Transcript I. Stable Orbits

Stable Orbits
Kepler’s Laws
Newton’s Gravity
Stable Orbits, Kepler’s Laws and Newton’s Law of Gravity
I. Stable Orbits
A. A satellite with no horizontal
velocity will __________________.
B. A satellite with some horizontal
velocity will follow a ___________.
C. A satellite with sufficient horizontal
velocity will fall at the same rate
that the Earth is curving away from
it, maintaining a constant height
above the ground. This satellite will
be in a _______________ orbit.
D. Essentially all satellites, moons and
planets move in __________ orbits.
I. Stable Orbits
A. A satellite with no horizontal
velocity will __fall straight down__.
B. A satellite with some horizontal
velocity will follow a ___________.
C. A satellite with sufficient horizontal
velocity will fall at the same rate
that the Earth is curving away from
it, maintaining a constant height
above the ground. This satellite will
be in a _______________ orbit.
D. Essentially all satellites, moons and
planets move in __________ orbits.
I. Stable Orbits
A. A satellite with no horizontal
velocity will __fall straight down__.
B. A satellite with some horizontal
velocity will follow a _curved path_.
C. A satellite with sufficient horizontal
velocity will fall at the same rate
that the Earth is curving away from
it, maintaining a constant height
above the ground. This satellite will
be in a _______________ orbit.
D. Essentially all satellites, moons and
planets move in __________ orbits.
I. Stable Orbits
A. A satellite with no horizontal
velocity will __fall straight down__.
B. A satellite with some horizontal
velocity will follow a _curved path_.
C. A satellite with sufficient horizontal
velocity will fall at the same rate
that the Earth is curving away from
it, maintaining a constant height
above the ground. This satellite will
be in a __stable circular__ orbit.
D. Essentially all satellites, moons and
planets move in __________ orbits.
I. Stable Orbits
A. A satellite with no horizontal
velocity will __fall straight down__.
B. A satellite with some horizontal
velocity will follow a _curved path_.
C. A satellite with sufficient horizontal
velocity will fall at the same rate
that the Earth is curving away from
it, maintaining a constant height
above the ground. This satellite will
be in a __stable circular__ orbit.
D. Essentially all satellites, moons and
planets move in _elliptical__ orbits.
F. Speeds vary for a planet as it moves around the Sun in an elliptical
orbit.
Speed
Distance From Sun
E. Planets near the Sun will orbit with a _______ speed. Planets far
from the Sun will orbit with a _________ speed.
F. Speeds vary for a planet as it moves around the Sun in an elliptical
orbit.
faster
Speed
slower
Distance From Sun
E. Planets near the Sun will orbit with a _______ speed. Planets far
from the Sun will orbit with a _________ speed.
F. Speeds vary for a planet as it moves around the Sun in an elliptical
orbit.
faster
Speed
slower
Distance From Sun
E. Planets near the Sun will orbit with a _faster_ speed. Planets far
from the Sun will orbit with a _________ speed.
Sun
F. Speeds vary for a planet as it moves around the Sun in an elliptical
orbit.
faster
Speed
slower
Distance From Sun
E. Planets near the Sun will orbit with a _faster_ speed. Planets far
from the Sun will orbit with a __slower__ speed.
Sun
F. Speeds vary for a planet as it moves around the Sun in an elliptical
orbit.
faster
Speed
slower
Distance From Sun
E. Planets near the Sun will orbit with a _faster_ speed. Planets far
from the Sun will orbit with a __slower__ speed.
faster
slower
II. Kepler’s 3 Laws
1. The orbit of a planet around the Sun is an
_______ with the Sun at one _______.
Sun
2. A line joining the Sun and the planet sweep
out equal ______ in equal _______.
3. The square of the planet’s orbital _______ is directly proportional
to the cube of the ______________ of the planet’s orbit.
II. Kepler’s 3 Laws
1. The orbit of a planet around the Sun is an
_ellipse_ with the Sun at one _focus_.
Sun
2. A line joining the Sun and the planet sweep
out equal ______ in equal _______.
3. The square of the planet’s orbital _______ is directly proportional
to the cube of the ______________ of the planet’s orbit.
focus
II. Kepler’s 3 Laws
1. The orbit of a planet around the Sun is an
_ellipse_ with the Sun at one _focus_.
focus
Sun
elliptical orbit
2. A line joining the Sun and the planet sweep
out equal ______ in equal _______.
3. The square of the planet’s orbital _______ is directly proportional
to the cube of the ______________ of the planet’s orbit.
focus
II. Kepler’s 3 Laws
1. The orbit of a planet around the Sun is an
_ellipse_ with the Sun at one _focus_.
focus
Sun
elliptical orbit
2. A line joining the Sun and the planet sweep
out equal _areas_ in equal _times_.
3. The square of the planet’s orbital _______ is directly proportional
to the cube of the ______________ of the planet’s orbit.
focus
II. Kepler’s 3 Laws
1. The orbit of a planet around the Sun is an
_ellipse_ with the Sun at one _focus_.
focus
Sun
elliptical orbit
A2
A1
A3
A1 = A2 = A3
3. The square of the planet’s orbital _______ is directly proportional
to the cube of the ______________ of the planet’s orbit.
1 month
2. A line joining the Sun and the planet sweep
1 month
out equal _areas_ in equal _times_.
focus
II. Kepler’s 3 Laws
1. The orbit of a planet around the Sun is an
_ellipse_ with the Sun at one _focus_.
focus
Sun
elliptical orbit
A2
A1
A3
A1 = A2 = A3
3. The square of the planet’s orbital _period_ is directly proportional
to the cube of the _semimajor axis_ of the planet’s orbit.
1 month
2. A line joining the Sun and the planet sweep
1 month
out equal _areas_ in equal _times_.
focus
II. Kepler’s 3 Laws
1. The orbit of a planet around the Sun is an
_ellipse_ with the Sun at one _focus_.
focus
Sun
elliptical orbit
A2
A1
A3
A1 = A2 = A3
3. The square of the planet’s orbital _period_ is directly proportional
to the cube of the _semimajor axis_ of the planet’s orbit.
T (period) = time it takes for the planet to make one orbit
a (semimajor axis) = average distance between the planet and the Sun
T2 ~ a3
1 month
2. A line joining the Sun and the planet sweep
1 month
out equal _areas_ in equal _times_.
III. Newton’s Law of Gravity
1. All masses ________ one another and never ______.
2. The gravitational force between two masses, m1 and m2, is
proportional to the ________ of the two masses.
3. The gravitational force between two masses is also
_____________________ to the distance between to the two
masses squared.
m2
m1
r
III. Newton’s Law of Gravity
1. All masses _attract_ one another and never _repel_.
2. The gravitational force between two masses, m1 and m2, is
proportional to the ________ of the two masses.
3. The gravitational force between two masses is also
_____________________ to the distance between to the two
masses squared.
m2
m1
r
III. Newton’s Law of Gravity
1. All masses _attract_ one another and never _repel_.
2. The gravitational force between two masses, m1 and m2, is
proportional to the _product_ of the two masses.
3. The gravitational force between two masses is also
_____________________ to the distance between to the two
masses squared.
m2
m1
r
III. Newton’s Law of Gravity
1. All masses _attract_ one another and never _repel_.
2. The gravitational force between two masses, m1 and m2, is
proportional to the _product_ of the two masses.
3. The gravitational force between two masses is also
_inversely_proportional_ to the distance between to the two
masses squared.
m2
m1
r
III. Newton’s Law of Gravity
1. All masses _attract_ one another and never _repel_.
2. The gravitational force between two masses, m1 and m2, is
proportional to the _product_ of the two masses.
3. The gravitational force between two masses is also
_inversely_proportional_ to the distance between to the two
masses squared.
m2
m1
r
F  G
Newton’s gravitational
constant
m1m2
r2