Gravitation

Additional reading: Higher Physics for CfE, p.55 – 63.

Notes p.34

Newton’s “Thought Experiment”Sir Isaac Newton, as well as giving us the three laws, came up with an ingenious thought experiment for satellite motion that predated the first artificial satellite by over 300 years!

Flat surface.Object takes a curved path and lands.

Surface curves away.Object takes longer to land.

Newton proposed that, if the object has a fast enough horizontal velocity and is launched from a suitable height above the atmosphere, so that there is no air resistance, then the object will continue to fall but never land. The Earth’s surface curves “away” from the object with the same flight path as the object.

The object has become a satellite in orbit around Earth.

Of course there is no mountain this high … satellites are taken to their launch position in rockets!

Points to Note

Higher altitude satellites require ___________ launch velocities.

lower

Objects in continual freefall (like satellites or space stations or astronauts in space stations) appear to be ___________ .weightles

s

At an altitude of almost 36 000 km a satellite needs to travel at 11 300 kmh-1. This orbit has a period of _____ making the satellite _______________.

24 hgeostationary

Which Statement is Correct?

“A geostationary satellite is one which remains above the same point on the Earth’s surface.”

“A geostationary satellite is one which remains at the same point above the Earth’s surface.”

OR

Find Out About …

1. “Escape velocity” of a planet. What’s Earth’s?

2. “Slingshot effect” … checkout this cool link and try

the animation.

http://galileoandeinstein.physics.virginia.edu/more_stuff/flashlets/Slingshot.htm

Gravity and Mass

Notes p.35

If there is one thing that causes confusion in physics [aye, it would be good if it was only one thing!] then the distinction between mass and weight could be it.

Mass is a measure of how much __________ an object contains. This will only change if _________ is added or taken away.matter

matter

We already know that large masses, for example planets and stars, have __________ fields around them.

gravitational

In fact ALL ________ produce gravitational fields it’s just that for small masses the field is negligible.

masses

I am attracted to you 

I am even attracted to you 

Gravitational field strength is defined as

__________________________________

__________________________________the force, caused by gravity, acting on

each 1 kg of mass. (Or the “weight per

kg”) Body Gravitational Field Strength (Nkg-1)

Sun 274.13

Moon 1.62

Mercury 3.59

Venus 8.87

Earth 9.81

Mars 3.77

Jupiter 25.95

Saturn 11.08

Uranus 10.67

Neptune 14.07

Newton’s Universal Law of GravitationNewton devised the following formula to calculate the force of attraction caused by gravity between two objects:

F = G m1 m2 r2

where:F = force between the masses (in N)G = the Universal Constant of Gravitation (= 6.67 x 10-11 m3kg-1s-2)m1 = mass of first object (in kg) m2 = mass of second object (in kg)r = distance between the mass centres (in m)

Notes p.36

Worked Example 1Mass of Earth = 6 x 1024 kgMass of Moon = 7.3 x 1022 kgMean distance between the centres of the Earth and the Moon = 3.84 x 108 m

Determine the gravitational force between the Moon and the Earth.

F = G m1 m2 r2m1 = 6 x 1024 kg

m2 = 7.3 x 1022 kgr = 3.84 x 108 mG = 6.67 x 10-11 m3kg-1s-2

= 6.67 x 10-11 x 6 x 1024 x 7.3 x 1022

(3.84 x 108) 2

= 1.98 x 1020 N

Worked Example 2Determine the gravitational force between 2 pupils of masses 50 kg and 65 kg who are sitting 1 m apart.

F = G m1 m2 r2m1 = 50 kg

m2 = 65 kg r = 1 mG = 6.67 x 10-11 m3kg-1s-2

= 6.67 x 10-11 x 50 x 65

(1) 2

= 2.2 x 10-7 N

1m

Consequences and Applications of Gravity

Read Notes page 37!Really, do, it’s interesting stuff! All about …

How stars and planets are formed … GRAVITY!

The slingshot effect for space travel … GRAVITY!

For most situations gravity is well approximated by Newton’s Universal Law of Gravitation.

However …

In modern Physics, gravitation is most accurately described by the General Theory of Relativity (proposed by Einstein). This describes gravitation as a consequence of the curvature of space - time.

Don’t worry … this is outwith the scope of the Higher course

Complete Problems from Tutorial IV Gravitation Q. 1 - 6

Answers1. F = m1 m2 / r2

2. 417 N3. 2.7 x 10-4 N4. 3.6 x 10-47 N5. 3.54 x 1022 N6. 4.00 x 10-15 m