3.3 Kepler’s Three Laws of Planetary Motion

Warm-up What keeps earth moving the way it does?(ie, why is it moving forward in a circle)

Kepler’s Laws of Planetary Motions 1. Planets move in elliptical orbits with the sun at one of the foci Vocab: Foci – 2 points that are equidistant from center on major axis. In a circle, it is in the center Ellipse – an oval Perigee – closest point in orbit Apogee – farthest point in orbit SUN

2. Law of Areas Line from the sun to a planet sweeps with equal areas in equal time. A planet will move through equal area of space in an equal amount of time Perihelion – closest to sun Ahelion – farthest from sun When a planet is in perihelion its orbital velocity increases (Moves faster) When a planet is in aphelion its orbital velocity decreases (Moves slower)

Closer to the sun, faster the velocity because of the gravitational pull. Farthest from sun Closest to sun Slower Velocity Faster Velocity Greater Gravitational Pull

3. Law of Periods - The farther a planet is from the focus, the longer the period of revolution. Ex: Earth is closer to the sun than Jupiter, therefore the Earth has a shorter period of revolution. Vocab: Revolution = orbit around another object Rotation = spin on its axis

Gravity! Defined as the force of attraction between two objects Does not require contact Affected by mass and distance NOT A ONE-WAY STREET!

Mass is not weight! Mass is the amount of atoms in a substance Density is mass per volume Weight is the measurement of the force of gravity on an object

Planetary orbits – why don’t’ they ‘fall in the well’? Velocity vs gravity When balanced it creates an orbit!

Not a one way street! Two objects orbit a common point – the center of the two masses Much of the time one object is so large, the ‘orbit’ is not noticeable (Sun and Earth)

Newton’s Law of Gravity The force of attraction between any two objects depends on their masses and the distance between them. Thus, the closer the objects, the ______________ the gravitational pull Thus, the bigger the object the __________ the gravitational pull greater greater

Closer to the sun in the winter, farther from sun in summer

SIDE NOTE The seasons are NOT caused by how close or far from the sun we are! Caused instead by how direct the light is with Earth’s tilt

Check Your Understanding Suppose that two objects attract each other with a gravitational force of 16 units. If the distance between the two objects is doubled, what is the new force of attraction between the two objects? Answer: F = 4 units If the distance is increased by a factor of 2, then force will be decreased by a factor of 4 (22). The new force is then 1/4 of the original 16 units. F = (16 units ) / 4 = 4 units

Suppose that two objects attract each other with a gravitational force of 16 units. If the distance between the two objects is reduced in half, then what is the new force of attraction between the two objects? Answer: F = 64 units If the distance is decreased by a factor of 2, then force will be increased by a factor of 4 (22). The new force is then 4 times the original 16 units. F = (16 units) • 4 = 64 units

Suppose that two objects attract each other with a gravitational force of 16 units. If the mass of both objects was doubled, and if the distance between the objects remained the same, then what would be the new force of attraction between the two objects? Answer: F = 64 units If each mass is increased by a factor of 2, then force will be increased by a factor of 4 (2*2). The new force is then 4 times the original 16 units. F = (16 units ) • 4 = 64 units

Suppose that two objects attract each other with a gravitational force of 16 units. If the mass of both objects was doubled, and if the distance between the objects was doubled, then what would be the new force of attraction between the two objects? Answer: F = 16 units If each mass is increased by a factor of 2, then force will be increased by a factor of 4 (2*2). But this affect is offset by the doubling of the distance. Doubling the distance would cause the force to be decreased by a factor of 4 (22); the result is that there is no net affect on force. F = (16 units) • 4 / 4 = 16 units

Challenge! Suppose that two objects attract each other with a gravitational force of 16 units. If the mass of both objects was tripled, and if the distance between the objects was doubled, then what would be the new force of attraction between the two objects? Answer: F = 36 units If each mass is increased by a factor of 3, then force will be increased by a factor of 9 (3*3). But this affect is partly offset by the doubling of the distance. Doubling the distance would cause the force to be decreased by a factor of 4 (22). the net affect on force is that it increased by 9/4. F = (16 units) * 9 / 4 = 36 units

Challenge! Suppose that two objects attract each other with a gravitational force of 16 units. If the mass of object 1 was doubled, and if the distance between the objects was tripled, then what would be the new force of attraction between the two objects? Answer: F = 3.56 units If the mass of one object is doubled. then the force of attraction will be doubled as well. But this affect is more than offset by the tripling of the separation distance. Tripling the distance would cause the force to be decreased by a factor of 9 (32). The net affect on force is that it decreased by a factor of 2/9. F = (16 units) • 2 / 9 = 3.56 units