The Earth, Moon, and Sky Lecture 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.

Summer Winter

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) Now:

Scorpius Night Day Day Night Orion

Summer: July Winter: January

13,000 years from now:

Scorpius Night Day Day Night Orion

Winter: July or January? Summer: January or July?

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

Summer Winter Sun low in Night Day Sun high in Day Night northern sky northern sky

• 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? 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 Orbit time or "synodic month” "sidereal month” 29.5 days 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. Earth Moon

Sun

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

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

Sun Moon Earth

5.2o

Side view

Moon's orbit slightly elliptical: Moon

Distance varies by ~14% Earth

Top view, exaggerated ellipse