6 Chapter 6 – How do planets orbit the Sun?
OpenStax Astronomy Chapter 3: Orbits and Gravity
Copernican Revolution
I. Revolution
A. Before Nicolaus Copernicus (1473-1543), people believed in a (Earth-centered)
1. Ptolemaic system
B. He realized the was (Sun-centered)
1. Not first person to suggest, but developed a (1543)
2. Other scientists work agreed: Tycho, Galileo, Kepler, (late 1500s) Newton (late 1600s)
Kepler’s Laws
How do planets orbit the Sun?
II. and
A. Tycho (1546-1601) motions of planets without telescopes (late 1500s)
1. Kepler (1571-1630) was his assistant
B. Kepler used Tycho’s to come up with for planet motion
1. Kepler expected orbits like Copernicus thought, but that didn’t match his
III. : Planet orbits are – squashed circles or ovals
A. Orbits have two or focus points
1. The is at one focus of a planet’s elliptical orbit
B. Orbit Size measured by the
1. Distance from center to orbit on the side
2. For Earth, semimajor axis = , near circle
C. Orbit Shape given by (e) of the ellipse
1. How the ellipse is and how the foci are
2. : foci are on top of one another and e =
3. : e = 1
4. Most : eccentricity near 0, Earth about e = 0.02
Kepler’s 1st law says orbits are ellipses. What word describes the shape of an ellipse?
III. Kepler’s 2nd Law: the Law of
A. Imaginary line between the Sun and the planet “sweeps” out equal in equal amounts of
B. Planet moves when to the Sun
C. when farthest away
IV. Kepler’s : P2 = A3 , relationship between period and distance from the Sun
A. (P) = to make one orbit around the Sun
B. Semimajor axis (A) = approximate from Sun
C. As distance , period
D. Distant planets take to orbit the Sun and travel at speeds
You read in the paper that a new planet was found. The article states that when it is closest to its star, it moves at 31 km/s. When it is farthest from its star, it moves at 35 km/s. This story has an error because:
Galileo and Inertia
Why do planets orbit the sun? (a detour into history and physics)
V. Galilei (1564-1642)
A. First to use a for astronomical observations (1609)
B. Saw , moon craters, and stars in the
C. Discovered four largest (Galilean moons)
D. Saw the supporting heliocentric view of Solar System
E. with moving objects
1. Developed idea of = tendency of objects to change in motion
Newton’s Laws
VI. Isaac (1642-1727)
A. Developed physical that apply to objects
B. Newton’s Laws explain objects move the way they do
1. Used work
2. Agree with and a heliocentric Solar System
VII. Newton’s 1st law: Law of (Galileo’s result)
A. An object at stays at
B. Moving object will stay in unless an acts on it
C. “Constant” motion means at a constant and in a constant
D. This is why planets keep around the Sun
VIII. Newton’s :
A. forces cause
1. Acceleration = change in and/or
2. Example:
3. For orbits, is the unbalanced force that causes a planet to change speed and direction
B. Force =
1. = amount of matter in a body
2. Mass changes in motion (inertia)
C. For a specific object (mass stays the same): force means acceleration
D. If you exert the same on objects of different mass: Object with mass will accelerate
An unbalanced force must be acting when:
IX. Newton’s :
A. Forces occur in pairs
B. For every action there is an and reaction.
C. Applies to forces, including
1. Example: Moon exerts size force on Earth as the Earth does on the Moon, but in opposite directions
Your weight is the force of the Earth on you. Suppose you weigh 60 pounds. Then the force of you on Earth is:
Gravity
X. Gravity on
A. Unbalanced force causing toward center of
B. Acceleration due to gravity (g) is the same for objects on , regardless of
C. = object experiences from gravity
1. F = ma becomes
2. g = 9.8 m/s2 on Earth
D. Weight on other planets because of different due to gravity “g”, because of planet is different from Earth
1. Example: Your weight would be on Moon because Moon is than Earth (g = 1.6 m/s2)
Imagine you are standing at the top of a tall tower. You drop 3 objects shaped like a ball made out of different materials. Neglecting air resistance, in what order do they hit the ground?
XI. Newton’s (not just on Earth)
A. Gravity is an force between two objects with
B. Acts on objects
1. Equal but opposite (Newton’s 3rd Law)
C. The greater either one of the , the the force of gravity on masses
1. Remember: Your weight greater on than on Moon
D. The greater the between the objects, the the force on masses
E. Put it all together:
1. G is the universal gravitational constant (6.67 x 10-11 m3/kg·s2)
2. M and m are the two
3. r is the between the masses
4. For Earth: g = GM/r2 for mass and radius of Earth
Your weight on Earth is simply the gravitational force between you and Earth. Would your weight be more, less, or the same on Mars?
Orbits
XII. = one body another because of
A. Less massive of two objects called a
B. used his laws to confirm Laws for planet orbits
1. Cannonball fired with enough would never hit the ground (ignoring air resistance)
C. Astronauts float because they and the space station are both at the around Earth
1. : Fall because of their weight (force due to gravity)
2. Both are satellites of Earth, in
The Space Station is in a circular orbit at a constant speed of about 17,500 mph. Is gravity acting on the spacecraft?
D. Gravity is the unbalanced (center-directed) force that keeps a planet in its around the Sun
1. (Newton’s 1st Law) says planet would keep moving in straight line, but gravity changes its and pulls it toward Sun (Newton’s 2nd Law)
E. Simplest orbit: moving in a at speed
1. Planet is , gravity only changes direction not speed
F. of orbit depends on speed
1. : speed needed to keep a circular orbit
2. If moving , will fall in
3. If moving than circular velocity, orbit will be an
XIII. orbits in the
A. Planets travel than circular velocity
B. Start to circular orbit into ellipse (Kepler’s Law)
C. Pull of slows it down then it back to Sun, always due to unbalanced force (Newton’s Law)
D. as gets closer to Sun again
1. As distance between planet and Sun, force of gravity increases (Newton’s Law of Gravity)
2. Moves faster closer and slower from Sun (Kepler’s Law)
XIV. Summary
A. : Observations (Tycho, Kepler, Galileo) led to hypotheses and theories (Newton)
B. Newton expanded results into three laws that explained not just how but why
C. physical laws were tested by Kepler’s observational laws. They agreed!
E. Today use Newton’s Universal Law of Gravitation to figure out the masses of planets, stars, and galaxies
Resources
NAAP Planetary Orbit Simulator: https://astro.unl.edu/naap/pos/animations/kepler.html
Tutorial Activities
Kepler’s Laws
“Elementary Astronomy Worksheet Handout 6: Kepler’s Laws” (modified by Kaisa E. Young) by Catherine Whiting via OER Commons, licensed under CC BY 4.0, https://oercommons.org/courses/elementary-astronomy-worksheets
• 1st Law:
• 2nd Law:
• 3rd Law:
3. The diagram below shows an orbit of a comet around the sun. Each of the dots represents the position of the comet every 10 years, i.e. it will appear in position B 10 years after position A, it will be at position C 10 years after position B, etc.
(b) Draw and label the semimajor axis.
(c) Draw lines from point A to the Sun and point B to the sun and shade in the area. Now draw lines from points E to theSun and points F to the Sun and shade in the area. Are the two areas roughly equal?
(d) At which point in the orbit is the comet moving the fastest? the slowest?
(e) At position C is the comet’s speed increasing or decreasing?
(f) What would the orbits of the planets look like, in comparison to this diagram? Sketch the orbit of the Earth to the right of the figure.
Figure 1: ”Eccentric Orbit” by Catherine Whiting, licensed under CC BY 4.0
4. Look at a table of solar system data.
(a) semimajor axis (distance from Sun)?
(b) orbital period around the Sun?
5. Which planet should have the slowest average orbital speed around the Sun? Which planet should have the fastest?
Newton’s Laws
“Elementary Astronomy Worksheet Handout 7: Newton’s Laws” (modified by Kaisa E. Young) by Catherine Whiting via OER Commons, licensed under CC BY 4.0, https://oercommons.org/courses/elementary-astronomy-worksheets
(b) Brainstorm some examples of an object that is accelerating.
2. (a) Make a prediction: If we drop a hammer and a piece of paper, which one will hit the ground first? Why?
(b) If we do the same experiment on the moon, which one will hit the ground first? Why?
(c) Will the acceleration of the hammer be the same as on Earth?
3. (a) Would you weigh more or less on the moon than you do on Earth?
(b) What about on Jupiter?
(c) How would your mass change?
4. What is Newton’s 1st law?
6. What is Newton’s 2nd law?
7. If two objects experience the same force, but object A is twice as massive as object B, which one will accelerate more?
9. When a bug splatters on your windshield, which is bigger: the force of the car on the bug, or the force of the bug on the car?
10. What is the equal and opposite force to your weight? Why do we hardly ever talk about that force?
Gravity
2. Suppose two planets have masses M1 and M2 and are separated by a distance d. They both experience a force due to gravity because of the other planet.
(b) How would the force change if the distance between the planets is doubled?
Figure 1: Newton’s Law of Gravity by Catherine Whiting, licensed under CC BY 4.0
(a) Which force is stronger on the spaceprobe, the force from Earth or the force from the Moon, or are they equal?
(b) Will the spaceprobe move if it has no power of its own? If so, which direction?
(c) Draw on the diagram (roughly) where you could place the spacecraft such that it will experience no net force (where the force from both the Earth and Moon are the same, so it will not move).
4. What would happen to Earth’s orbit if the Sun suddenly turned into a black hole with the same mass as the Sun?
