Summary 3 - Quiz 3 Wed Oct 11th

CONCEPT SUMMARY- 3

For Quiz 3 on Wednesday October 11th (20 mins of review, 30 mins multiple choice):

Read the textbook - particularly chapter 6

Go through the sessions on the website

check understanding of concepts, not just definitions but how things work.

Make up your own questions - there are only so many things to ask!

Go to the review session on Mon 6.30-8.30pm in G1B27 (may change to bigger room)

Newton's 3 Laws of Motion

1st - A body at rest or in uniform motion tends to stay so

2nd - A body accelerates when a force is applied

Acceleration = Force / Mass of body

Force = Mass x Acceleration

3rd - For every action there is an equal and opposite reaction

Force of Gravity

Newton saw that gravity keeps the Moon in orbit as well as explaining falling apples - explains WHY Kepler’s Laws of planetary motion work.

Gravitational force between two objects pulls them together - the force is proportional to the mass of each object and inversely proportional to the square of the distance between their centers of mass.

Force of gravity = G x Mass1 x Mass2 / Distance²

Force of gravity due to Earth

= G xM_Earth x M_object /R_Earth²

"Weight" of an object = the force of gravity - depends on where the object is - the mass is the amount of "stuff" - does not vary with location

Acceleration Due to Gravity

Acceleration of Object = Force it experiences / Mass of object

Acceleration of Object = G x M_{Earth /}R_Earth²

Does NOT depend on Mass of Object -Everything falls at the same rate.

In Orbit

Objects in orbit are constantly changing direction -> accelerating

In "free fall" around the Earth - Gravity provides an inward force

a = semi-major axis of orbit = orbital distance from center of Earth for a SIMPLE, CIRCULAR ORBIT.

Acceleration of Object orbiting Earth = G x M_Earth / a²

Does NOT depend on Mass of orbitER - only depends of Mass of orbitEE

Sub-Orbital

Speed < 8 km/s falls back onto the Earth.

Bound Orbits - Ellipses.

Speed > 8 km/s -> into orbit.

Center of Mass of orbitEE at focus.

The larger the eccentricity, the more elongated the ellipse.

OrbitEE provides the gravity to hold the orbitER in orbit

The orbitER changes direction (it is accelerating)

Orbital speed for circular orbit

= (GM/a)^1/2
= DISTANCE / TIME
=2 p a / P

where P = orbital period

At Low Earth Orbit = 8 km/s = 18,000 mph

SAME for ALL orbitERs.

Unbound orbits - Escape.

Speed > escape speed (2 x orbital speed) orbitEE's gravity is insufficient,

so orbitER escapes.

Newton’s Version of Kepler’s 3rd Law - NVK3L

Applies ALWAYS and EVERYWHERE - ALL orbitERs and ALL orbitEEs

(while Kepler’s 3rd Law only applies to planets orbiting the Sun)

P² = [4 p² / GM]      a³

Kepler’s 3rd Law (P / years)² = (A / AU)³ can only be used for planets orbiting the Sun.

The POWER of NVK3L is that if we can measure P and a then we can determine M=Mass of the ObitEE

MorbitEE = [ 4 p²  /G] [a³ / P²]

4 p² /G = 4 x (3.14....)² / 6.6 x 10^-11 = 6 x 10¹¹ = a NUMBER

a is measured in meters, P is measured in seconds, then M is given in kg

NVK3L allows determination of the mass of the orbitEE.

This is a VERY POWERFUL tool - it is how we can measure the mass of planets, stars, black holes, galaxies......

Key Words: Force, Acceleration, Mass, Weight, Center of Mass, OrbitEE, orbitER, Circular orbital speed, orbital period, orbital distance, ellipse, eccentricity, bound, unbound, escape velocity.

YOU WILL BE GIVEN THE FOLLOWING FORMULAE ON THE TEST

F = M A

Force of gravity = G x Mass1 x Mass2 / Distance²

Orbital speed for circular orbit = (GM/a)^1/2

P² = [4 p² / G]  a³