Chapter 3: Motion of Astronomical Bodies

3.1

Geocentric Universe Models

What an Astronomer sees: Retrograde Motion

• backward motion

• if we are interior to a planet and we are zooming past it, the planet looks like it is moving backwards because it is not as fast

Epicycles

• Ptolemy - epicycles in 150 CE

  • circles within a circle

Heliocentric Models

• Copernicus proposed a heliocentric model

Two Types of Planets: Superior

• conjunction

• opposition - form earth’s perspective, the sun and planet are opposite of each other

• Superior - outside

  • best seen during opposition

Inferior

• superior conjunction

• inferior conjunction

• inferior planets are always visible close to sunrise or sunset

Superior Planets: Periods

• sidereal period

  • in respect to the stars

    • how long does one complete orbit take

• synodic period

  • in respect to the alignment with the Earth and the sun

    • 1/P = 1/E - 1/S

      • where P is the sidereal period, S is the synodic period, and E is Earth’s sidereal period, which is 1 year

Saturn is a superior planet with a synodic period of 378 days. Calculate the sidereal period.

1/P = 1/E - 1/S

1/P = 1/365.25 - 1/378

P = 10,828d/29

Inferior Planets: Periods

1/P = 1/E + 1/S

• where P is the sidereal period, S is the synodic period and E is the Earth’s sidereal period, which is 1 year

Mercury is an inferior planet with a synodic period of 115.88 days. Calculate the sidereal period.

P = 87.97d

Quiz 3

3.2 Keplers Laws Describe Planetary Motion

Tycho Brahe (1546-1601_

• he created geoheliocentric model with other planets orbiting the sun, but with the sun orbiting earth

• begged Kepler to find a model

Johannes Kepler (1571-1630)

• Johannes Kepler worked as an assistant to Tycho

• Empirical rules to describe planetary orbits in a heliocentric system

• these empirical rules are known as Kepler’s laws

Kepler’s First Law: Ellipses

• planet orbits are ellipses, not circles

  • the greater the eccentricity the more elongated the ellipse

• the sun is at the focus of a planet’s elliptical orbit

• the average distances between the Sun and the planet is the semimajor axis

Astronomical unit = (average) distance between the sun and the earth

Real Shape of Planetary Orbits

• in our solar system, most planetary orbits are nearly circular

Kepler’s Second Law

• equal areas in equal times

• planets are moving faster when they are moving closer to the sun and slower when they are moving further away

Kepler’s Third Law

• Law of Harmonies

• Kepler’s third law relates the orbital period to the size of the orbit

a³=p² <— orbital period of planet; years

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semi major axis

• half long axis of an ellipse; measured in Au

Practice

3.4 Newton’s Three Laws Help Explain How Celestial Bodies Move

Isaac Newton (1642-1727)

• physical laws explain how things work, while empirical laws only describe nature

Newton’s First Law of Motion

• a moving object will stay in constant motion and an object at rest will stay at rest unless acted on by a net force

• Galoileo’s law of inertia

• “Constant” motion means at a constant speed and in a constant direction: This is an inertial frame of reference

  • velocity - speed and direction of an object’s motion

  • speed: driving 60 miles/hour

  • acceleration

    • change in velocity called acceleration

Newton’s Second Law of Motion

F= ma

• if a net force acts upon an object, the object’s motion changes

• forces causes an acceleration

Acceleration Depends on Force and Mass

Newton’s Third Law of motion

• for every action, there is an equal and opposite reaction