Astronomers have observed a small, massive object at the center of our Milky Way galaxy. A ring of material orbits this massive object; the ring has a diameter of about 15 light years and an orbital speed of about 200×10m/s3 Many astronomers believe that the massive object at the center of the Milky Way galaxy is a supermassive black hole. The Schwarzschild radius of such an object is the distance within which nothing, not even light, can escape its gravitational attraction. General relativity gives the Schwarzschild radius as RS=2GM/c2 is the gravitational constant, G and Mis the mass of the object, and C is the speed of light. What is the Schwarzschild radius of the object at the center of our galaxy?

My dear hand written solution is not allowed.

A pirate starship in the distant future is being chased by the space police. The pirates are traveling at 1273 km/h while the police are traveling at 1431 km/h. The pirate ship needs 25 minutes to turn on its faster-than-light drive so it can jump into hyperspace to escape.   How long, in minutes, will it take the space police to catch up to the pirates if they are 50 km away from one another? min   Will the pirates be able to escape?

Two newly discovered planets follow circular orbits around a star in a distant part of the galaxy. The orbital speeds of the planets are determined to be 35.1km/s and 53.1km/s. The slower planet's orbital speed is 7.53years. What is the mass of the star, and what is the orbital period of the faster planet, in years?

The acceleration of gravity near a black hole is so large that not even light can escape. Which two factors would increase the acceleration of gravity near a black hole? O A black hole with more mass and the same radius A black hole with a larger radius and the same mass A black hole with less mass and the same radius A black hole with a smaller radius and the same mass O O O

The Oort Cloud extends out to (possibly) one light-year from the sun.  Objects in the Oort Cloud are still gravitationally bound to the sun.  Suppose one such iceball orbits the sun in a circle.  I'm going to alter some numbers, such as the mass of the sun and even G.  The gravitational force is directed toward the sun and has the following magnitude: Calculate the force on the object if these are the numbers: G = 6.1*10-11 N*m2/kg2 M = 2.7*1030 kg m = 1.5*108 kg r = 19*1015 m Calculate your answer in microNewtons (10-6 N).

Designing an interplanetary mission from Earth to Jupiter. Given the position and velocityvectors for the Earth parking orbit, r = 8228 I +389 J +6888 K (km)v = -0.7 I +6.6 J -0.6 K (km/s) 1.) Assuming that the satellite will enter the Hohmann transfer elliptical orbit from perigee of its current Earth parking orbit, determine the total velocity increment, Δvtotal required for a Hohmann transfer from the Earthparking orbit to 200km altitude Jupiter parking orbit. 2.) Calculate the semi-major axis, period in earth years, and eccentricity of the Hohmann transfer ellipse.

Wonder Woman and Superman fly to an altitude of 1630 km,1630 km, carrying between them a chest full of jewels that they intend to put into orbit around Earth. They want to make this tempting treasure inaccessible to their evil enemies who are trying to gain possession of it, yet keep it available for themselves for future use when they retire and settle down. But perhaps the time to retire is now! They accidentally drop the chest, which leaves their weary hands at rest, and discover that they are no longer capable of catching it as it falls into the Pacific Ocean. At what speed ?fvf does the chest impact the surface of the water? Ignore air resistance (in reality, it would make large difference). The radius and mass of Earth are 6370 km6370 km and 5.98×1024 kg,5.98×1024 kg, respectively.

Wonder Woman and Superman fly to an altitude of 1630 km, carrying between them a chest full of jewels that they intend to put into orbit around Earth. They want to make this tempting treasure inaccessible to their evil enemies who are trying to gain possession of it, yet keep it available for themselves for future use when they retire and settle down. But perhaps the time to retire is now! They accidentally drop the chest, which leaves their weary hands at rest, and discover that they are no longer capable of catching it as it falls into the Pacific Ocean. At what speed does the chest impact the surface of the water? Ignore air resistance, although in the real world it would make a world of difference. The radius and mass of Earth are 6370 km and 5.98×10^24 kg, respectively.

Black holes are difficult to observewith telescopes because they, bydefinition, don’t emit or reflect any light. They can be found by look-ing for other nearby objects orbit-ing them, however. Here is a dia-gram of a star in a circular orbit around a black hole. a. The period of the star’s orbit is 90 days, and its orbital radius around the black hole isobserved to be 3.6 : ×10^11 m. Find the orbital velocity of the star in units of m/s. (You need to convert 90 days to seconds, first). The circumference of a circle is 2πr.  b. The mass of the star is known to be 4 × 10^30 kg. Find the centripetal acceleration of thestar and the strength of the gravitational force on the star.  c. Find the mass of the black hole.