ERTH 105 OL

VOYAGE THROUGH THE SOLAR SYSTEM

SPRING 2023

THE SOLAR SYSTEM

• Overview of celestial bodies and astronomical phenomena.

HISTORICAL CONTEXT

THE ORBS OF HEAVEN

• Title of a work: "The Orbs of Heaven, or, The Planetary and Stellar Worlds"
• Author: O. M. Mitchell, A.M.
• Position: Director of the Cincinnati Observatory.
• Publication Info: 1851, London, Office of the National Illustrated Library, 198, Strand.
• Mention of Galileo Galilei (1564-1642 CE)

ACHIEVEMENTS IN ASTRONOMY

Observational Highlights

• Moons of Jupiter (discovered by Galileo)
• Phases of Venus (observational evidence for heliocentric theory)
• Surface of the Moon (detailed observations)
• Sunspots (variations in solar activity)
• Laws of Motion (formulated by Isaac Newton)

ISAAC NEWTON (1642 – 1727 CE)

Characterization of Newton's Laws

Newton's Laws of Motion

• Modification of Kepler’s Laws:
  • Kepler: described the motions of planets.
  • Newton: explained the the mechanics behind those motions.

NEWTON'S LAWS OF MOTION

First Law

• Explanation: A body at rest, or in uniform motion, will remain so unless acted upon by an unbalanced force.

Second Law

• Explanation: The change in motion (acceleration) is proportional to the unbalanced force.
• Mathematical Representation: $F = m imes a$

Third Law

• Explanation: For every action, there is an equal and opposite reaction.

GRAVITY

Definition and Effects of Gravity

• General Definition: The force that holds us to the Earth, causes a rock to fall towards the ground, keeps the Earth in orbit around the Sun, and drives the Sun's motion towards the center of the Milky Way galaxy.
• Universal Applicability: Gravity acts between any two objects even if they are far apart; describes an “action at a distance.”

DESCRIPTION OF MOTION

Key Questions

• How do we describe motion?
• How is mass different from weight?

Precise Definitions

Speed

• Definition: Rate at which an object moves.
• Example: 10 m/s.

Velocity

• Definition: Speed in a given direction.
• Example: 10 m/s, due east.

Acceleration

• Definition: Any change in velocity.
• Units: m/s².
• Formula: $a = \frac{\Delta v}{\Delta t}$ where $\Delta v$ is change in velocity and $\Delta t$ is change in time.

Acceleration of Gravity

• Observation: All falling objects accelerate at the same rate, ignoring air resistance.
• On Earth: $g \approx 10 \, \text{m/s}^{2}$; speed increases by 10 m/s each second during free fall.

Historical Experiment

• Apollo 15 Demonstration: Galileo demonstrated that all falling objects accelerate at the same rate regardless of their mass.

MOMENTUM AND FORCE

Definition of Momentum

• Formula: Momentum = mass x velocity.
• Impact of Force: A net force changes momentum, often resulting in acceleration.
• Angular Momentum: The rotational momentum of a spinning or orbiting object.

THOUGHT QUESTIONS ON FORCES

Scenarios to Analyze Net Force

• A car coming to a stop: Yes (Y)
• A bus speeding up: Yes (Y)
• An elevator moving up at constant speed: No (N)
• A bicycle going around a curve: Yes (Y)
• A moon orbiting Jupiter: Yes (Y)

WEIGHT AND MASS

Conceptual Understanding

Differences

• Mass: The amount of matter in an object.
• Weight: The force acting upon an object due to gravity.

Weight on the Moon

• Thought Analysis:
  • My weight is the same, my mass is less?
  • My weight is less, my mass is the same?
  • My weight is more, my mass is the same?
  • My weight is more, my mass is less?

Astronauts in Space

Weightlessness

• Explanation: Weightlessness is a result of free-fall, despite the presence of gravity in space.

LEARNING SUMMARIES

Describing Motion

• Final Notes:
  • Speed = distance/time
  • Velocity includes direction.
  • Acceleration is a change in velocity.
  • Momentum = mass x velocity.
  • Force causes change in momentum, leading to acceleration.

Difference Between Mass and Weight

• Final Notes:
  • Mass = quantity of matter.
  • Weight = force acting on mass.
  • Objects are weightless in states of free-fall.

IMPACT OF NEWTON'S WORK

Contributions to Science

• Newton unified physical laws on Earth and in celestial mechanics, establishing the principle that the same laws govern both realms.
• Key Discoveries: Laws of motion, gravitational law, experiments in light, development of the first reflecting telescope, and contributions to calculus.

RECAP: NEWTON'S LAWS

Summary of the Three Laws of Motion

• First Law: An object remains at rest or in uniform motion until acted upon by an external force.
• Second Law: The force acting on an object equals the mass times the acceleration: $F = m \times a$
• Third Law: For every action, there is an equal and opposite reaction.

THOUGHT QUESTIONS

Force Comparisons

• How does the force the Earth exerts on you compare with the force you exert on it?
  • Options:
  • Earth exerts a larger force on you.
  • You exert a larger force on Earth.
  • Earth and you exert equal and opposite forces on each other.