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• Topics covered include distance scales, unit conversions, coordinate systems, and Newton's Laws

Astronomy

• Astronomy studies everything in the Universe from Earth's perspective
• The laws of physics explain all phenomena in the Universe
• Cosmology focuses on the Universe's origin, evolution, and large-scale structure
• Astronomy studies celestial objects and their behavior
• Cosmology is more theoretical, while astronomy is observational and object-specific
• Concepts of physics will be introduced as needed throughout the course
• Topics covered will be well-supported by evidence, with speculative ideas clearly identified as conjecture
• Conjecture: a guess, untested
• Theory: a framework for describing nature that is comprehensive and self-consistent
• Model: a framework validated through observation and experimental testing
• Laws of Physics: well-established theories that have passed every test

Distance Scales

• Size of an atom: 1 nanometer (nm) is 0.000 000 000 1 meter (m)
• Average height of an adult: 1.65 m
• Diameter of the Earth: 12,756 kilometers (km), which is 12,714,000 m
• Distance to the moon: 384,400 km
• Distance to the Sun: 149.6 million km, which is 149,600,000,000 m
• Distance to the nearest star (Proxima Centauri): 4.24 light-years, equivalent to 40.13 x 10^15 m
• Distance to the nearest Galaxy: 2.5 million light-years, equivalent to 23.6 x 10^21 m

Scientific Notation

• 10^1 equals 10
• 10x10x10 = 10^3 = 1,000 (thousand)
• 10^6 = 1,000,000 (million)
• 10^9 = 1,000,000,000 (billion)
• 10^0 = 1
• 1/100 = 1/10^2 = 10^-2 = 0.01
• 10^-1 = 0.1 (one tenth)
• 10^-3 = 0.001 (one thousandth)
• 10^-6 = 0.000 001 (one millionth)
• 10^-9 = 0.000 000 001 (one billionth)

Metric Unit Prefixes

• Tera (T) equals 10^12
• Giga (G) equals 10^9
• Mega (M) equals 10^6
• Kilo (k) equals 10^3
• Centi (c) equals 10^-2
• Milli (m) equals 10^-3
• Micro (µ) equals 10^-6
• Nano (n) equals 10^-9

Physical Quantities and Units

• Fundamental quantities in physics include mass, time, length, charge, and spin
• Mass is measured in kilograms (kg) using the SI system
• Time is measured in seconds using the SI system
• Length is measured in meters using the SI system

Standards of Measurement

• Physical quantities use the base dimensions of Length (L), Mass (M), and time (T)
• The fundamental SI units of measurement are in meters, kilograms and seconds

Astronomy-Specific Distance Scales

• Three other commonly used units include the astronomical unit (AU), the light year (ly), and the parsec (pc)
• The Astronomical Unit (AU) is the average distance between the Earth and the Sun
• 1 AU is 1.496 x 10^8 km or 92.96 million miles
• The average distance between the sun and Jupiter is 5.2 AU

Light Year

• A light year (ly) is the distance light travels in one year
• Light travels at approximately 3.00 x 10^8 m/s
• 1 ly is calculated as 9.46 x 10^12 km or 63,240 AU

Parsec

• 1 parsec (pc) is equal to 3.26 ly
• 1 pc is equal to 3.09 x 10^13 km
• kilo (k) and mega (M) prefixes are often used for large prefixes
• 1 km = 10^3 m
• 1 kly = 10^3 ly
• 1 Mpc = 10^6 pc
• An example is the distance from the sun to the center of the Milky Way, being 28 kly

Unit Conversions

• Conversion factors are written as a fraction such that the unwanted units are cancelled when multiplied by the quantity
• examples: convert 2.5km to m, convert 5 mi to m given that 1 mi = 1609 m, convert 20 in. to cm given that 1 in. = 0.0254m = 2.54cm, convert v=21m/s to mi/s, convert a=20 m/s^2 to km/min^2
• An example is Mars, at is 1.524 AU from the Sun, which is calculated as 2.28 × 10^8km

Coordinate Systems

• Coordinate systems are use to specify locations in space
• They use a fixed reference point, (the origin), a set of specified axes or directions, as well instructions on labeling a point in space relative to the origin and axes
• Useful two-dimensional coordinate systems are Cartesian (rectangular) and Plane Polar

Trigonometry Review

• r^2 = x^2 + y^2
• sin θ = opposite/hypotenuse = y/r
• cos θ = adjacent/hypotenuse = x/r
• tan θ = opposite/adjacent = sin θ/cos θ = y/x

Relating Polar and Cartesian Coordinates

• To convert from polar (r, θ) to Cartesian (x, y):
  • x = rcos(θ)
  • y = rsin(θ)
• To convert from Cartesian (x, y) to polar (θ):
  • tan^-1(y/x) = θ
• Important to note distinction between degrees and radians

Force

• A force is defined as a push or a pull
• Forces can be categorized as either contact forces or field forces
• Contact forces involve physical contact between interacting objects
• Field forces: an object creates an invisible ´influence’ or field around it, other objects experience a force when they interact with the field
• Force is a vector quantity, described by both magnitude and direction
• Direction of a vector is a physical direction in space

Newton's First Law

• An object moves with a constant velocity unless a non-zero net force acts
• An object's velocity remains constant if and only if the net force is zero
• This law pertains to the net force, not just a single force influencing an object

Net Force

• The vector sum of all external forces exerted on an object (the net force) determines the motion of the object
• Fnet = ΣF = F1 + F2 + ... + Fn
• The unit of force is the Newton (N)

Inertia

• Inertia is the tendency of an object to maintain its motion in the absence of a force
• Inertia also describes the tendency of an object to resist changes in its motion

Newton's Second Law

• The acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass
• a = ΣF/m
• ΣF = ma
• ΣFx = max, ΣFy = may, ΣFz = maz
• When there is no net force, the acceleration is zero, and velocity is constant

Gravitational Force

• Newton's Law of Universal Gravitation describes the gravitational forces between two objects
• F = (Gm1m2) / r^2
• r is distance between centers
• G = 6.67 x 10^-11 N⋅m²/kg²

Weight

• Consider an object of mass m near the Earth's surface (r ≈ RE)
• An object in free-fall near the Earth's surface experiences an acceleration of magnitude g
• Net force (gravitational force) causes acceleration
• The magnitude of the gravitational force is called weight, w
• ΣF = ma
• Fgrav = mgrav
• w = mg

Substituting from Newton's Law of Universal Gravitation

• G(MEM/RE^2) = mg
• G(ME/RE^2) = g
• The relationship between mass and weight formula: w = mg
• Value of g depends on location, geologic formations beneath, and altitude
• Effective value of g is influenced by Earth's rotation
• The value of g differs on the Moon or other planets

Newton's Third Law

• Forces always occur in pairs
• Force always involves interaction between two objects, each exerting force on the other
• Forces exist as an action/reaction pair
• Action and reaction forces act on different objects
• Action and reaction forces have the same magnitude and are in opposite directions
• "For every action, there is an equal and opposite reaction."
• If object 1 exerts force F12 on object 2, then object 2 exerts force F21 on object 1
• F12 = -F21

Important Notes

• When an object is in static equilibrium, the net force acting on it is zero
• ΣF = 0 implies ΣFx = 0 and ΣFy = 0 and ΣFz = 0
• Even with a non-zero net force, aligning a coordinate axis with the acceleration direction means the net force component in that direction will be the only nonzero component