Physics Fundamentals
2nd Edition
ISBN: 9780971313453
Author: Vincent P. Coletta
Publisher: PHYSICS CURRICULUM+INSTRUCT.INC.
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Chapter 7, Problem 64P
To determine
To Calculate: The kinetic energy of the mass of the debris relative to the satellite.
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The first artificial satellite to orbit the Earth was Sputnik I, launched October 4, 1957. The mass of Sputnik I was 83.5 kg, and its distances from the center of the Earth at apogee and perigee were 7330 km and 6610 km, respectively. Find the difference in gravitational potential energy for Sputnik I as it moved from apogee to perigee?
A satellite from the Glonass navigation system weighs 7,350 N on the surface of Earth. How much work is donein propelling the satellite from the surface of the Earth to a medium Earth orbit (MEO) of 19,000 km above Earth’ssurface? Use 6,371 km as the radius of Earth. (Express the result with unit N·km rounded to the nearest integer.)
Show that the values vA and vP of the speed of an earth satellite at the apogee A and the perigee P of an elliptic orbit are defined by the relationswhere M is the mass of the earth, and rA and rP represent, respectively, the maximum and minimum distances of the orbit to the center of the earth.
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Physics Fundamentals
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- A space probe is fired as a projectile from the Earths surface with an initial speed of 2.00 104 m/s. What will its speed be when it is very far from the Earth? Ignore atmospheric friction and the rotation of the Earth. P11.26 Ki+Ui=Kf+Uf12mvi2+GMEm(1rf1ri)=12mvf212vi2+GME(01RE)=12vf2orvf2=v122GMEREandvf=(v122GMERE)1/2,vf=[(2.00104)21.25108]1/2m/s=1.66104m/sarrow_forwardCheck Your Understanding The U.S. Air Force uses “10gs” (an acceleration equal to 109.8m/s2 ) as the maximum acceleration a human can withstand (but only tot several seconds) aid survive. How much time must the Enterprise spend accelerating if the humans on board are to experience an average at most 10gs of acceleration? (Assume the inertial dampeners are offline.)arrow_forwardA Molniya orbit is a highly eccentric orbit of a communication satellite so as to provide continuous communications coverage for Scandinavian countries and adjacent Russia. The orbit is positioned so that these countries have the satellite in view for extended periods in time (see below). If a satellite in such an orbit has an apogee at 40,000.0 km as measured from the center of Earth and a velocity of 3.0 km/s, what would be its velocity at perigee measured at 200.0 km altitude?arrow_forward
- Check Your Understanding If we send a probe out of the solar system starting form Earth’s surface, do we only have to escape the Sun?arrow_forwardGiven the perihelion distance, p , and aphelion distance, q , for an elliptical orbit, show that the velocity at perihelion, vp , is given by vp=2GMSun(q+p)qp . (Hint: Use conservation of angular momentum to relate vp and vq , and then substitute into the conservation fo energy equation.)arrow_forwardThe perihelion of Halley’s comet is 0.586 AU and the aphelion is 17.8 AU. Given that its speed at perihelion is 55 km/s, what is the speed at aphelion ( IAU=1.4961011m )? (Hint: You may use either conservation of energy or angular momentum, but the latter is much easier.)arrow_forward
- Using Figure 13.9, carefull sketch a free body diagram for the case of a simple pendulum hanging at latitude lambda, labeling all forces acting on the point mass,m. Set up the equations of motion for equilibrium, setting one coordinate in the direction of the centripetal accleration (toward P in the diagram), the other perpendicular to that. Show that the deflection angle , defined as the angle between the pendulum string and the radial direction toward the center of Earth, is given by the expression below. What is the deflection angle at latitude 45 degrees? Assume that Earth is a perfect sphere. tan(+)=gg2REtan , where is the angular velocity of Earth.arrow_forwardWhat is the ratio of the speed at perihelion to that at aphelion for the comet Lagerkvist in the previous problem?arrow_forwardCheck Your Understanding Can Earth’s gravity ever be a constant force for all paths?arrow_forward
- Using the technique shown in Satellite Orbits and Energy, show that two masses m1 and m2 in circular orbits about their common center of mass, will have total energy E=K+E=K1+K2Gm1m2r=Gm1m22r . We have shown the kinetic energy of both masses explicitly. (Hint: The masses orbit at radii r1 and r2 , respectively, where r=r1+r2 . Be sure not to confuse the radius needed for centripetal acceleration with that for the gravitational force.)arrow_forwardCheck Your Understanding By what factor must the radius change to reduce the orbital velocity of a satellite by one-half? By what factor would this change the period?arrow_forwardShow that the areal velocity for a circular orbit of radius r about a mass M is At=12GMr . Does your expression give the correct value for Earth’s areal vilocity about the Sun?arrow_forward
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