Kepler ’ s Laws of Planetary Motion. (COMPARING PLANETS). Kepler ’ s Third Law : P : orbital period of planet ( sidereal period ) A : planet ’ s average distance from Sun ( semi-major axis ). Sun. A. applet. 1 AU (Astronomical Unit) is Earth ’ s average distance from Sun
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P: orbital period of planet (sidereal period)
A: planet’s average distance from Sun (semi-major axis)
1 AU (Astronomical Unit) is Earth’s average distance from Sun
1 AU = 1.5 × 1011 m
applet - defunct
If it takes Eris 557 years to orbit the Sun, what is its average distance from the Sun?
(Enter your answer rounded to the nearest whole number of AU.)
The asteroid Apophis has an orbit with the following characteristics:
If Earth’s orbit has a semi-major axis of 1 AU and Venus has a semi-major axis of 0.723 AU, does Apophis’ orbit cross the planet orbits?
For Friday, Feb. 21
Reading: Appendix 7
Assignments: Homework #3 (due Wed. Feb 26)
GAS PEDAL (change speed)
STEERING WHEEL (change direction)
a: acceleration (units: )
m: mass(units: kg)
F: force (units: Newton = )
MASS REDUCES ACCELERATION
trying to blow up a BIG asteroid is not a great idea…
… even a big explosion wouldn’t accelerate it much Newton’s Second Law
… fragments would keep moving in mostly the same direction Newton’s First Law
A ball is attached to a string and swung in a circular path above my head. At the point shown below, I suddenly release the string. If this is viewed from directly above, which of the paths below would the ball most closely follow when released?
VIEW FROM ABOVE:
Newton’s First Law says: If object travels on a curved path, there MUST BE an unbalanced force.
(friction between tires and road)
Newton’s Second Law says: object accelerates (turns) in direction of unbalanced force
force is NOT pushing planet forward
force IS pulling toward inside of orbit (toward Sun)
A rotating tube makes it feel like there is gravity…
Your body tries to move in a straight line (Newton’s 1st), but floor exerts a force to change your direction…
For Monday, Feb. 24
Reading: Section 4.1, 4.2 (including Math Tools 4.1, 4.2)
Assignments: Homework #3 (due Wed. Feb. 26)
The picture below shows the velocity of a planet at different times in its orbit (larger arrow means larger speed).
Draw the direction of the force on the planet at the different positions shown.
For position #3, which combination of these describes the direction of the force is acting:
To the right of the velocity arrow
To the left of the velocity arrow
Forward (with the velocity arrow)
Back (against the velocity arrow)
Enter all that apply.
(ALWAYS TANGENT TO ORBIT)
SUN’S FORCE TURNS AND SPEEDS PLANET
SUN’S FORCE JUST TURNS PLANET
SUN’S FORCE TURNS AND SLOWS PLANET
THE FORCE POINTS TOWARD THE SUN!
GAS FORCE ON ROCKET
ROCKET’S FORCE ON GAS
SKATER FORCES ON EACH OTHER
Newton’s Third Law: star moves slightly as planet orbits
“wobble” of star depends on star and planet masses, and size of planet orbit
PLANET’S FORCE ON STAR
STAR’S FORCE ON PLANET
A compact car and a large truck collide head-on and stick together.
(Enter both letters of your answers, then hit “Enter”.)
Forces have equal strength, but accelerations may differ:
MAN’S FORCE ON BOAT
BOAT’S FORCE ON MAN
MORE MASS, LESS ACCELERATION
center of mass
“balance point” is closer to more massive object:
The Earth has about 80 times the mass of the Moon, and the distance to the Moon is about 60 Earth radii. How far is the center of mass from the center of Earth?
center of mass?
At which positions does a rocket feel a greater gravitational force from Earth than from the Moon? (There may be more than one answer.)
A hypothetical planet system has planets in equally-spaced circular orbits. The planet masses are given in terms of the mass of the innermost planet. Which of the planets exerts the greatest gravitational force on the star?