Transcript a force
Gliese 581A: red dwarf star Mass ~ 1/3 Sun 20.3 light-years distant 87th closest star At least 7 planets Three in or close to the habitable zone Gliese 581c: similar to Venus? – too hot Gliese 581d: similar to Mars? – too cold Gliese 581g: Goldilocks planet – just right! Nearly circular 37 day orbit Orbital radius of ~ 0.15 AU Mass ~ 3.1 times the Earth’s Radius ~ 1.5 Earth Surface gravity ~ 1.1 to 1.7 times Earth’s Homework #4 will be posted shortly. We must to understand how planets are formed and what determines their habitability. What does any theory of the formation and evolution of the solar System have to account for? The Sun: A central star Predominately H and He Most of the mass in the solar system. Rotates in same sense that planets orbit. Terrestrial Jovian Two “flavors” of planets Terrestrial Planets Size: Location: Composition: Temperature: Rings: Rotation rate: Surface: Atmosphere: Moons: small closer to Sun rocky/metallic hotter none slow solid minimal few to none Jovian Planets large distant gaseous/icy cold ubiquitous rapid not solid substantial many Planetary orbits: 1) Prograde 2) approximately coplanar 3) approximately circular Rotation: 1) Mostly Prograde 2) Includes sun 3) Includes large moons Craters are ubiquitous on solid objects There are lots of smaller objects in the Solar System, some are rocky and some are icy Asteroids small Rocky Odd-shapes nearly circular orbits orbit planes are near Ecliptic Plane orbits in inner part of solar system The “asteroid belt” Comets small nucleus very large tails “dirty snow ball” highly eccentric orbits all orbit inclinations Comets are found mainly in two regions of the solar system Kuiper Belt Objects UB313 (1500 miles) To understand why these features exist, we need a little more background material… the phases – solid – liquid – gas – plasma depend on how tightly the atoms and/or molecules are bound to each other • As temperature increases, these bonds are loosened: ● Phases of Matter In thinking about phases of matter, recall that temperature measures the average kinetic energy of particles. Faster (hotter) particles can escape electrical bonds easier. Matter, Forces and Motion Scalars and Vectors Scalar: a quantity described solely by its size (and units) Vector: a quantity described by its size AND direction • speed – rate at which an object moves [e.g., m/s]. A scalar quantity. • velocity – an object’s speed AND direction, [e.g.,10 m/s east]. A vector quantity. • acceleration – a change in an object’s velocity, i.e., a change in speed OR direction [m/s2]. A vector quantity. Momentum (p) – the mass of an object times its velocity (p=mv) Force (f) – anything that can cause a change in an object’s momentum As long as the object’s mass does not change, a force causes a change in velocity, or an acceleration (a) Force, momentum, and acceleration are all vectors Newton's Laws of Motion A body in motion remains in motion and a body a rest remains at rest unless acted upon by an outside force. F = ma (= rate of change of momentum) For every applied force, a force of equal size but opposite direction arises. Newton’s First Law of Motion A body in motion remains in motion and a body at rest remains at rest unless acted upon by an outside force. OR If the net force acting on an object is zero, then there is no change in the object’s motion. Newton’s Second Law of Motion The change in a body’s velocity due to an applied force is in the same direction as the force, and is proportional to the force, but is inversely proportional to the body’s mass. F = ma Or F = rate of change of momentum Because force is a vector, forces only affect motion in the direction of the force. Motion perpendicular to the force is unchanged. Gravity & Orbits A planet is always changing its direction of motion. Newton’s second law therefore states that a force must be acting on the planet. Gravity provides this force. F = ma can be rewritten to show that for a given force, the acceleration is inversely proportional to the mass: a=F/m Do not confuse mass and density Mass = amount of matter Density = amount of matter per volume Higher density means more matter packed into same volume Law of Conservation of Momentum • If the net force acting on an object is zero, then the total momentum of a system remains constant. Momentum: p = mv Newton’s Third Law of Motion “For every applied force, a force of equal size but opposite direction arises” or For every action there is an equal and opposite reaction Major Conservation Laws Conservation of energy Conservation of momentum Conservation of angular momentum Angular Momentum • angular momentum – the momentum involved in spinning /circling = mass x velocity x radius ● torque – anything that can cause a change in an object’s angular momentum (twisting force) Conservation of Angular Momentum • In the absence of a net torque, the total angular momentum of a system remains constant. Angular Momentum & Orbits The angular momentum of an orbiting planet is conserved, i.e., it is always the same. This provides yet another reason why planets move fastest at perihelion and slowest at aphelion. The Acceleration of Gravity (a force) As objects fall, they accelerate (a = g = Fgrav/m). We use the special symbol g to represent the acceleration due to the force of gravity. At sea level on the Earth, g = 9.8 m/s each second, or g = 9.8 m/s2. The higher you drop the ball, the greater its velocity will be at impact (force will be acting on it longer). Weight is the force of gravity acting upon an object : W = Fg = mg Galileo demonstrated that g is the same for all objects, regardless of their mass! Is Mass the Same Thing as Weight? ● ● mass – the amount of matter in an object weight – a measurement of the force due to gravity acting upon an object W = mg F = ma (weight) When in free-fall, you still have weight! “weightless” is a misnomer ● ● Objects do have weight in space Free-fall often confused with weightlessness Tidal Forces Because the gravitational force decreases with (distance)2, the attractive force experienced by one object (e.g., the Earth) due to the gravitational field of a second object (e.g., the Moon) varies with position (closest parts attracted most strongly). ● Now look at what happens when we measure the forces relative to the center of the Earth. Tidal Friction Tidal Friction ● ● ● This fight between Moon’s pull & Earth’s rotation causes friction. Earth’s rotation slows down (1 sec every 50,000 yrs.) Conservation of angular momentum causes the Moon to move farther away from Earth. Synchronous Rotation ● ● ● ● …is when the rotation period of a moon, planet, or star equals its orbital period about another object. Tidal friction on the Moon (caused by Earth) has slowed its rotation down to a period of one month. The Moon now rotates synchronously. – We always see the same side of the Moon. Tidal friction on the Moon has ceased since its tidal bulges are always aligned with Earth. ● Most of the large moons in the solar system are in synchronous rotation.