Motion of Planets Seen from Earth
Motion of the Planets Seen from the Sun
In the movie below, you will see the Sun, Mercury, Venus, Earth,
Mars, Jupiter, and Saturn looking down on the plane of the solar
system from the Earth’s perspective
ISP 205 - Astronomy Gary D. Westfall
Lecture 3
Now you will see the Sun, Mercury, Venus, Earth, Mars, Jupiter, and
Saturn looking down on the plane of the solar system from the
Sun’s perspective
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ISP 205 - Astronomy Gary D. Westfall
Orbits and Gravity
• Kepler showed that the orbit of Mars is an ellipse
measurements of the motions of the planets
• Johannes Kepler worked with Brahe and
interpreted these data
• Kepler’s Three Laws
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with the Sun at one focus
Sun
Orbits are ellipses, not circles
Line from planet to sun sweeps out equal area in equal
time
Period2 proportional to Semimajor axis3
X
Focus 1
Semimajor axis is also the average distance of the planet
from the Sun
ISP 205 - Astronomy Gary D. Westfall
Lecture 3
Focus 2
Semiminor axis
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Elliptical Orbits
• Tycho Brahe made a long series of careful
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Lecture 3
Semimajor axis
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ISP 205 - Astronomy Gary D. Westfall
Lecture 3
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Kepler’s Second Law
Kepler’s Third Law
• A line from the
• (distance)3 = (period)2
• Distance is given in units of the distance of the
planet to the Sun
sweeps out equal
areas in equal times
Earth to the Sun
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• When the planet is
• Period is given in terms of the time it takes for the
near the Sun, it
moves quickly
Earth to go around the Sun
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far from the Sun, it
moves slowly
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•
•
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the force acting on it and is made in the direction
the force is acting
• Force has a magnitude and a direction
• Change of motion is acceleration
Conservation of momentum
An object on motion tends to remain in motion
An object at rest tends to remain at rest
The amount of material in the body
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An object has a speed
An object has a direction
Speed combined with direction is velocity
Momentum is mass times velocity
ISP 205 - Astronomy Gary D. Westfall
Lecture 3
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• The change of motion of a body is proportional to
• An object has mass
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Lecture 3
Newton’s Second Law
• In the absence of any external forces we have
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(distance)3 = (1.52)3 = 3.51
(period)2 = (1.88)2 = 3.53
ISP 205 - Astronomy Gary D. Westfall
Newton’s First Law
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1 year
• Example - Mars
• When the planet is
ISP 205 - Astronomy Gary D. Westfall
Astronomical unit (AU)
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Acceleration has a magnitude and a direction
Acceleration is change of momentum
• Force equals mass times acceleration
• The force and the acceleration are in the same
direction
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ISP 205 - Astronomy Gary D. Westfall
Lecture 3
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Newton’s Third Law
Mass, Volume, Density
• For every action there is an equal and opposite
• Mass is a measure of the amount of material in an
reaction
• The mutual actions of two bodies on each other
are always equal and opposite
• This is the principle behind a rocket
object
• Volume is the size of an object
• Density is the mass per unit volume
• We will use the unit gram per cubic centimeter
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Fuel is burned, hot gases are ejected, the rocket goes
the other way
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Q
Q
Q
ISP 205 - Astronomy Gary D. Westfall
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Angular Momentum
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• The force that hold the planets in orbit is gravity
• Gravity is a property of mass
• The force of gravity between any two objects is
terms of its mass, its velocity, and its distance
from the fixed point about which it turns
• Angular momentum is conserved in the absence
of any external force just like momentum
• Angular momentum equals mass times velocity
times distance
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ISP 205 - Astronomy Gary D. Westfall
The Law of Gravity
• The angular momentum of an object is defined in
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g/cm3
Water has a density of 1 g/cm3
Gold has a density of 19.3 g/cm3
Wood has a density of 0.8 g/cm3
equal to the gravitational constant G times the
mass of object 1 times the mass of object 2
divided by the distance between the planet and the
sun squared
If distance is decreased, velocity must
increase
If distance is increased, velocity must
decrease
If mass is decreased,distance must
increase
Force = G
m1m 2
R2
• Ice skaters, divers, gymnasts
ISP 205 - Astronomy Gary D. Westfall
Lecture 3
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ISP 205 - Astronomy Gary D. Westfall
Lecture 3
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Example - Gravity
Orbital Motion and Mass
• If the radius of the Earth were increased by a
• Newton’s Law of Gravity extended Kepler’s
factor of 2 and the masses remained the same, by
what factor would the force of gravity on the
Earth’s surface change?
Force = G
Third Law
• Kepler
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• Newton
m1m 2
R2
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X
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Examples, Orbital Motion
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acceleration of you and elevator will be the same and you
will feel no forces (for a while)
(distance)3 = (M1 + M2)(period)2
The orbit would not change much because the mass of
the Earth is small compared to the mass of the Sun
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Weightless
• Astronauts in orbit around the
Earth feel no gravity because
the forces are balanced, not
because they are so far away
from the Earth that gravity is
weak
• Suppose the mass of the Sun suddenly decreased
by a factor of 2 and the Earth stayed the same
distance from the Sun, what would happen to the
period of the Earth;s orbit?
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ISP 205 - Astronomy Gary D. Westfall
• When a object is in orbit, it is falling “around” the Earth
• If you are in an elevator and the cable breaks, the
by a factor of 2, what would happen to the period
of its orbit around the Earth?
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M1 = mass of the Sun
M2 = mass of the planet
Masses of the planets are much smaller than the mass of the
Sun
Free Fall
• Suppose the mass of the Earth suddenly decreased
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(distance)3 = (M1 + M2)(period)2
X
The distance from the center of the Earth would
change by a factor of 2 so the force would
decrease by a factor of 4
ISP 205 - Astronomy Gary D. Westfall
(distance)3 = (period)2
The period would have to be longer
ISP 205 - Astronomy Gary D. Westfall
Lecture 3
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ISP 205 - Astronomy Gary D. Westfall
Lecture 3
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Interplanetary Spacecraft
• The exploration of the solar
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system has been carried out
by robot spacecraft
These spacecraft are given a
velocity larger than the
Earth’s escape velocity
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25,000 miles per hour
• After launch, these spacecraft have little ability to
maneuver
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Only small thrusters
• To make large course corrections, the spacecraft are
steered near planets
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“slingshot”
ISP 205 - Astronomy Gary D. Westfall
Lecture 3
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