Charting the Heavens, Foundations of Astronomy

1/22/2018

Lecture 2

The Metric System • The world uses the metric system and so do astronomers.

• 1 meter = 3.28 feet, I am 1.92 meters tall.• The French originated the meter in the 1790s as one/ten-millionth of the

distance from the equator to the north pole along a meridian through Paris.• Now defined as the distance light travels in 1 second

• 1 kilogram = 2.20 pounds, I weigh 92.9 Kg• a cylinder of platinum-iridium alloy

• Units of time are seconds• "the duration of 9,192,631,770 periods of the radiation corresponding to the

transition between the two hyperfine levels of the ground state of the Caesium133 atom”

• Units of temperature are Kelvins• No Negative temperatures• 295 Kelvin is 750 F

Scientific Notation and the Metric system

• Large number are hard to write and read• 1,652,000,000 meters = 1.652x109 meters = 1.652 gigameters• 0.003 seconds = 3x10-3 seconds = 3 milliseconds

• Unlike imperial units, larger metric units are converted by multiplying/dividing by 10.• 72,000 feet = 7.2x104 feet = 2.4x104 yards = 13.63 miles

Light Speed

• Light travels really fast at 299,792,458 meters per second

• Large distance can be measure using light speed:• The moon is 1.28 light seconds away

• The sun is 8.31 light minutes away

• Neptune is 4.02 light hours away

• The edge of our solar system is about 0.2 light days away

• The nearest star is about 4.37 light years away

• Nothing can travel faster than the speed of light!

Astronomers use angles to denote the positions

and apparent sizes of objects in the sky

• The basic unit of angular measure is the degree (°).

• Astronomers use angular measure to describe the apparent size of a celestial object—what fraction of the sky that object seems to cover

• The angular diameter (or angular size) of the Moon is ½° or the Moon subtends an angle of ½°.

• 1° = 60 arcmin = 60´, 1´ = 60 arcsec = 60”

Measuring Distances in Astronomy

• If two angles and a side are know for a right triangle, all other angles and sides can be calculated.

• Any distance to an object can be measured this way if one can measure angles and distances accurately.

Measuring Distances in Astronomy

If the angle between B’ and A’ is measured and the baseline between A and B is know, the distance to the object in space can be measured.

Eratosthenes Determines the Size of the Earth in about 200 B.C.

SyeneAlexandria

Sun's rays

7.2oS

N

Earth

In Syene Egypt, the sun shown directly overhead on the summer solstice

In Alexandria Egypt, the sun shown at 7.2o on the summer solstice

He knows the distance between the two cities is 5000 "stadia".

From geometry then:

7.2o = 5000 stadia360o Earth’s circumference

=> circumference is 250,000 stadia, or 40,000 km.

So radius is:40000km = 6366km

2π

Very close to today’s value of 6378 km!

Inverse Square Laws

• What in an inverse square relation?

𝑌 =1

𝑥2

• As x gets bigger, y decreases and visa versa.

• If x is distance and Y is the force of gravity…• Double the distance -> gravity decrease by factor of 4

• Triple the distance -> gravity decreases by 9

• If x is distance and Y is the apparent brightness…• If the star is 100 miles away, it would appear 1002 = 10,000 times dimmer

than if you were at its surface (do not try at home)

The Celestial Sphere

• Think of objects in the night sky as pasted on some distant sphere that encompasses the earth.

• The sphere slowly rates at a rate of about one rotation per day (23 hr 56 mi).

The Sun’s Daily Motion

• Sun’s motion is not quite the same as stars motion on celestial sphere.

• The Sun moves on the sphere over the course of a year.

• The Sun takes 24 hours to return to the same spot in the sky. (solar day)

• The stars take 23 hours and 56 minutes to return to the same spot in the sky. (sidereal day)

As the Sun moves across the celestial sphere, it covers up different constellations.

• The path the sun takes across the celestial sphere is called the ecliptic

• Note that the celestial equator is tilted 23.50

• Other objects “wander” across the sky in more complex paths. These objects are planets.

• Planets are some of the brightest objects in our night sky

Constellations

• Most stars movement across the celestial sphere is not noticeable with the human eye.• Moving very slow relative to us

• Very far away (almost always this!)

• Human instinct to form patterns from the chaos of nature.

• Constellations are a way of organizing the sky:• Story telling/ Mythology

• Night time navigation

• Astronomy