e R M V₁ = is very close to 0 1) what angle does the block (mass) lose contact with the sphere? 2) What if there's friction MK? * use forres V= C
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- . How many years would you have to wait to observe a 1° angular shift in the perihelion of Mercury due to general relativistic effects?(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.Can classical physics be used to accurately describe a satellite moving at a speed of 7500 m/s? Explain why or why not.
- Show that the velocity of a star orbiting its galaxy in a circular orbit is inversely proportional to the square root of its orbital radius, assuming the mass of the stars inside its orbit acts like a single mass at the center of the galaxy. You may use an equation from a previous chapter to support your conclusion, but you must justify its use and define all terms used.Our solar system orbits the center of the Milky Way galaxy. Assuming a circular orbit 30,000 ly in radius and an orbital speed of 250 km/s, how many years does it take for one revolution? Note than this is approximate, assuming constant speed and circular orbit, but it is representative of the time for our system and local stars to make one revolution around the galaxy.Show that the velocity of a star orbiting its galaxy in a circular oibit is inversely proportional to the square root of its orbital radius, assuming the mass of the stars inside its orbit acts like a single mass at the center of the galaxy. You may use an equation from a previous chapter to support your conclusion, but you must justify its use and define all terms used.
- (a) Use the distance and velocity data in Figure 3.64 to find the rate of expansion as a function of distance. (b) If you extrapolate back in time, how long ago would all of the galaxies have been at approximately the same position? The two parts of this problem give you some idea of how the Hubble constant for universal expansion and the time back to the Big Bang are determined, respectively. Figure 3.64 Five galaxies on a straight line, showing their distances and velocities relative to the Milky Way (MW) Galaxy. The distances are in millions of light years (Mly), where a light year is the distance light travels in one year. The velocities are nearly proportional to the distances. The sizes of the galaxies are greatly exaggerated; an average galaxy is about 0.1 MlY across.A neutron star is a cold, collapsed star with nuclear density. A particular neutron star has a mass twice that of our Sun with a radius of 12.0 km. (a) What would be the weight of a 100-kg astronaut on standing on its surface? (b) What does this tell us about landing on a neutron star?The Sun produces energy at a rate of 4.001026 W by the fusion of hydrogen. (a) How many kilograms of hydrogen undergo fusion each second? (b) If the Sun is 90.0% hydrogen and half of this can undergo fusion before the Sun changes character, how long could it produce energy at its current rate? (c) How many kilograms of mass is the Sun losing per second? (d) What fraction of its mass will it have lost in the time found in part (b)?
- Collapse of a dust ball under Newtonian gravity. Suppose that a spherical ball of dust with no internal pressure and with an initial radius R0 and total mass M gravitationally collapses from rest. Show that the outer shell of the collapsing dust ball obeys the equation of motion Solve this equation of motion and show that the time to collapse is given by Hint: Write Newton’s law as . Let f(R) = dF(R)/dR and multiply both sides of by by . The resulting equation may be immediately integrated with respect to time by recognizing that . Integrating again with respect to time, this general technique yields t as a function of R where and C and C1 are constants determined by the initial conditions. Find the time of collapse of a dust ball with a mass and radius equal to that of the Sun. (RS = 6.96 × 1010 cm, MS = 1.99 × 1033 g, G = 6.67 × 10−8 cgs units) What prevents the Sun from collapsing in this way?Which of Einstein's postulates of special relativity includes a concept that does not fit with the ideas of classical physics? Explain.(a) Wliat is the approximate velocity relative to us of a galaxy near the edge of the known universe, some 10 Gly away? (b) What fraction of the speed of light is this? Note that we have observed galaxies moving away from us at greater than 0.9c.