AST MT1 - Heliocentric Universe and Newton

Lessons 5 and 6

Kepler’s first law

Each planet moves around the Sun in an orbit that is an ellipse, with the Sun at one focus

Kepler’s second law

A planet moves faster in the part of the orbit closest to the Sun and slower when farther from the Sun, sweeping out equal areas in equal times

Kepler’s third law

More distant planets orbit the Sun at slower average speeds, obeying a precise mathematical relationship

What is the equation that describes Kepler’s third law?

T = 365.24 √r³

• T = orbital period in days

• r = orbital radius in AU

Who disproved the belief that “everything in the heavens are perfect circles and spheres”?

Galileo Galilei

• Observed the fact that the Moon has mountains and craters

What did Galileo observe about Venus?

That it has phases and that the apparent size changes throughout the year

• “New” phase happens when it appears largest

• “Full” phase happens when it appears smallest and is in line with the Sun

Define “speed”

The rate of change of position.

Define “velocity”

Speed and direction.

Define “acceleration”

The rate of change of velocity / Speed or direction or both changing.

Newton’s first law

An object in motion remains in motion unless acted upon by an outside force.

Newton’s second law

Acceleration is proportional to force and inversely proportional to mass.

• A = F/m

• More force = more acceleration

• More mass = less acceleration

Newton’s third law

For every force, there is always an equal and opposite reaction force.

Define “momentum”

An unchanged measure of a body’s motion in the absence of any outside influence

• Mass x velocity

• p = mV

Define “angular momentum”

The measure of the rotation of a body as it revolves around some fixed point

• Mass x velocity x distance

• w = mVr

What is the equation for Newton’s Universal Law of Gravitation?

F = G (M₁ x M₂ / d²)

• F = gravitational force between two objects

• M1 and M2 = masses of the two objects

• d = their separation

• Force is proportional to the product of the masses

• Force is inversely proportional to the square of the distance

What happens when you double the mass of either object?

The force doubles.

What happens when you halve the mass of either object?

The force halves.

What happens when you double the distance?

The force reduces by a factor of four.

What happens when you halve the distance?

The force increase by a factor of four.

What happens when you drop something on Earth?

It speeds up as it falls, gaining an acceleration of 10 m/s

Define ‘aphelion’

Where a planet is farthest from the Sun and moves the slowest.

Define ‘perihelion’

Where a planet is closest to the Sun and moves the fastest.