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 38 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
- Kepler'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_forwardPolice use the formula: v = V20L to estimate the speed of a car, v, in miles per hour, based on the length, L, in feet, of its skid marks when suddenly braking on a dry, asphalt road. At the scene of an accident, a police officer measures a car's skid marks to be 158 feet long. Approximately how fast was the car traveling? Round your answer to the nearest tenth (one decimal place) of a unit. Answer: The car was traveling at approximately miles per hour. Question Help: Video D Post to forum Submit Question fa ho 144 %23 & 4. 6. 7. R. T Y 60 24arrow_forwardNewton’s version of Kepler’s third law is: P2 = 4 π2 / [G (M1 + M2)] × a3. The space shuttle orbits 271 km above the Earth's surface. How often do the astronauts see a sunrise (in minutes)? Use the gravitational constant G = 6.67 × 10-11 m3 kg-1 s-2, the mass of the Earth M = 5.97 × 1024 kg, and the radius of the Earth to be 7000 km.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_forwardAccording to Kepler's law, the period of revolution (T) of a planet and its mean distance from the sun (r) are related by the equation. (a) T?r = constant (b) T? r³ = constant (c) T r = constant (d) T³ r = cònstant %3D %3Darrow_forwardFor about 10 years after the French Revolution, the French government attempted to base measures of time on multiples of ten: One week consisted of 10 days, one day consisted of 10 hours, one hour consisted of 100 minutes, and one minute consisted of 100 seconds. What are the ratios of (a) the French decimal week to the standard week and (b) the French decimal second to the standard second? Assume that the definition of a "day" remains the same. (a) Number 1.43 Units (b) Number 0.864 Units Sarrow_forward
- . In an experiment to measure the gravitational acceleration g, the distance of fall y and the time taken were measured to be 60.0 + 0.3 cm and 0.351 + 0.001 s.Find the gravitational acceleration g and its percentage uncertainty Δg /g. The accepted value for g is 9.80 m/s2. Find the percentage error. ( ? = 1/2 ??^2)arrow_forwardWe sent a probe out to orbit the planet Kerbal at a distance of 5.5x107m from the middle of the planet. It took our probe 3.5x105s to orbit the planet. Which formula will be used to solve this problem? Possible Formulas that can be used to answer the question: v=(2πr)/T ac=v2/r ac=(4π2r)/T2 Fc=mac Fg=mg F=(Gm1m2)/d2 g=Gm/r2 T2=(4π2/Gm)r3 v=√(Gm)/r g=9.80m/s2 G=6.67x10-11 (N∙m2)/kg2arrow_forwardNewton’s version of Kepler’s third law is P2 = 4 π2 / [G (M1 + M2)] · a3, where G is the gravitational constant, which is equal to 6.67*10-11 m3 kg-1 s-2. NASA's New Horizons mission found that Pluto's moon Charon orbits Pluto every 5.7 days at an average distance of 19200.0 km. What is the combined mass (in kg) of Pluto and Charon?arrow_forward
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