Newton’s Universal Law of Gravitation and planetary orbits

PTYS/ASTR 206 Gravity (cont.) / Night Sky / Seasons1/23/07

Newton’s Universal Law of Gravitation and planetary orbits


Announcements

• The first homework due Thursday (at the start of class).– The next assignment will be posted on the

website on Thursday

• Weekly preceptor-led study group– Every Monday 10:30AM-12:00Noon

• Mission update volunteers?


Tonight's Public-Lecture Series: Dr. Martin Tomasko

Mission to the Surface of Saturn’s Moon Titan(7:30 PM, 308 of Kuiper – this room)


STEREO “first light” image of Comet McNaught


Today’s Topics

• Gravity continued– Newton’s Universal law of Gravitation– orbits

• Diurnal and seasonal variations– The motion of stars and planets in the sky– What is the reason for the seasons?


Newton’s Law of Universal Gravitation

• Gravitation force between two bodies

• G = Gravitational Constant = 6.67x10-11 N • m2 / kg2

• m1 and m2 = the masses of the two objects

• r = the distance between the two (more precisely, the distance between the two centers)


Example #1

• A boy with a mass of 25 kg experiences how much less of a gravitational force by the Earth than a man with a mass of 100 kg?

• (possibly) Useful info MEarth = 5.97x1024 kg REarth = 6378 km


Example #2

• Suppose that Earth were at 10 AU. How much less of a gravitational force from the Sun would it experience?

• Note 1AU = 1.5x108 km

MSun = 2x1030 kg


Example #3

• How much would a man weight on Mars if he weighs 200 pounds on Earth?

Useful info: The mass of Mars = 10 times less than Earth The radius of Mars = ½ times smaller than Earth


Orbits • The law of universal gravitation accounts for planets not falling into the Sun nor the Moon crashing into the Earth

• Paths A, B, and C do not have enough horizontal velocity to escape Earth’s surface whereas Paths D, E, and F do.

• Path E is where the horizontal velocity is exactly what is needed so its orbit matches the circular curve of the Earth


Physics of spaceflight: Weightlessness

• Astronauts are actually still falling – they are falling with the

spacecraft

• They sometimes train for missions in large airplanes.


New Subject: The Night Sky

• The night sky changes in a number of ways– Diurnal variations– Seasonal variations– Pole-star wander

• These variations can be understood in terms of the combined effects of the spinning of the Earth on its axis, the orbit of Earth about the Sun, and the precession of Earth’s spin axis.


Diurnal motion

• “Diurnal” means having a period of 1 day.

• Stars appear to rise in the east, slowly rotate about the earth and set in the west.

• This diurnal or daily motion of the stars is caused by the ~24-hour rotation of the Earth on its axis.


Diurnal Motion


Seasonal variations in the night sky

• The stars also appear to slowly shift in position throughout the year

• This is due to the orbit of the Earth around the Sun, relative to the (essentially) fixed stars

• If you follow a particular star on successive evenings, you will find that it rises approximately 4 minutes earlier each night, or 2 hours earlier each month


ConstellationsOrion – A Winter/Spring Constellation

Sagittarius – A Summer Constellation

• Zodiac Constellations are those that the planets and Sun move through– Near the ecliptic plane!– Leo, Sagittarius, Scorpio, Taurus, etc.

• The constellation that the Sun is in on your birth date defines which zodiac sign you are


What causes the change of seasons?


The source of energy that heats Earth’s surface – the Sun


Proximity to the Sun partly determines the temperature of a planet’s surface

• The closer a planet is to the Sun, the warmer its surface will be

• The received solar energy decreases with the square of the distance to the Sun

– If Earth were at 2AU, it would receive 22 = 4 times less solar energy


These Solar magnetograms show that the size of the Sun as seen from Earth changes depending on where

Earth in its orbit_________________________________________________________

_________________________________________________________

July, 1989 January, 1989

The Earth is closer to the Sun in January


• Recall that Earth’s orbits is very nearly circular – The Earth’s orbital eccentricity = 0.017

This is too small to effect the seasons

The solar energy at Earth’s orbit at:

Perihelion = 1420 W/m2

Aphelion = 1330 W/m2

This is not enough of a difference to lead to a change in seasons


The seasons are caused by the tilt of Earth’s axis of rotation

• The Earth’s axis of rotation is not perpendicular to the plane of the Earth’s orbit

• It is tilted about 23½° away from the perpendicular

• The Earth maintains this tilt as it orbits the Sun, with the Earth’s north pole pointing toward the north celestial pole


• In Tucson, when the Sun at its highest point in the sky on Dec 21 (the winter solstice) is at an angle of 35 degrees above the horizon– Solar flux absorbed by Earth per square meter = 450 W/m2

• In Tucson, when the Sun at its highest point in the sky on June 21 (the summer solstice) is at an angle of 82 above the horizon– Solar flux absorbed by Earth per square meter = 1350 W/m2

• Thus, by far, the angle of incidence is the most important factor in leading to a change in seasons on Earth


Stonehenge, England

Sun Dagger, Chaco, NM

• Reading Assignment:– Please read the textbook

discussions of the following topics (this is in Chapter 2) as they will not be covered in lectures

• Celestial Coordinates– Right Asscension– Declination

• Zenith and Meridian• Solstices and Equinoxes


Reading for next class

• Chapter 3– pp. 42-55

• Also, re-read section 4-2 and box 4-2 (pages 65-69).


Additional slides


Precession

• The Earth precesses as it rotates on its axis, much like a top

• Has a period of about 19,000 years

• Causes the “pole” star to change


What is the North Star?

• Polaris -- for now, but it wont be forever!

• Vega will be the pole star in about 14,000 years

Newton’s Universal Law of Gravitation and planetary orbits

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