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Motion of Planets Seen from Earth In the movie below, you will see the Sun, Mercury, Venus, Earth, Mars, Jupiter, and Saturn looking down on the plane of the solar system from the Earth’s perspective QuickTime™ and a Sorenson Video decompressor are needed to see this picture. ISP 205 - Astronomy Gary D. Westfall Lecture 3 1 Motion of the Planets Seen from the Sun Now you will see the Sun, Mercury, Venus, Earth, Mars, Jupiter, and Saturn looking down on the plane of the solar system from the Sun’s perspective QuickTime™ and a Sorenson Video decompressor are needed to see this picture. ISP 205 - Astronomy Gary D. Westfall Lecture 3 2 Orbits and Gravity • Tycho Brahe made a long series of careful measurements of the motions of the planets • Johannes Kepler worked with Brahe and interpreted these data • Kepler’s Three Laws Orbits are ellipses, not circles Line from planet to sun sweeps out equal area in equal time Period2 proportional to Semimajor axis3 Semimajor axis is also the average distance of the planet from the Sun ISP 205 - Astronomy Gary D. Westfall Lecture 3 3 Elliptical Orbits • Kepler showed that the orbit of Mars is an ellipse with the Sun at one focus Sun Focus 2 Semiminor axis Focus 1 Semimajor axis ISP 205 - Astronomy Gary D. Westfall Lecture 3 4 Kepler’s Second Law • A line from the planet to the Sun sweeps out equal areas in equal times • When the planet is near the Sun, it moves quickly • When the planet is far from the Sun, it moves slowly ISP 205 - Astronomy Gary D. Westfall QuickTime™ and a Graphics decompressor are needed to see this picture. Lecture 3 5 Kepler’s Third Law • (distance)3 = (period)2 • Distance is given in units of the distance of the Earth to the Sun Astronomical unit (AU) • Period is given in terms of the time it takes for the Earth to go around the Sun 1 year • Example - Mars (distance)3 = (1.52)3 = 3.51 (period)2 = (1.88)2 = 3.53 ISP 205 - Astronomy Gary D. Westfall Lecture 3 6 Newton’s First Law • In the absence of any external forces we have Conservation of momentum An object on motion tends to remain in motion An object at rest tends to remain at rest • An object has mass • • • • The amount of material in the body An object has a speed An object has a direction Speed combined with direction is velocity Momentum is mass times velocity ISP 205 - Astronomy Gary D. Westfall Lecture 3 7 Newton’s Second Law • The change of motion of a body is proportional to the force acting on it and is made in the direction the force is acting • Force has a magnitude and a direction • Change of motion is acceleration Acceleration has a magnitude and a direction Acceleration is change of momentum • Force equals mass times acceleration • The force and the acceleration are in the same direction ISP 205 - Astronomy Gary D. Westfall Lecture 3 8 Newton’s Third Law • For every action there is an equal and opposite reaction • The mutual actions of two bodies on each other are always equal and opposite • This is the principle behind a rocket Fuel is burned, hot gases are ejected, the rocket goes the other way ISP 205 - Astronomy Gary D. Westfall Lecture 3 9 Mass, Volume, Density • Mass is a measure of the amount of material in an object • Volume is the size of an object • Density is the mass per unit volume • We will use the unit gram per cubic centimeter g/cm3 Water has a density of 1 g/cm3 Gold has a density of 19.3 g/cm3 Wood has a density of 0.8 g/cm3 ISP 205 - Astronomy Gary D. Westfall Lecture 3 10 Angular Momentum • The angular momentum of an object is defined in terms of its mass, its velocity, and its distance from the fixed point about which it turns • Angular momentum is conserved in the absence of any external force just like momentum • Angular momentum equals mass times velocity times distance If distance is decreased, velocity must increase If distance is increased, velocity must decrease If mass is decreased,distance must increase • Ice skaters, divers, gymnasts ISP 205 - Astronomy Gary D. Westfall Lecture 3 11 The Law of Gravity • The force that hold the planets in orbit is gravity • Gravity is a property of mass • The force of gravity between any two objects is equal to the gravitational constant G times the mass of object 1 times the mass of object 2 divided by the distance between the planet and the sun squared m1m2 Force G 2 R ISP 205 - Astronomy Gary D. Westfall Lecture 3 12 Example - Gravity • If the radius of the Earth were increased by a factor of 2 and the masses remained the same, by what factor would the force of gravity on the Earth’s surface change? m1m2 Force G 2 R The distance from the center of the Earth would change by a factor of 2 so the force would decrease by a factor of 4 ISP 205 - Astronomy Gary D. Westfall Lecture 3 13 Orbital Motion and Mass • Newton’s Law of Gravity extended Kepler’s Third Law • Kepler (distance)3 = (period)2 • Newton (distance)3 = (M1 + M2)(period)2 M1 = mass of the Sun M2 = mass of the planet Masses of the planets are much smaller than the mass of the Sun ISP 205 - Astronomy Gary D. Westfall Lecture 3 14 Examples, Orbital Motion • Suppose the mass of the Earth suddenly decreased by a factor of 2, what would happen to the period of its orbit around the Earth? (distance)3 = (M1 + M2)(period)2 The orbit would not change much because the mass of the Earth is small compared to the mass of the Sun • Suppose the mass of the Sun suddenly decreased by a factor of 2 and the Earth stayed the same distance from the Sun, what would happen to the period of the Earth;s orbit? The period would have to be longer ISP 205 - Astronomy Gary D. Westfall Lecture 3 15 Free Fall • When a object is in orbit, it is falling “around” the Earth • If you are in an elevator and the cable breaks, the acceleration of you and elevator will be the same and you will feel no forces (for a while) Weightless • Astronauts in orbit around the Earth feel no gravity because the forces are balanced, not because they are so far away from the Earth that gravity is weak ISP 205 - Astronomy Gary D. Westfall Lecture 3 16 Interplanetary Spacecraft • The exploration of the solar • system has been carried out by robot spacecraft These spacecraft are given a velocity larger than the Earth’s escape velocity 25,000 miles per hour • After launch, these spacecraft have little ability to maneuver Only small thrusters • To make large course corrections, the spacecraft are steered near planets “slingshot” ISP 205 - Astronomy Gary D. Westfall Lecture 3 17