Physics for Scientists and Engineers
6th Edition
ISBN: 9781429281843
Author: Tipler
Publisher: MAC HIGHER
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Chapter 11, Problem 17P
To determine
To Find: The mass of galaxy.
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The Sun, which is 2.2 * 10^20 m from the centerof the Milky Way galaxy, revolves around that center once every2.5 * 10^8 years. Assuming each star in the Galaxy has a mass equalto the Sun’s mass of 2.0 * 10^30 kg, the stars are distributed uniformlyin a sphere about the galactic center, and the Sun is at theedge of that sphere, estimate the number of stars in the Galaxy.
According to Lunar Laser Ranging experiment the average distance Lm from the Earth to the Moon is approximately {LL} × 105 km. The Moon
orbits the Earth and completes one revolution relative to the stars in approximately 27.5 days (a sidereal month).
Calculate mass of the Earth ME. Give the answer in 1024 kg.
Astronomical observations of our Milky Way galaxy indicate that it has a mass of about 8 ✕ 1011 solar masses. A star orbiting near the galaxy's periphery is 6.0✕ 104 light years from its center.
(a)
What should the orbital period (in y) of that star be?
y
(b)
If its period is 5.1✕ 107 y instead, what is the mass (in solar masses) of the galaxy? Such calculations are used to imply the existence of "dark matter" in the universe and have indicated, for example, the existence of very massive black holes at the centers of some galaxies.
solar masses
Chapter 11 Solutions
Physics for Scientists and Engineers
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- Check Your Understanding Consider the density required to make Earth a black hole compared to that required for the Sun. What conclusion can you draw from this comparison abut what would be required to create a black hole? Would you expect the Universe to have many black holes with small mass?arrow_forwardCheck Your Understanding Why not use the simpler expression U=mg(y2y1) ? How significant would the error be? (Recall the previous result, in Example 13.4, that the value g at 400 km above the Earth is 8.67m/s2 .)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
- Is Earth an inertial frame of reference? Is the sun? Justify your response.arrow_forwardCheck 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_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_forward
- An asteroid has speed 15.5km/s when it is located 2.00 AU from the sun. At its closest approach, it is 0.400 AU from the Sun. What is its speed at that point?arrow_forwardA spacecraft starts from being at rest at the origin and accelerates at a constant rate g, as seen from Earth, taken to be an inertial frame, until it reaches a of c/2. (a) Show that the increment of time is related to the elapsed time in Earth's frame by: d=1v2/c2dt. (b) Find an expression for the elapsed time to reach speed c/2 as seen in Earth's frame. (c) Use the relationship in (a) to obtain a similar expression for the elapsed proper time to reach c/2 as seen in the spacecraft, and determine the ratio of the time seen from Earth with that on the spacecraft to reach the final speed.arrow_forwardUsing 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_forward
- In a particle accelerator, a proton has mass 1.6710-27kg and an initial speed of 2.00105m/s . It moves in a straight line, and its speed increases to 9.00105m/s in a distance of 10.0 cm. Assume that the acceleration Is constant. Find the magnitude of the force exerted on the proton.arrow_forwardRepeat the preceding problem with the ship heading directly away from the Earth.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_forward
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