Physics 101 THursday 10/27/11 Class 19 Chapter 12.2 – 12.3 Gravitational attraction of spherical bodies Keplers laws

Gravity The space shuttle orbits about 200 km above the earths surface. The shuttle's "pre-launch weight" is its weight measured on the ground. (Neglecting the fuel) The magnitude of the force of gravity on the shuttle while it is in orbit is (the earth’s radius is 6370 km): A: Slightly greater than pre-launch. B: Equal to pre-launch C: Slightly less than pre-launch D:Lots less than pre-launch, almost (but not quite) zero. E: Precisely zero.

Gravity

An astronaut is floating around in the space shuttle's cabin. Her acceleration, as measured from the earth's surface, is A: zero - she's floating B: very small, in some random direction C: quite large, nearly g, directed towards the center of the earth D: quite large, nearly g, directed along the line of travel of the shuttle

gravity Astronaut Dave Bowman is standing in the centrifuge of the spaceship Discovery. He drops his pen and observes it fall to the floor. Which statement below is most accurate? A: After he releases the pen, the net force on the pen is zero. B: The pen falls because the centrifugal force pulls it toward the floor. C: The pen falls because the artificial gravity pulls it toward the floor.

If you weigh yourself at the equator of Earth, would you get a bigger, smaller, or similar value than if you weigh yourself at one of the poles (assume the Earth is completely spherical, but spinning)? a) bigger value b) smaller value c) same value

You weigh yourself on a scale inside an airplane that is flying with constant speed at an altitude of 20,000 feet. How does your measured weight in the airplane compare with your weight as measured on the surface of the Earth? a) greater than b) less than c) same

Gravity At a new moon the sun, moon and earth are aligned as shown below. The force between the moon and Sun is: A) 4 x N B) 4 x N C) 7 x N D) 7 x N G = 6.67x N m 2 /kg M e = 6 x kg M s = 2 x kg M m = 7 x kg R earth-moon = 4 x 10 5 km R earth-sun = 1.5 x 10 8 km Note: km not m Also note F due to gravity between earth and moon is 1.8 x N Sun Moonearth

A planet of mass m is a distance d from Earth. Another planet of mass 2m is a distance 2d from Earth. Which force vector best represents the direction of the total gravitation force on Earth? a b c d e 2d2d d 2m2m m Earth

Gravity At what point above the earths surface does the gravitation acceleration of the earth decrease to 1/4 the value at the surface? (note: the radius of the earth is 6 x 10 3 km) A) 3 x 10 3 km B) 6 x 10 3 km C) 12 x 10 3 km D) 24 x 10 3 km

Keplers laws

Orbits A satellite is in circular orbit around a planet that has a very tenuous atmosphere extending up to the altitude of the satellite. Due to atmospheric drag, the speed of the satellite… A: increases B: decreases C: remains constant

Orbits

Keplers laws Kepler's 3rd law: T^2/R^3=constant for all planets. The period T for the earth is 1 year (!) The distance of the earth to the sun is called 1 A.U. Suppose an asteroid is in circular orbit around the sun at a distance of 2 A.U. How long does it take the asteroid to orbit the sun once? A 2 years B: 3 years C: 2^(3/2) = 2.83 years D:2^(2/3) = 1.59 years E: Not enough information (An asteroid is not a planet - can't figure it out from Kepler's third law.)

Orbits Kepler's 3rd law: T^2/R^3=constant for all planets. The period T for the earth is 1 year. The distance of the earth to the sun is called 1 A.U. Suppose a satellite orbits the earth at a distance of about 1/1000 AU. How long does it take the satellite to orbit the earth once? A: Not enough information given. B: 1/1000 year. C: 1000 years. D: (1/1000)^(3/2) years E:(1/1000)^(2/3) years

Orbits Two communications satellites are in orbit at the same height, but one weighs twice as much as the other. The speed of the heavier satellite is A: Less thanB: Equal toC: Greater than D: (need more information) the speed of the lighter one.

Orbits

Astronauts in the space shuttle float because: a) they are so far from Earth that Earth’s gravity doesn’t act any more b) gravity’s force pulling them inward is cancelled by the centripetal force pushing them outward c) while gravity is trying to pull them inward, they are trying to continue on a straight-line path d) their weight is reduced in space so the force of gravity is much weaker

Keplers 3 rd law Weighing planets: Astronomers can use the Keplers 3 rd law to weigh a planet, by measuring the orbit of a moon of the planet (knowing T and radius then: If Mercury orbits the sun at a radius of m, with a period of 90 days (8x10 6 s), the mass of the sun is (close to what order of magnitude)? A) kg B) kg C) kgD) kg

Reading Assignment Tuesday 11/ – 13.3 Thursday 11/ – 13.7

Conservation of mechanical work Problems 12.8, 12.15, 12.30, 12.32