4) The acceleration due to gravity at the surface of a planet of mass M, radius R, is given by the expression, g = GM/R? . Farth = 9,8mb2-GHE RE %3D a) Mars's diameter is about .5 what earth is and the mass is about .1 that of earth, what would g be in m/s? ? Mars : G(.1)ME %3D RE =3.92m. Gravity can be simulated by rotating a hollow cylinder, that rotation simulates gravity by its centripetal acceleration. If you were standing on the inside of the cylinder the acceleration would push your feet against the wall with your head pointing to the center. If the radius of the cylinder is 300 m... b) What speed v should the rotation be in order to give you the same feeling as if you are standing on Earth? V=N8. = 19.8m/s2.300m=154.22 ms c) What speed v should the rotation be in order to give you the same feeling as if you are standing on

4) The acceleration due to gravity at the surface of a planet of mass M, radius R, is given by the expression, g = GM/R? . Farth = 9,8mb2-GHE RE %3D a) Mars's diameter is about .5 what earth is and the mass is about .1 that of earth, what would g be in m/s? ? Mars : G(.1)ME %3D RE =3.92m. Gravity can be simulated by rotating a hollow cylinder, that rotation simulates gravity by its centripetal acceleration. If you were standing on the inside of the cylinder the acceleration would push your feet against the wall with your head pointing to the center. If the radius of the cylinder is 300 m... b) What speed v should the rotation be in order to give you the same feeling as if you are standing on Earth? V=N8. = 19.8m/s2.300m=154.22 ms c) What speed v should the rotation be in order to give you the same feeling as if you are standing on

Glencoe Physics: Principles and Problems, Student Edition

1st Edition

ISBN:9780078807213

Author:Paul W. Zitzewitz

Publisher:Paul W. Zitzewitz

Chapter7: Gravitation

Section: Chapter Questions

Problem 5STP

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Suppose astronomers find an earthlike planet that is twice the size of Earth (that is, its radius is twice that of Earth’s). What must be the mass of this planet such that the gravitational force (Fgravity) at the surface would be identical to Earth’s?
I0 orbits Jupiter with an average radius of 421,700 km and a period of 1.769 days. Based upon these data, what is tha mass of Jupiter?
What is the difference between the force on a 1.0-kg mass on the near side of I0 has mean radius of 1821 km and a mean orbital radius about Jupiter of 421,700 km. (b) Compare this difference to that calculated for the difference for Earth due to the Moon calculated in Example 13.14. Tidal forces are the cause of I0 ’s volcanic activity.
What is the gravitational acceleration close to the surface of a planet with a mass of 2ME and radius of 2RE where ME, and RE are the mass and radius of Earth, respectively? Answer as a multiple of g, the magnitude of the gravitational acceleration near Earths surface. (See Section 7.5.)
Check Your Understanding There is another consideration to this last calculation of ME. We derived Equation 13.8 assuming that the satellite orbits around the center of the astronomical body at the same radius used in the expression for the gravitational force between them. What assumption is made to justify this? Earth is about 81 times more massive than the Moon. Does the Moon orbit about the exact center of Earth? Which is about 17,000 mph. Using Equation 13.8, the period is T=2r3GME=2( 6.37 10 6+4.00 10 5m)3(6.67 10 11N m 2 /kg 2)(5.96 10 24kg)=5.55103s
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What percentage of the acceleration at Earth's surface is the acceleration due to gravity at the position of a satellite located 300 km above Earth?