Concept explainers
A space probe describes a circular orbit of radius nR with a velocity v0 about a planet of radius R and center O. Show that (a) in order for the probe to leave its orbit and hit the planet at an angle θ with the vertical, its velocity must be reduced to αv0, where
(b) the probe will not hit the planet if α is larger than
Want to see the full answer?
Check out a sample textbook solutionChapter 13 Solutions
Vector Mechanics for Engineers: Statics and Dynamics
- A spacecraft approaching the planet Saturn reaches point A with a velocity vA of magnitude 68.8 × 103 ft/s. It is to be placed in an elliptic orbit about Saturn so that it will be able to periodically examine Tethys, one of Saturn’s moons. Tethys is in a circular orbit of radius 183 × 103 mi about the center of Saturn, traveling at a speed of 37.2 × 103 ft/s. Determine (a) the decrease in speed required by the spacecraft at A to achieve the desired orbit, (b) the speed of the spacecraft when it reaches the orbit of Tethys at B.arrow_forwardTwo small balls A and B with masses 2m and m , respectively, are released from rest at a height h above the ground. Neglecting air resistance, which of the following statements is true when the two balls hit the ground? a. The kinetic energy of is the same as the kinetic energy of B.b. The kinetic energy of A is half the kinetic energy of B.c. The kinetic energy of A is twice the kinetic energy of B.d. The kinetic energy of A is four times the kinetic energy of B.arrow_forwardCommunication satellites are placed in a geosynchronous orbit, i.e., in a circular orbit such that they complete one full revolution about the earth in one sidereal day (23.934 h), and thus appear stationary with respect to the ground. Determine (a) the altitude of these satellites above the surface of the earth, (b) the velocity with which they describe their orbit. Give the answers in both SI and U.S. customary units.arrow_forward
- It was observed that during the Galileo spacecraft’s first flyby of the earth, its minimum altitude was 600 mi above the surface of the earth. Assuming that the trajectory of the spacecraft was parabolic, determine the maximum velocity of Galileo during its first flyby of the earth.arrow_forwardA satellite describes an elliptic orbit about a planet of mass M . The minimum and maximum values of the distance r from the satellite to the center of the planet are, respectively, r0 and r1. Use the principles of conservation of energy and conservation of angular momentum to derive the relationwhere h is the angular momentum per unit mass of the satellite and G is the constant of gravitation.arrow_forwardA communications satellite is in a circular orbit above the earth such that it always remains directly over a point on the earth’s surface. As a result, the period of the satellite must equal the rotation of the earth,which is approximately 24 hours. Determine the satellite’s altitude h above the earth’s surface and its orbital speed.arrow_forward
- Determine the altitude reached by the spacecraft of Prob. 14.95 when all the fuel of its launching rocket has been consumed.Reference to Problem 14.95:A 540-kg spacecraft is mounted on top of a rocket with a mass of 19 Mg, including 17.8 Mg of fuel. Knowing that the fuel is consumed at a rate of 225 kg/s and ejected with a relative velocity of 3600 m/s, determine the maximum speed imparted to the spacecraft if the rocket is fired vertically from the ground.arrow_forwardA meteor starts from rest at a very great distance from the earth. Knowing that the radius of the earth is 6370 km and neglecting all forces except the gravitational attraction of the earth, determine the speed of the meteor (a) when it enters the ionosphere at an altitude of 1000 km, (b) when it enters the stratosphere at an altitude of 50 km, (c) when it strikes the earth’s surface.arrow_forwardCar A was traveling west at a speed of 15 m/s and car B was traveling north at an unknown speed when they slammed into each other at an intersection. Upon investigation it was found that after the crash the two cars got stuck and skidded off at an angle of 50° north of east. Knowing the masses of A and B are m mA and mB, respectively, draw the impulse-momentum diagram that can be used to determine the velocity of B before impact.arrow_forward
- A 1.5-lb ball that can slide on a horizontal frictionless surface is attached to a fixed point O by means of an elastic cord of constant k= 1 lb/in. and undeformed length 2 ft. The ball is placed at point A, 3 ft from O , and given an initial velocity v0 perpendicular to OA ., allowing the ball to come within a distance d = 9 in. of point O after the cord has become slack. Determine (a) the initial speed v0 of the ball, (b) its maximum speed.arrow_forwardA satellite is in circular orbit around Earth at an altitude of three Earth radii above the surface. If the satellite uses onboard retro rockets to cut its speed to one half, at what distance from Earth can it establish a new stable circular orbit? Hint: vorbit =arrow_forwardFrom experimental tests, smaller boulders tend to have a greater coefficient of restitution than larger boulders. Rock A falls a distance of 20 meters before striking an incline with a slope of a= 45°. Knowing that h = 30 m and d= 20 m, determine if a boulder will land on the road or beyond the road for a coefficient of restitution of (a)e= 0.2, (b) e = 0.1.arrow_forward
- Elements Of ElectromagneticsMechanical EngineeringISBN:9780190698614Author:Sadiku, Matthew N. O.Publisher:Oxford University PressMechanics of Materials (10th Edition)Mechanical EngineeringISBN:9780134319650Author:Russell C. HibbelerPublisher:PEARSONThermodynamics: An Engineering ApproachMechanical EngineeringISBN:9781259822674Author:Yunus A. Cengel Dr., Michael A. BolesPublisher:McGraw-Hill Education
- Control Systems EngineeringMechanical EngineeringISBN:9781118170519Author:Norman S. NisePublisher:WILEYMechanics of Materials (MindTap Course List)Mechanical EngineeringISBN:9781337093347Author:Barry J. Goodno, James M. GerePublisher:Cengage LearningEngineering Mechanics: StaticsMechanical EngineeringISBN:9781118807330Author:James L. Meriam, L. G. Kraige, J. N. BoltonPublisher:WILEY