ASTR MIDTERM 1

what is a scientific notation and how do we use it?

• used to write big or small numbers in terms of powers of 10

Example #1: 1 AU=149,000,000,000 m

• Step 1: Get number between 1 and 10. Move decimal place to come after first non-zero digit → 1.49

• Step 2: Count number of places decimal moves: 11 → power of 10 → 10¹¹. Move left → positive exponent. Move right → negative exponent.

• Step 3: Result: 1.49 × 10¹¹ m

what is the definition of an AU?

• average distance between the Earth and Sun is one astronomical unit

  • 1 AU = 93 million miles = 149 billion meters

    • pluto ~ 40 AU away

    • nearest star 300,000 AU away

    • our galaxy 10 billion AU across

what is the definition of a light year?

• the distance light can travel in one year

  • found by multiplying the speed of light (300,000 km/s) by the number of seconds in a year

how many seconds are there in a year?

31.5 million seconds in a year

what is the scale of the solar system (in AU)?

ask professor

what is the scale of the milky way (in light years)?

100,000 light years across

what is the celestial sphere?

the sky around the entire earth that looks like a dome…a hemisphere

define right ascension

measured along the the Celestial Equator (increasing eastward) from a reference point in the sky (called the First Point of Aries; like the Prime Meridian of Longitude)

define declination

the angle (above or below) the Celestial Equator — the projection of Earth’s equator onto the sky

define the ecliptic

the annual path of the Sun through the celestial sphere, which is just a projection of Earth’s orbital plane on the sky

define celestial equator

the extension of Earth’s equator onto the celestial sphere (titled 23.5 degree to the ecliptic)

define equinoxes

where the ecliptic intersects the celestial equator

define the north celestial pole

the point in the sky directly above Earth’s north poles (coincides with Polaris)

how many degrees are there in a circle?

360 degree

how do we convert between degrees, arcminutes, and areseconds?

• Full circle = 360º

• 1º = 60 arcmin

• 1 arcmin = 60 arcsec

• 1º = 3600 arcsec

what is polaris? where is polaris?

the north star above Earth’s north pole

define altitude

elevation angle

define azimuth

direction along the horizon

define meridian

a line from the northern horizon point through the zenith and down to the southern horizon

define zenith

the point directly above you

what is the cause of Earth’s seasons?

• tilt of the axis causes different portions of the Earth to receive more or less direct sunlight at different times of year

what is earth’s axis tilt?

23.5 degrees from its orbital plane

what is precession?

when Earth wobbles like a spinning top once every 26,000 years

• it changes the positions in the sky of the celestial poles and the equinoxes

what causes the phases of the moon?

• at any time, half the moon is illuminated by the Sun and half is darkness

  • as moon orbits, we see different combination of bright and dark faces

what causes a solar eclipse? lunar eclipse?

eclipses occur only when the nodes of the Moon’s orbit are nearly aligned with the Earth and the Sun

• solar eclipse at new moon

• lunar eclipse at full moon

who was ptolemy (AD 100-170)?

• made the most sophisticated geocentric model — the Ptolemaic Model

  • sufficiently accurate to remain in use for 1,500 years

  • explained retrograde motion

who was aristarchus of samos (c. 310-230 BC)?

• proposed one of the first heliocentric model

  • calculated relative distances to and size of the Earth, Moon, and Sun

    • used Earth’s shadow during eclipse to estimate relative size of Earth and Moon

    • used timing of first and third quarter moons to estimate relative distances to the Moon and the Sun

who was eratosthenes (c. 276-194 BC)?

• measured the Earth’s circumference

  

what is retrograde motion of the planets?

• planets move west relative to the stars for a few weeks or months

• occurs when we “lap” another planet as Earth orbits the sun

what is stellar parallax and what causes it?

the apparent angular shift of a stars position as Earth orbits the Sun

• stars are so far away that stellar parallax is too small for the naked eye to notice

who was copernicus (polish, 1473-1543)?

• proposed the sun-centered ‘model’ (1543)

• used heliocentric concept to determine layout of the solar system

• found planetary distances in terms of earth’s distance from the sun

• “Copernican Revolution”

BUT

• his model no more accurate than ptolemaic model in planetary positions because he still used perfect circles for the orbits

who was tycho (danish, 1546-1601)?

• compiled the most accurate (~ 1 arcminute) naked eye measurement made of planetary positions

• recognized that other planets go around sun

BUT

• could not detect stellar parallax and though earth must be at the center of the solar system

SO

• he hired johannes kepler who used his observations to discover the truth

who was galileo (1564-1642?

he overcame major objections to the copernican view:

• earth could not be moving because objects in air would be left behind.

• non-circular orbits are not “perfect” as heavens should be

• if Earth were really orbiting Sun, we’d detect stellar parallax

who was kepler (german, 1571-1630)?

• initially tried to match Tycho’s observations (planet’s circular orbits around the sun)

BUT

• an 8 arcminute discrepancy in predicted vs observed orbit of Mars led him to propose ellipses for orbits

SO

• heliocentric, elliptical orbits

who was newtwon (1643-1727)?

• built the first reflecting telescope

• investigated light, color, refraction

• invented calculus

• quantified laws of motion

• connected gravity and planetary forces

• realized that the same physical laws applied on earth and in space

how long does it take an asteroid at an orbit of 4 AU to orbit the Sun? (hint: p² = a³)

8 years

what is the difference between a vector and a scalar?

scalar only have magnitude (size) while vector have both magnitude and direction

what is the difference between mass and weight?

• mass: the amount of matter in an object (units of kg)

• weight: the force that acts upon an object (units of newtons or kg(m/s²)

what is momentum?

product of a body’s mass and velocity

what is speed?

rate which object moves

what is velocity?

speed and direction

what is acceleration?

any change in velocity (either speed or direction)

what is force?

“push” or “pull”

• a method for changing a body’s monentum

what is angular momentum?

the momentum involved in spinning/circling

kepler’s first law

the orbit of each planet around the sun is an ellipse with the sun at one focus

kepler’s second law

as a planet moves around its orbit, it sweeps out equal areas in equal times

• this means that a planet travels faster when it is nearer to the Sun and slower with it is farther from the Sun

  • the speed of a planet’s motion is NOT constant

kepler’s third law

more distant planets orbit the sun at slower average speeds, obeying the relationship:

newton’s first law of motion

an object at rest or moving at constant velocity stays that way unless a net force acts to change its speed or direction

• INERTIA

newton’s second law of motion

the change in a body’s velocity due to an applied force is in the same direction as the force and proportional to it, but is inversely proportional to the body’s mass

• force = mass x acceleration

“a larger mass needs a greater force to achieve the same acceleration”

newton’s third law of motion

for every force, there is always an equal and opposite reaction force

• EX: a rocket is propelled upward by a force equal and opposite to the force with which gas is expelled out its back

The same force, F, is applied to M1 and M2. M2 is 4 times more massive than M1. How do the accelerations of M1 and M2 (a1 and a2) compare?

the acceleration of M1 is 4 times greater than the acceleration of M2 because acceleration is inversely proportional to mass when the same force is applied.

what are three conserved quantities in a physical system that is not subject to any external forces?

• linear momentum

• angular momentum

• energy

what are the units of kinetic energy?

joule

what are the fundamental units of a joule?

1 joule = 1 kg(m²/s²)

what is the difference between temperature and heat?

• temperature is the average kinetic energy of the many particles in a substance

• heat is the transfer of thermal energy between objects due to temperature difference