Review. In 1963, astronaut Gordon Cooper orbited the Earth 22 times. The press stated that for each orbit, he aged two-millionths of a second less than he would have had he remained on the Earth. (a) Assuming Cooper was 160 km above the Earth in a circular orbit, determine the difference in elapsed time between someone on the Earth and the orbiting astronaut for the 22 orbits. You may use the approximation
for small x. (b) Did the press report accurate information? Explain.
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Chapter 39 Solutions
EBK PHYSICS FOR SCIENTISTS AND ENGINEER
- According to Kepler's third law of planetary motion, the mean distance D, in millions of miles, from a planet in our solar system to the sun is related to the time P, in years, that it takes for the planet to complete a revolution around the sun, and the relationship is D = 93P 2/3. It takes the planet Pluto 248 years to complete a revolution around the sun. What is the mean distance from Pluto to the sun? What is the mean distance from Earth to the sun? Give your answers to the nearest million miles. from pluto to sun _____ million miles from earth to sun _____ million milesarrow_forwardAccording to Kepler's third law of planetary motion, the mean distance D, in millions of miles, from a planet in our solar system to the sun is related to the time P, in years, that it takes for the planet to complete a revolution around the sun, and the relationship is D = 93P2/3 It takes the planet Pluto 248 years to complete a revolution around the sun. What is the mean distance from Pluto to the sun? What is the mean distance from Earth to the sun? Give your answers to the nearest million miles. from Pluto to the sun X million miles from Earth to the sun million milesarrow_forwardIn 1999, NASA lost the Mars Climate Orbiter because one group of engineers used metric units in their calculations while another group used English units. Consequently, the orbiter descended too far into the Martian atmosphere and burned up. Suppose that the orbiter was to have established orbit at 157 km and that one group of engineers specified this distance as 1.57 x 10³ m. Suppose further that a second group of engineers programmed the orbiter to go to 1.57 x 10³ ft. The $125 million Mars Climate Orbiter was lost in the Martian atmosphere in 1999 because two groups of engineers failed to communicate with each other about What was the difference in kilometers between the two altitudes? Express your answer with the appropriate units. Value Submit HA Provide Feedback Part B Complete previous part(s) Units Request Answer ?arrow_forward
- To complete this exercise, you need to know that the circumference of a circle is proportional to its radius, and that the constant of proportionality is 2π. You do not need to know either the radius of the Moon’s orbit or the radius of Earth. For purposes of this exercise, we assume that the Moon’s orbit around Earth is circular. In one trip around Earth, the Moon travels approximately 2.4 million kilometers. Another satellite orbits Earth (in a circular orbit) at a distance from Earth that is 1/4 that of the Moon. How far does this satellite travel in one trip around Earth? (Use decimal notation. Give your answer to one decimal place.) A rope is tied around the equator of Earth. A second rope circles Earth and is suspended 77 feet above the equator. How much longer is the second rope than the first?arrow_forwardKepler's Third Law of planetary motion states that the square of the period T of a planet (the time it takes for the planet to make a complete revolution about the sun) is directly proportional to the cube of its average distance d from the sun. (a) Express Kepler's Third Law as an equation. (Use k for the constant of proportionality.) (c) The planet Neptune is about 2.79 × 109 mi from the sun. Find the period of Neptune. (Round your answer to the nearest whole number of years.)arrow_forwardAccording to Newton's law of universal gravitation, the attraction force between two bodies is given by: where mi and m2 are the masses of the bodies, r is the distance between the bodies, and G=6.67 × 10-" N-m²/kg² is the universal gravitational constant. Determine how many times the attraction force between the sun and the Earth is larger than the attraction force between the Earth and the moon. The distance between the sun and Earth is 149.6 x 10°m, the distance 28 between the moon and Earth is 384.4 × 10°m, mEarth = 5.98 x 10“ kg, = 2.0 x 10" kg, and mn =7.36 x 102 kg.arrow_forward
- Schwarzschild radius RS of a black hole is the maximum distance from the black hole’s center at which light cannot escape its gravitational field. The quantity RS (with dimensions of length) is dependent on the mass of the black hole M, the speed of light c, and the gravitational constant G. Based on the dimensions of these four parameters, predict an equation for the Schwarzschild radius. Hint: G has dimensions of [L3/MT2]arrow_forwardIf you make multiple measurements of your height, you are likely to find that the results vary by nearly half an inch in either direction due to measurement error and actual variations in height. You are slightly shorter in the evening, after gravity has compressed and reshaped your spine over the course of a day. One measurement of a man’s height is 6 feet and 1 inch. Express his height in meters, using the appropriate number of significant figures.arrow_forwardAn unmanned reconnaissance drone is flying over enemy territory using a preprogrammed flight pattern for a total flight time of 28 minutes. Its height (in feet) can be modeled by the function H(t)=−1/2t^2+17t+683, where t is the number of minutes of flight time since takeoff. Due to the terrain, the enemy's radar cannot track the drone when it is below 827 feet. For what values of t will the drone be exactly 827 feet high? A) Earliest time= ___ minutes B) Latest time=____ minutesarrow_forward
- A climber who is 75 kgs in mass reaches the peak of a mountain. If the mutual attraction between the climber and the Earth is 735.09 N, how tall is the mountain in meters? radius of the Earth = 6.38 x 106 m mass of the Earth = 5.98 x 1024 kgsarrow_forwardConsider a track in the shape of a perfect circle of radius 1 kilometer. A biker rides counter-clockwise at a constant speed around the track completing 3 laps every hour. Write a formula for the position of the biker (x(t), y(t)) t minutes after starting, where the origin is at the center of the track and the biker's starting position is on the posi- tive x-axis. Use this formula to compute how far the biker travels in their first 200 minutes of biking.arrow_forwardA person’s arm rotates around the shoulder (S) and elbow (E) joint axes. The arm has the length a = 9 1/2", the forearm has the length b = 11". The shoulder joint angle is θ = 43°. The elbow joint angle is γ = 21°. a) Compute the Cartesian coordinates of the endpoint H by using a+b. b) Identify the origin of your reference frame.arrow_forward
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