The magnitude of the tidal force between the International Space Station (ISS) and a nearby astronaut on a spacewalk is approximately 2GmMa/r3. In this expression, M is the mass of the Earth, r = 6.79 × 106 m is the distance from the center of the Earth to the orbit of the ISS, m = 125 kg is the mass of the astronaut, and a = 10 m is the distance from the astronaut to the center of mass of the ISS. (a) Calculate the magnitude of the tidal force for this astronaut. This force tends to separate the astronaut from the ISS if the astronaut is located along the line that connects the center of the Earth with the center of mass of the ISS. (b) Calculate the force of gravitational attraction between the astronaut and the ISS if they are 10 m apart and the ISS has a mass of 420,000 kg. (c) Is the ISS orbit inside or outside the Roche limit?
Want to see the full answer?
Check out a sample textbook solutionChapter 12 Solutions
Physics, Books a la Carte Edition (5th Edition)
Additional Science Textbook Solutions
Chemistry: Structure and Properties (2nd Edition)
Organic Chemistry (8th Edition)
Chemistry: A Molecular Approach (4th Edition)
Microbiology: An Introduction
Human Anatomy & Physiology (2nd Edition)
Microbiology: An Introduction
- Let gM represent the difference in the gravitational fields produced by the Moon at the points on the Earths surface nearest to and farthest from the Moon. Find the fraction gM/g, where g is the Earths gravitational field. (This difference is responsible for the occurrence of the lunar tides on the Earth.)arrow_forwardThe Sun has a mass of approximately 1.99 1030 kg. a. Given that the Earth is on average about 1.50 1011 m from the Sun, what is the magnitude of the Suns gravitational field at this distance? b. Sketch the magnitude of the gravitational field due to the Sun as a function of distance from the Sun. Indicate the Earths position on your graph. Assume the radius of the Sun is 7.00 108 m and begin the graph there. c. Given that the mass of the Earth is 5.97 1024 kg, what is the magnitude of the gravitational force on the Earth due to the Sun?arrow_forwardOn a planet whose radius is 1.2107m , the acceleration due to gravity is 18m/s2 . What is the mass of the planet?arrow_forward
- Comet Halley (Fig. P11.21) approaches the Sun to within 0.570 AU, and its orbital period is 75.6 yr. (AU is the symbol for astronomical unit, where 1 AU = 1.50 1011 m is the mean EarthSun distance.) How far from the Sun will Halleys comet travel before it starts its return journey?arrow_forwardCalculate the effective gravitational field vector g at Earths surface at the poles and the equator. Take account of the difference in the equatorial (6378 km) and polar (6357 km) radius as well as the centrifugal force. How well does the result agree with the difference calculated with the result g = 9.780356[1 + 0.0052885 sin 2 0.0000059 sin2(2)]m/s2 where is the latitude?arrow_forwardIf a planet with 1.5 times the mass of Earth was traveling in Earth’s orbit, what would its period be?arrow_forward
- The force of attraction between two masses m1 and m2, having dimensions that are small compared with their separation distance R, is given by Newton’s third law, F=Gm1m2/R2 , where G=6.67259x10-11 N-m 2 /kg2 . What is the total gravitational force that the sun (1.97x1030 kg) and the earth (5.95x1024 kg) exert on the moon (7.37x1022 kg) at an instant when the earth, moon, and sun form a 90° angle? The earth-moon and sun-moon distances are 380x103 km and) 150x106 km, respectivelyarrow_forwardA newly discovered planet has four times the mass of the Earth, but a person's weight on the new planet's surface is the same as the person's weight on the Earth's surface. The radius of the new planet in terms of the radius R of Earth isarrow_forwardNewton's Law of Gravitation says that the magnitude F of the force exerted by a body of mass m on a body of mass M is GmM F= where G is the gravitational constant and r is the distance between the bodies. (a) Find dF/dr. dF dr = What is the meaning of dF/dr? O dF/dr represents the amount of force per distance. O dF/dr represents the rate of change of the mass with respect to the distance between the bodies. O dF/dr represents the rate of change of the distance between the bodies with respect to the force. O dF/dr represents the rate of change of the mass with respect to the force. O dF/dr represents the rate of change of the force with respect to the distance between the bodies. What does the minus sign indicate? O The minus sign indicates that the force between the bodies is decreasing. O The minus sign indicates that as the distance between the bodies increases, the magnitude of the force decreases. O The minus sign indicates that as the distance between the bodies increases, the…arrow_forward
- The planet Mars has mass 6.4 × 1023 kilograms and radius 3.4 × 106 meters. What is the gravitational force acting on a 75-kilogram astronaut?arrow_forwardthe weight, w, of an object varies inversely as the square of the distance, d, between the object and the center of Earth. If a man weighs 75kg on the surface of Earth, how much would he weigh 300km above the Earth's surface? (given the radius of the earth is approximately 6400km)arrow_forwardThe mass of the sun is 1.99×1030kg1.99×1030kg and its distance to the Earth is 1.50×1011m1.50×1011m.What is the gravitational force of the sun on the earth? The mass of the moon is 7.36×1022kg7.36×1022kg and its distance to the Earth is 3.84×108m3.84×108m.What is the gravitational force of the moon on the earth? The moon's force is what percent of the sun's force?arrow_forward
- Physics for Scientists and Engineers: Foundations...PhysicsISBN:9781133939146Author:Katz, Debora M.Publisher:Cengage LearningGlencoe Physics: Principles and Problems, Student...PhysicsISBN:9780078807213Author:Paul W. ZitzewitzPublisher:Glencoe/McGraw-HillPrinciples of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning
- University Physics Volume 1PhysicsISBN:9781938168277Author:William Moebs, Samuel J. Ling, Jeff SannyPublisher:OpenStax - Rice UniversityClassical Dynamics of Particles and SystemsPhysicsISBN:9780534408961Author:Stephen T. Thornton, Jerry B. MarionPublisher:Cengage Learning