of another.

• Weight Fg = mg. Where g is known.

Mass can be measured in 2 ways

• Inertial mass - the mass of a body as determined by its momentum, as opposed to gravitational mass. How it accelerates

• m = Fnet/a

• Gravitational mass -the mass of a body determined by its response to the force of gravity.

1. Prove that the acceleration of gravity g = GM/r2, where M is the mass of a planet or star r is its radius.

Fg = m2g = GM1m2. r2.

g = GM1 is accl due to gravity r2.

Mass of the object cancels out.Acceleration depends only on the mass of the

planet (or star).

• Is heavier body attracted to the Earth with more force than a light body.

•Does the heavier object free fall faster?

•Explain.

Questions: Raise Hands.

Newton’s Universal Law of Gravitation

• Fg = GMm.

R2.

Describes Force btw point masses.What is a point mass?

Gravitational Field deals with space around the mass.

Gravitational Field Strength/Intensity -Force per unit mass experienced by a

small “test mass” in space.

Gravitational Field Linesdrawn in direction of acceleration of small

mass.

Gravitational Field = g.

The value for acceleration, g, is also called the gravitational field. Set the weight equal the Fg. The units of the gravitational field are N/kg.

Since mg = GMm. The small mass m cancels

r2.

Grav Field g = GM units N/kg. r2.

Use to find acceleration or gravitational field.

2. What is the gravitational field strength due to Earth at a point

450 km above the surface?

• g = GM r2.

• (6.67 x 10-11)(6 x 1024kg)(6.4 x 106m + 450 x 103m)2.

• 4 x 1014.(6 850 000)2.

• 4 x 1014.

4.7 x 1013. 8.5 N/kg

Fields are vectors. Forces resulting from more than 1 field is the sum of the field strengths.

Ex 3. Two spheres lie along a straight line. The sphere on the left has m = 1000-kg, and the right on the right has m = 100-kg. The distance between their centers is 5-m.

Point A lies between the spheres at 2.5-m from the center of each.

Calculate the field strength at point A.

9.63 x 10 – 9 N/kg left

Rd Hamper 127 – 129 do pg 129 - 131.Purple boxes #1 – 5.Show all work.

Einstein vs. Newton9.5 min

• http://www.youtube.com/watch?v=4yyb_RNJWUM

Orbits Maintained By Gravity

4. Derive an equation to express the minimum

velocity a satellite must have to stay in orbit.

v = (GMe)1/2. (r) 1/2.

Fg keeps the satellite in orbit.

Set Fc equal to gravitational force.

Fg = Fc

GMem = mv2. r2 r

5. What is the velocity needed for a satellite to stay in orbit 200 km above the Earth’s surface?

First find the total distance between their centers.

6.37 x 106 m.

2.0 x 105 m.

6.57 x 106m total r.

v = (GMe)1/2. (r) 1/2.

(6.67x10-11)(5.98x1024 kg)1/2

(6.57 x 106m )1/2.

7790 m/s.

Cavendish Torsion Balancemeasurement of G.

Einstein vs. Newton9.5 min

• http://www.youtube.com/watch?v=4yyb_RNJWUM

http://www.phy.ntnu.edu.tw/java/projectileOrbit/projectileOrbit.html• Newton’s Cannon Launch Satellite

• Apparent weightlessness. Satellites are in freefall around the Earth! That is why astronauts appear weightless. They are constantly falling toward Earth. Their rate of fall is balanced by their tangential momentum.

The universe season 2 Gravity, Roller Coasters, Space Travel & PEg.

https://www.youtube.com/watch?v=EiljzeDL0co 45 minutes