A 1000 kg spacecraft is approaching Jupiter (which is at the origin). The position of the spacecraft is given by the vector RSC = (0.0,-2.533) x 106km. The velocity is given by VSC= (+6.00, +8.00) km/sec. The mass of Jupiter, (MJ=318 MEarth) and MEarth = 5.97 x 1024 kg.A) What is the potential and kinetic energy of the spacecraft (write each to 3 sig figs.) What is the total energy of the spacecraft? Call the total energy Ei.B) Can it escape Jupiter? Justify your answer.C) What is the angular momentum of the spacecraft around Jupiter? Call this Li.

Name: A 1000 kg spacecraft is approaching Jupiter (which is at the origin).
Uploaded: 2024-03-20T06:57:25.000Z
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Description: A 1000 kg spacecraft is approaching Jupiter (which is at the origin). The position of the spacecraft is given by the vector RSC = (0.0,-2.533) x 106km. The velocity is given by VSC= (+6.00, +8.00) km/sec. The mass of Jupiter, (MJ=318 MEarth) and MEar

Given data: Mass of spacecraft, m=1000 kg Position, RSC=0.0,-2.533×106km Velocity, VSC=+6.00,+8.00km/s Mass of Jupiter, MJ=318MEarth Mass of Earth, MEarth=5.97×1024kgTo determine: Potential and kinetic energy of the spacecraft, total energy of the spacecraft. Whether the spacecraft can escape or not. Angular momentum of spacecraft around Jupiter.Explanation: Mass of Jupiter is given by: MJupiter=3185.97×1024kg=1898.5×1024kg a. Potential energy can be given as: U=-GMJmRSCU=-6.67×10-111898.5×1024kg1000 kg2.533×106×103mU=-4.999×1010J Kinetic energy can be given as: K=12mVSC2K=121000 kg6×103m/s2+8×103m/s22K=5.000×1010J Hence the total energy can be given by: Ei=U+KEi=-4.999×1010J+5.000×1010JEi=0.792×107Jb. Spacecraft can escape Jupiter because the total energy is positive. c. Angular momentum can be calculated as follows: Li=RSC×mVSCLi=2.533×106×103×10006×103Li=1.519×1016kg.m/sAnswer: Potential and kinetic energy of spacecraft are: U=-4.999×1010J; K=5.000×1010J and total energy is Ei=0.792×107J Spacecraft can escape Jupiter. Angular momentum is Li=1.519×1016kg.m/s

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College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

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A 1000 kg spacecraft is approaching Jupiter (which is at the origin). The position of the spacecraft is given by the vector R_SC = (0.0,-2.533) x 10⁶km. The velocity is given by V_SC= (+6.00, +8.00) km/sec. The mass of Jupiter, (M_J=318 M_Earth) and M_Earth = 5.97 x 10²⁴ kg.

A) What is the potential and kinetic energy of the spacecraft (write each to 3 sig figs.) What is the total energy of the spacecraft? Call the total energy E_i.

B) Can it escape Jupiter? Justify your answer.

C) What is the angular momentum of the spacecraft around Jupiter? Call this L_i.

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