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4. Gravitation and Orbits
Kepler Developes Laws of Planetary Motion
German mathematician Johannes Kepler used Tycho
Brahe’s data to develop three empirical laws of planetary motion, published in 1609 and 1619.
Kepler’s First Law of Planetary Motion
Each planet moves in an elliptical orbit, with the Sun at one
focus. This holds true for everything in an orbit—planets, moons, asteroids, comets, spacecraft, stars,
galaxies.
Kepler’s Second Law of Planetary Motion
An imaginary line from the Sun to a planet sweeps out
equal areas in equal times. This means that a planet is moving fastest when it’s closest to the Sun, and
is moving slowest when it’s furthest from the Sun.
Kepler’s Third Law of Planetary Motion
There’s a mathematical relationship between orbital
distance and orbital period, expressed as: P2 = a3,when “P” (the period) is given in Earth years, and
“a” (the distance) is given in Astronomical units. This allows us to calculate the distance, knowing the
period, and vice versa.
What is physics? Physics is the study of forces and energy. Topics include: motion, gravitation,
electricity, light, radioactivity, heat, magnetism, sound, optics, …
What is mass?
Mass is the quantity of matter. How much stuff: number of protons, neutrons, etc.
Mass is generally expressed in units: kilogram. Wherever you take something, the mass is the same
What is velocity? Velocity is how fast and in what direction something is moving. (Speed is just “how
fast,” not the direction.) When something goes in a circle, the velocity is constantly changing, though the
speed stays the same.
What is acceleration? Acceleration is the rate of change of velocity. (How quickly velocity changes.) It
can change three ways, by: speeding up, slowing down, changing direction.
What is force?
Force is a push or a pull, Expressed in units: Newton
What is weight? Weight is the downward force due to gravity, expressed in units: Newton. Since weight
is due to gravitation, weight is different according to where you are
Newton Formalizes Laws of Motion and Gravitation
Newton formalized Three Laws of Motion
(applicable to everything) and devised the law of universal gravitation (based on Kepler’s laws of
Planetary Motion), published in 1687. This quantified the reasons for planetary movements.
Newton’s First Law of Motion: Inertia
Objects naturally keep the motion (or non-motion) that
they have. This means that anything that’s moving will keep moving until a force stops it, and you need
a force to make something start moving.
Newton’s Second Law: F = ma
This is the relationship between force, mass, and acceleration:
Force = mass x acceleration, F = ma. It takes more force to accelerate a large mass than a small
mass. Without air, everything falls at the same rate.
Newton’s Third Law: Forces can’t occur in isolation
Every force has an opposite counterpart. If you
push something, you feel the opposite force against your hands. The effect makes rockets work.
Newton’s Law of Gravitation: relationship between mass, force, & distance This formula gives the
amount of gravitational force between any two masses in the universe. At double the distance, the force
is one quarter. Gravity is never zero.
Centripetal Force Centripetal Force is the force needed to make an object turn in a circle. Normally,
objects move in a straight line (inertia). So, to make something go in a circle, you have to continually
change the direction of movement— that’s acceleration, which requires a force. To move in a circle, the
centripetal force is toward the center. The force doesn’t make the object move—the force just changes
the direction of the movement.
Getting into Orbit
To get into orbit, you have to go so fast that the curve of falling matches the curve
of the Earth. (This is when the gravitational force provides the centripetal force.) For Earth, this orbital
velocity (just above the atmosphere) is about 17,000 miles per hour (twenty times faster than sound).
Too fast, and it flies away. Too slow, and it crashes.
Surface Gravity
Surface gravity determines how much things weigh on the surface of a planet. The
surface gravity depends on the mass of a planet and its radius. A planet’s gravity pulls itself into a
spherical shape. A planet’s gravity holds onto its atmosphere Massive planets hold gasses easier, Cold
planets hold gasses easier, Planets hold heavy gasses easier
Escape Velocity For a space ship (or a gas molecule) to get completely away from a planet, it has to
travel at the escape velocity. The escape velocity depends on the mass of a planet and its radius. For
Earth, the escape velocity is about 25,000 miles per hour. Other escape velocities: Moon: 5400 mph,
Venus: 23,000 mph, Mars:
11,000 mph. So, travel to Venus is impractical, but to Mars might be
possible. The escape velocity from the “surface” of a black hole is the speed of light.
Measuring the Mass of a Planet
Since the orbital velocity is determined by the mass of the planet
and the height of the orbit, by observing the orbit of a moon around a planet, we can calculate the mass
of the planet. Or, if two stars orbit each other, we can determine their masses. Or, by measuring the
motion of a star around a galaxy, we can determine the mass of the galaxy.
Questions to be Answered:
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What does Kepler’s First Law of Planetary Motion tell us about the orbits of planets (and other
objects)?
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What does Kepler’s Second Law tell us about orbits?
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What does Kepler’s Third Law tell us about orbits?
•
What are mass, velocity, acceleration, force, and weight?
•
What does Newton’s First Law of Motion tell us about inertia?
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What does Newton’s Second Law tell us about force needed for acceleration?
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What does Newton’s Third Law of Motion tell us about forces in isolation?
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What does Newton’s Law of Universal Gravitation tell about the force of gravity?
•
What are the basic principles that allow planets to stay in orbit?
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What factors determine a planet’s surface gravity?
– How does this affect a planet’s atmosphere?
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What factors determine a planet’s escape velocity?
– How does this affect the difficulty of space flight?
•
How do we measure the mass of a planet or star?