The Earth, Moon, and SkyLecture 5

1/31/2017

From Last Time:Stable Orbits

• The type of orbit depends on the initial speed of the object

• Stable orbits are either circular or elliptical.

• Too slow and gravity pulls the object back in

• Too fast and gravity is not strong enough. This is called the escape velocity

From Last Time:Difference between Mass and Weight

• Newton’s Second Law: Force = mass x acceleration

• Mass is a measure of how much material an object has.

• Weight (force) is a measure of home much acceleration a mass is feeling.

• Earth’s surface acceleration 9.8 m/sec2 -> • My weight is 889 Newtons (mass = 90.7 Kg)

• Jupiter’s surface acceleration 24.79 m/sec2 ->• My weight is 2248.4 Newtons

• We as a society conflate mass and weight since everyone feels the same gravity. We mix up Newtons and Kilograms, though not the same.

Locating Places on Earth• We live on a sphere and thus define our position

using two angles.

• Latitude measures North/South angular distances with 0 degrees at the Equator

• Longitude measures East/West angular distances with 0 degrees on the Prime Meridian (Greenwich, England).

• Washington, DC is at 38.9072° N, 77.0369° W

• Albuquerque is at 35.0853° N, 106.6056° W

• Melbourne Australia is at 37.8136° S, 144.9631° E

The Seasons

• The Earth is on an elliptical orbit, sometimes it is farther away to Sun, sometimes it is closer. Does this create Seasons?• It is summer in the southern hemisphere.

• Earth is actually its closest to the Sun in January.

• Earth varies its distance to the Sun by about 3% over a year.

• Conclusion: Earth changing its distance to the Sun create seasons.

• Axial tilt, 23.5o, does create seasons.

• The Suns position in the sky changes throughout the year because of the tilt

Axial Tilt: 23.5o

• Summer occurs for a certain hemisphere, when it is “leaning” towards the Sun.

• Hemispheres distance to the Sun is changing, but it is insignificant relative to the distance from the Sun to the Earth.

• Sun light is more direct in Summer and more spread out in Winter.

WinterSummer

Seasons also depend of the amount of daylight.

Solstices

• Around June 21, the Sun is the most over head it will be all year.

• At Latitude 23.50 N, Tropic of Cancer, the Sun appears directly overhead at noon.

• 90° – 23° (or 67° N), Article Circle, the Sun does not set that day.

Equinoctia

• Halfway between the solstices, on about March 21 and September 21.

• The Sun is on the celestial equator and whole planet receives ~12 hours day/night

• At the poles of the Earth, the Sun only rises or sets once per year on the equinox.

Length of the Day

• A day is a measure of how long the Earth takes to rotate relative to…

• Relative to the Sun: Solar Day (24 hours)

• Relative to distance stars: Sidereal Day (23 hours 56 minutes)

Winter: July or January?

Winter: January

Scorpius OrionDayNight Day Night

Scorpius OrionNightDayNight Day

Summer: January or July?

Summer: July

Now:

13,000 years from now:

We choose to keep July a summer month, but then in 13,000 years, summer occurs on other side of orbit!

The Year

• The Earth revolves around the Sun in 365.256 days (“sidereal year”). But the year we use is 365.242 days (“tropical year”). Why?

• Why do we have a leap year?

Summer Winter

DayNight Day NightSun high in northern sky

Sun low in northern sky

The Motion of the Moon

• Half of the Moon's surface is lit by the Sun.

• The Moon has a cycle of "phases", which lasts about 29 days.

• During this cycle, we see different fractions of the sunlit side.

Which way is the

Sun here?

Cycle of phases slightly longer than time it takes Moon to do a complete orbit around Earth.

Cycle of phases or "synodic month”

29.5 days

Orbit time or "sidereal month”

27.3 days

Tides

• A feature of oceans (but solid materials have small tides too).

• Two high and two low tides per day.• Tides are due to the gravitational pull being

stronger on side of Earth closest to it (Sun causes smaller tides)

• Earth-Moon gravity keeps them orbiting each other. But side of Earth closest to Moon has slightly stronger pull to Moon => bulges towards it.

• Other side has weaker pull => bulges away compared to rest of Earth.

• The Earth spins once a day while the bulge always points towards and away from the Moon => high and low tides.

Eclipses

Lunar eclipse: When the Earth passes directly between the Sun and the Moon.

Solar eclipse: When the Moon passes directly between the Sun and the Earth.

Sun

Earth Moon

Sun

EarthMoon

Moon's orbit tilted compared to Earth-Sun orbital plane:

SunEarthMoon

Moon's orbit slightly elliptical:

Earth

Moon

Side view

Top view, exaggerated ellipse

Distance varies by ~14%

5.2o