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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
Physics for Scientists and Engineers with Modern Physics
- Write down an expression for the velocity of a satellite of mass m in a circular orbit of radius R around the Earth. Take the mass of the Earth as M and use G for the gravitational constant. Please use appropriate algebraic symbols for multiplication (* for a × b), division (/ for a/b), exponents (a^b for a³), square root (sqrt(a*b/c) for √a × b/c) etc. Display responsearrow_forwardTo 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_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_forwardThe gravitational acceleration constant gx on Planet X can be approximated by determining the acceleration of an object assuming Newton's Law of Universal Gravitation. If gx = 3.8 m/s^2 , G = 6.7 x 10^-11 Nm^2/kg^2, and Planet X's radius is 4000 km, what is the approximate mass of planet X? Give answer in kg.arrow_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_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
- One of Saturn's moons is named Mimas. The mean orbital distance of Mimas is 1.87 x 108 m. The mean orbital period of Mimas is approximately 23 hours (8.28x104 s). Use this information to estimate a mass for the planet Saturn.arrow_forwardIn the movie Interstellar, the main characters are on a planet where 1 hour = 7 years on Earth. If you are 30 years old on Earth how many hours have passed by on the planet?arrow_forwardOne type of engine used in space travel is an ion thruster. These engines produce a low force that results in small acceleration changes. If an ion-thrust engine is used to apply 87 millinewtons [mN] of force on a satellite with a mass of 1.7 megagrams [Mg], what is the acceleration produced in units of meters per second squared [m/s2]?arrow_forward
- Principles of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningAn Introduction to Physical SciencePhysicsISBN:9781305079137Author:James Shipman, Jerry D. Wilson, Charles A. Higgins, Omar TorresPublisher:Cengage LearningPhysics for Scientists and Engineers: Foundations...PhysicsISBN:9781133939146Author:Katz, Debora M.Publisher:Cengage Learning
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