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
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- In 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_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
- Police 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_forwardSchwarzschild 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_forward
- For 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_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?arrow_forward
- We 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_forwardThe distance to the Andromeda Galaxy is estimated at about 2 x 106 light years. A light year is the distance traveled by light in one year; if the speed of light is 3 x 108 m/s, about how far is it from our galaxy to Andromeda.arrow_forward
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