Physics for Scientists and Engineers
6th Edition
ISBN: 9781429281843
Author: Tipler
Publisher: MAC HIGHER
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A comet of mass me is in an elliptical orbit around the sun (mass Mo), which is located
at one focus of the ellipse. The comet is a distance ra from the sun at its greatest distance
(aphelion) and rp at its closest pass (perihelion). Let G be the gravitational constant and recall
that F₁(r) = GMm and Ug(r) =
==
p²
GMm
r
1. What physical concepts would you need in order to calculate the speed of the comet at
aphelion and perihelion (va and vp)?
2. Apply these concepts to get two independent equations for the unknown quantities va and
Up in terms of G, mc, Mo, Tp, and rɑ. You do not need to solve these equations.
The radius Rhand mass Mh of a black hole are related by Rh = 2GMh/c2, where c is the speed of light. Assume that the gravitational acceleration agof an object at a distance ro= 1.001Rh from the center of a black hole is given by ag = G M / r2 (it is, for large black holes).(a) In terms of Mh, find ag at ro.(c) What is ag at rofor a very large black hole whose mass is 1.69 × 1015 times the solar mass of 1.99 × 1030 kg?(d) If an astronaut with a height of 1.73 m is at rowith her feet toward this black hole, what is the difference in gravitational acceleration between her head and her feet ahead-afeet?
(a) Evaluate the gravitational potential energy (in J) between two 6.00 kg spherical steel balls separated by a center-to-center distance of 19.0 cm.
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Chapter 11 Solutions
Physics for Scientists and Engineers
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- Check 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_forwardCheck Your Understanding Galaxies are not single objects. How does the gravitiational force of one galaxy exerted on the “closer” stars of the other galaxy compare to those farther away? What effect would this have on the shape of the galaxies themselves?arrow_forwardCheck Your Understanding Assume you are in a spacecraft in orbit about the Sun at Earth’s orbit, but far away from Earth (so that it can be ignored). How could you redirect your tangential velocity to the radial direction such that you could then pass by Mars’s orbit? What would be required to change just the direction of the velocity?arrow_forward
- On a planet whose radius is 1.2107m , the acceleration due to gravity is 18m/s2 . What is the mass of the planet?arrow_forwardUsing 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 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)=5.55103sarrow_forward
- The gravitational force exerted on an astronaut on the Earths surface is 650 N directed downward. When she is in the space station in orbit around the Earth, is the gravitational force on her (a) larger, (b) exactly the same, (c) smaller, (d) nearly but not exactly zero, or (e) exactly zero?arrow_forwardFind the Hohmann transfer velocities, vEllipseEarth and vEllipseMars ,needed for a trip to Mars. Use Equation 13.7 to find the circular orbital velocities for Earth and Mars. Using Equation 13.4 and the total energy of the ellips (with semi-major asix a), given by E=GmMs2a , find the velocities at Earth (perihelion) and at Mars (aphelion) required to be on the transfer ellipse. The difference, v , at each point is the velocity boost or transfer velocity needed.arrow_forwardEstimate the gravitational force between two sumo wrestlers, with masses 220 kg and 240 kg, when they are embraced and their centers are 1.2 m apart.arrow_forward
- If a spacecraft is headed for the outer solar system, it may require several gravitational slingshots with planets in the inner solar system. If a spacecraft undergoes a head-on slingshot with Venus as in Example 11.6, find the spacecrafts change in speed vS. Hint: Venuss orbital period is 1.94 107 s, and its average distance from the Sun is 1.08 1011 m.arrow_forward(a) What is the approximate force of gravity on a 70kg person due to the Andromeda galaxy, assuming its total mass is 1013 than of our Sun and acts like a single mass 2 Mly away? (b) What is the ratio of this force to the person's weight? Note that Andromeda is the closest large galaxy.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
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