Your answer is partially correct. A pulsar is a rapidly rotating neutron star that emits a radio beam the way a lighthouse emits a light beam. We receive a radio pulse for each rotation of the star. The period T of rotation is found by measuring the time between pulses. Suppose a pulsar has a period of rotation of T = 0.0379 s that is increasing at the rate of 3.61 x 10-6 s/y. (a) What is the pulsar's angular acceleration a? (b) If a is constant, how many years from now will the pulsar stop rotating? (c) Suppose the pulsar originated in a supernova explosion seen 777 years ago. Assuming constant a, find the initial T. (a) Number -4.98e-10 Units rad/s^2 (b) Number 1.05e+4 Units years (c) Number i 0.040 Units
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- The radius Rh of a black hole is the radius of a mathematical sphere, called the event horizon, that is centered on the black hole. Information from events inside the event horizon cannot reach the outside world. According to Einstein's general theory of relativity, Rh = 2GM/c2, where M is the mass of the black hole and c is the speed of light. Suppose that you wish to study a black hole near it, at a radial distance of 48Rh. However, you do not want the difference in gravitational acceleration between your feet and your head to exceed 10 m/s2 when you are feet down (or head down) toward the black hole. (a) Take your height to be 1.5 m. What is the limit to the mass of the black hole you can tolerate at the given radial distance? Give the ratio of this mass to the mass MS of our Sun.A massive black hole is believed to exist at the center of our galaxy (and most other spiral galaxies). Since the 1990s, astronomers have been tracking the motions of several dozen stars in rapid motion around the center. Their motions give a clue to the size of this black hole. (a) One of these stars is believed to be in an approximātely circular orbit with a radius of about 1.50 x 10° AU and a period of approximately 30 yr. Use these numbers to determine the mass of the black hole around which this star is orbiting. kg (b) What is the speed of this star? V star m/s How does it compare with the speed of the Earth in its orbit? V star VEarth How does it compare with the speed of light? V starAstronomical 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. What should the orbital period (in y) of that star be?
- A star has a mass of 1.03 x 1030 kg and is moving in a circular orbit about the center of its galaxy. The radius of the orbit is 2.4 x 104 light-years (1 light-year = 9.5 x 1015 m), and the angular speed of the star is 1.0 x 10-15 rad/s. (a) Determine the tangential speed of the star. (b) What is the magnitude of the net force that acts on the star to keep it moving around the center of the galaxy?A solid uniform sphere has a mass of 4.00 x 10* kg and a radius of 1.5 m. (Use the following as necessary: r and m. Assume SI units. Do not enter units in your ansWers.) (a) What is the magnitude of the gravitational force due to the sphere on a particle of mass m located at a distance of 1.6 m from the center of the sphere? F = N. (b) What if it is 1.4 m from the center of the sphere? F = N. (c) Write a general expression for the magnitude of the gravitational force on the particle at a distancer 1.5 m from the center of the sphere. F = Additional Materials eBook Powers of TenYou are visiting a newly discovered exoplanet (mass M and radius R) that completes one rotation about its axis every 12 hours (Earth hours). You place your spaceship in a geostationary orbit at an altitude h = 6R above the planet's surface. While in orbit you decided to beam down to the planet to investigate the surface. While on the surface you perform a simple kinematics experiment and discover that the gravitational acceleration at the surface is ap = 0.60g, where g is the gravitational acceleration on the Earth's surface. You can assume that the exoplanet is a uniform sphere, and that your spaceship's orbit is circular. Note: A geostationary orbit is a special type of geosynchronous orbit where the satellite/spaceship remains at the same position above the equator throughout its orbit. Technically the prefix "geo" indicates the Earth, but we'll go ahead and use the term here in reference to this new planet. (a) What is the radius of the planet? R = km (b) What is the mass of the…
- After landing on an unfamiliar planet, a space explorer constructs a simple pendulum of length 46.0 cm. The explorer finds that the pendulum completes 98.0 full swing cycles in a time of 145 s. What is the magnitude of the gravitational acceleration on this planet? Express your answer in meters per second per secondgPlanet=(?)m/s^2A satellite is traveling around a planet in a circular orbit with radius R. It moves in a constant speed of v = 1.02 × 104 m/s. The mass of the planet is M = 5.94 × 1024 kg. The mass of the satellite is m = 4.7 × 103 kg. Enter an expression for the magnitude of the gravitional force F in terms of M,R,m and the gravitional constant G. Enter an expression for the radius in terms of G,M and R. Enter an expression for the gravational potetial energy PE in terms of G,M,m and R. Enter an expresssion for the centripal acceleration of the satellite ac in terms of the speed of the satellite v, and r.Two spherical objects have masses of 1.8*10^6 kg and 4.1*10^4 kg. The gravitational attraction between them is 69 N. How far apart are their centers? What is the gravitational acceleration from the center of a spherical object whose mass is 4.3*10^23 kg at a distance of 5.0*10^6 m?
- You are an alien on an alien planet orbiting the planet's sun in a circular orbit. You want to find the mass of your sun. You determine the center-to-center distance between your planet and sun to be 6.75E+10 meters. The period of motion of your planet (the length of your year) is 1.21E+7 seconds. You know G=6.67*10^−11Nm2kg2 . What is the mass of your sun?You are trapped on an earth-like planet with a mass of 5.00×1024 kg and a radius of 4000 km. You were able to build a cannon capable of launching a human. What velocity will you need to escape the planet? (We can simplify the Gravitational Constant G to 6.7x10-11 Nm2/kg)