Transcript Lec4-012307

Newton’s Universal
Law of Gravitation
and planetary orbits
PTYS/ASTR 206
Gravity (cont.) / Night Sky / Seasons
1/23/07
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?
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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)
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STEREO “first light” image of Comet McNaught
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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?
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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)
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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
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Example #2
• Suppose that Earth were at 10 AU. How much
less of a gravitational force from the Sun would it
experience?
• Note
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1AU = 1.5x108 km
MSun = 2x1030 kg
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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
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Orbits
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• 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
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Physics of spaceflight: Weightlessness
• Astronauts are actually
still falling
– they are falling with the
spacecraft
• They sometimes train
for missions in large
airplanes.
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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.
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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.
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Diurnal Motion
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Diurnal Motion
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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
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Constellations
Orion – 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.
• PTYS/ASTR
The constellation
that
the Sun is in on your birth date
206
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defines which zodiac sign you
What causes the
change of seasons?
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The source of energy that heats Earth’s
surface – the Sun
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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
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These Solar magnetograms show that the size of the
Sun as seen from Earth changes depending on where
Earth in its orbit
_________________________________________________________
_________________________________________________________
January, 1989
July, 1989
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The Earth is closer to the Sun in January
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• 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
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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
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• 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
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• Reading Assignment:
– Please read the textbook
discussions of the following
topics (this is in Chapter 2)
as they will not be covered
in lectures
Stonehenge, England
• Celestial Coordinates
– Right Asscension
– Declination
• Zenith and Meridian
• Solstices and
Equinoxes
Sun Dagger, Chaco, NM
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Reading for next class
• Chapter 3
– pp. 42-55
• Also, re-read section 4-2 and box 4-2
(pages 65-69).
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Additional slides
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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
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What is the North Star?
• Polaris -- for
now, but it
wont be
forever!
• Vega will be
the pole star
in about
14,000 years
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