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Motion of Planets Seen from Earth
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
QuickTime™ and a
Sorenson Video decompressor
are needed to see this picture.
ISP 205 - Astronomy Gary D. Westfall
Lecture 3
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Motion of the Planets Seen from the Sun
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
QuickTime™ and a
Sorenson Video decompressor
are needed to see this picture.
ISP 205 - Astronomy Gary D. Westfall
Lecture 3
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Orbits and Gravity
• Tycho Brahe made a long series of careful
measurements of the motions of the planets
• Johannes Kepler worked with Brahe and
interpreted these data
• Kepler’s Three Laws
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Orbits are ellipses, not circles
Line from planet to sun sweeps out equal area in equal
time
Period2 proportional to Semimajor axis3

Semimajor axis is also the average distance of the planet
from the Sun
ISP 205 - Astronomy Gary D. Westfall
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Elliptical Orbits
• Kepler showed that the orbit of Mars is an ellipse
with the Sun at one focus
Sun
Focus 2
Semiminor axis
Focus 1
Semimajor axis
ISP 205 - Astronomy Gary D. Westfall
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Kepler’s Second Law
• A line from the
planet to the Sun
sweeps out equal
areas in equal times
• When the planet is
near the Sun, it
moves quickly
• When the planet is
far from the Sun, it
moves slowly
ISP 205 - Astronomy Gary D. Westfall
QuickTime™ and a
Graphics decompressor
are needed to see this picture.
Lecture 3
5
Kepler’s Third Law
• (distance)3 = (period)2
• Distance is given in units of the distance of the
Earth to the Sun

Astronomical unit (AU)
• Period is given in terms of the time it takes for the
Earth to go around the Sun

1 year
• Example - Mars
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(distance)3 = (1.52)3 = 3.51
(period)2 = (1.88)2 = 3.53
ISP 205 - Astronomy Gary D. Westfall
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Newton’s First Law
• In the absence of any external forces we have
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Conservation of momentum
An object on motion tends to remain in motion
An object at rest tends to remain at rest
• An object has mass
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•
•
•
•
The amount of material in the body
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
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Newton’s Second Law
• The change of motion of a body is proportional to
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
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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
ISP 205 - Astronomy Gary D. Westfall
Lecture 3
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Newton’s Third Law
• For every action there is an equal and opposite
reaction
• The mutual actions of two bodies on each other
are always equal and opposite
• This is the principle behind a rocket

Fuel is burned, hot gases are ejected, the rocket goes
the other way
ISP 205 - Astronomy Gary D. Westfall
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Mass, Volume, Density
• Mass is a measure of the amount of material in an
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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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
ISP 205 - Astronomy Gary D. Westfall
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Angular Momentum
• The angular momentum of an object is defined in
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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If distance is decreased, velocity must
increase
If distance is increased, velocity must
decrease
If mass is decreased,distance must
increase
• Ice skaters, divers, gymnasts
ISP 205 - Astronomy Gary D. Westfall
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The Law of Gravity
• 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
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
m1m2
Force  G
2
R
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Example - Gravity
• If the radius of the Earth were increased by a
factor of 2 and the masses remained the same, by
what factor would the force of gravity on the
Earth’s surface change?
m1m2
Force  G
2
R
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
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Orbital Motion and Mass
• Newton’s Law of Gravity extended Kepler’s Third
Law
• Kepler
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(distance)3 = (period)2
• Newton
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(distance)3 = (M1 + M2)(period)2
M1 = mass of the Sun
 M2 = mass of the planet
 Masses of the planets are much smaller than the mass of the
Sun

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Examples, Orbital Motion
• Suppose the mass of the Earth suddenly decreased
by a factor of 2, what would happen to the period
of its orbit around the Earth?
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(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
• 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?

The period would have to be longer
ISP 205 - Astronomy Gary D. Westfall
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Free Fall
• When a object is in orbit, it is falling “around” the Earth
• If you are in an elevator and the cable breaks, the
acceleration of you and elevator will be the same and you
will feel no forces (for a while)
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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
ISP 205 - Astronomy Gary D. Westfall
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Interplanetary Spacecraft
• The exploration of the solar
•
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”
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