Suppose you are standing on a field, which is at a latitude of 40 5/6', and that you are 2.0 m tall. (a) Analytically find the speed of your feet, v, due to the rotation of the Earth. (Assume that the Earth is a perfect sphere, which is not, of radius R = 6378 km and that a day is exactly 24 hours long.) (b) Using your result from (a), determine the centripetal acceleration of your feet. 1 (c) Repeat parts (a) and (b) for your head and compute the difference between the acceleration at your head and feet. Show how round-off can corrupt your calculation and offer a way to fix the problem.

The days on Mars and Earth are of nearly identical length. Earth's mass is 9.35 times Mars's mass, Earth's radius is 1.88 times Mars's radius, and Mars is on average 1.52 times farther away from the Sun than Earth is. The Martian year is 1.88 times longer than Earth's year. Assume that they are both uniform spheres and that their orbits about the Sun are circles. Estimate the ratio (Earth to Mars) of the following. (a) their spin angular momenta(b) their spin kinetic energies(c) their orbital angular momenta(d) their orbital kinetic energies

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Let the radius of the Earth be R, and we approximate the Earth as a sphere. In order for an object to glide along the equator of the Earth at sea level, what is the speed at which it needs to be moving? gR gR VgR O (gR)?

In 1993 the spacecraft Galileo sent home an image of asteroid 243 Ida and an orbiting tiny moon (now known as Dactyl), the first confirmed example of an asteroid moon system. Other such systems have since been discovered. Assume an asteroid's moon is 1.4 km wide, and that its center is 130 km from the center of the asteroid, which is 55 km long. The moon's orbit is circular with a period of 22 h. (a) What is the mass of the asteroid? kg (b) The volume of the asteroid is 14,100 km³. What is the density of the asteroid? |kg/m³

Мon Gravity: on off O Gravity Force Velocity > Path U Grid Star Mass 0.5 Our Sun 1.5 2.0 Planet Mass 0.5 Earth 1.5 2.0 Fast 392 Earth Days Normal Clear Slow

A race-car starts at the 3 o’clock position and drives counterclockwise on a circular track with a radius 4 miles. a/ What distance (in miles) has the race-car traveled if the angle swept out by the race-car is: (i). 90◦ (degree)? (ii). 5 radians? b/ What is the angle measure (in radians) swept out if the race-car has traveled 4 miles counterclockwise? c/ What does it mean about the path of the car for the angle measure to be greater than 4π radians? Explain.

Taking the age of Earth to be about 4 ✕ 109 years and assuming its orbital radius of 1.5 ✕ 1011 m has not changed and is circular, calculate the approximate total distance Earth has traveled since its birth (in a frame of reference stationary with respect to the Sun). ..............m   Answer and simplify

Verify Kepler’s Laws of Planetary Motion. Assume that each planet moves in an orbit given by the vectorvalued function r. Let r = || r||, let G represent the universal gravitational constant, let M represent the mass of the sun, and let m represent the mass of the planet.