Astronomy - Topic 8 - Planetary motion and gravity

What did Brahe observe?

his naked eye observations showed that planets didn’t fit in perfectly circular orbit, allowing Kepler to replace the data, replacing the Geocentric model with a heliocentric, elliptical model (image)

How did Copernicus contribute to the heliocentric model?

made the heliocentric model, removing the complex epicycles

How did Kepler contribute to the heliocentric model?

using the data from Brahe, he discovered planets move in ellipses, and produced his 3 laws, mathematically proving this model

How does gravity create a stable elliptical orbit?

gravity pulls planets into orbit, using the inverse square law

What is perihelion?

when a planet moves fastest, closest to the sun

What is aphelion?

when a planet moves slowest, furthest from the sun

How is a stable orbit formed?

the balance between forward motion and gravitational pull creates this

What is Kepler's 1st law?

planets orbit in ellipses, with the sun as the focus

What is Kepler's 2nd law?

planets orbit in equal areas in equal time, perihelion and aphelion

What is Kepler's 3rd law?

period

What does the T in constant = T^2/r^3 stand for?

orbital period

What dies the r in constant = T^2/r^3 stand for?

mean orbital radius

What is perihelion?

closest to the sun (applies to solar orbits)

What is aphelion?

furthest from the sun (applies to solar orbits)

What is perigee?

closest to Earth (applies to Earth orbits)

What is apogee?

furthest from Earth (applies to Earth orbits)

Why do these occur?

because orbits are elliptical

When does Kepler's 3rd law constant work?

when comparing bodies orbiting the same thing, everybody has a different constant

Why does a constant depend on central mass?

the constant in inversely proportional to the moss of the central body

How does this work?

a bigger central mass means a stronger gravity, meaning a shorter orbital period, meaning a smaller constant

How does this work?

a smaller central mass means a weaker gravity, meaning a longer orbital period, meaning a bigger constant

How does Newton explain Kepler's laws?

Newton's law of universal gravitation shows Kepler's laws naturally form gravity, providing a centripetal force, and planets following paths determined by inverse

What is a centripetal force?

an inward force keeping an object in curved or circular motion

How is gravity related to the product of the masses?

gravity is proportional to the product of the masses (F (proportional sign) Mxm)

How is gravity related to the distance?

gravity is inversely proportional to the distance squared (F (proportional sign) 1/d^2)