8.32 Prove that for circular orbits around a given gravitational force center (such as the sun) the speed of the orbiting body is inversely proportional to the square root of the orbital radius.
Q: The first known collision between space debris and a functioning satellite occurred in 1996: At an…
A:
Q: A satellite is in a circular Earth orbit of radius r. The area A enclosed by the orbit depends on r²…
A: Circular earth orbit of radius = r Area enclosed by the orbit A= π * r2
Q: m A r M. /3
A:
Q: A projectile is shot directly away from Earth's surface. Neglect the rotation of the Earth. What…
A: Escape speed can be defined as the minimum speed needed for non- propelled object to escape from the…
Q: Zero, a hypothetical planet, has a mass of 5.5 x 1023 kg, a radius of 2.8 x 106 m, and no atmosphere…
A: Given:- A hypothetical planet has a mass of M = 5.5 x 1023 kg, a radius of Ri = 2.8 x 106 m, and no…
Q: Sun is far. beyond.the.orbit of Pluto. What is its speed when it is 6 x 1012 m from the Sun? (This…
A: Given: A comet is in an elliptical orbit around the sun.its closet distance is 4.6x1010 m, at which…
Q: In the figure, two satellites, A and B, both of mass m = 36.8 kg, move in the same circular orbit of…
A: using conservation of momentum and orbital velocity concept.
Q: Zero, a hypothetical planet, has a mass of 5.0 * 102^3 kg, a radius of 3.0 * 10^6 m, and no…
A:
Q: A space capsule of mass 445 kg is at rest 2.50 ✕ 107 m from the center of the Earth. When it has…
A: Mass of space capsule (m) = 445 kg is at rest 2.50×107 m from the centre of Earth. It has fallen…
Q: A projectile is fired vertically from a planet's surface with an initial speed of 6.5 km/s. Neglect…
A:
Q: Find the z component of the gravitational field due to these five point masses at a point P on the z…
A:
Q: In a shuttle craft of mass m = 4500 kg, Captain Janeway orbits a planet of mass M = 9.70 x 1025 kg,…
A: Given: mass of shuttle craft m = 4500 kg Mass of planet M = 9.70*1025 kg radius of circular orbit r…
Q: Given the mass of the Earth is 5.98 x1024 kg and a satellite orbits the Earth once every (a) Find…
A:
Q: A bullet is fired vertically upwards with velocity v from the surface of a spherical planet. When it…
A: Let h represent the bullet's climb in height. Gravitational acceleration changes with height as…
Q: In the figure, two satellites, A and B, both of mass m = 49.1 kg, move in the same circular orbit of…
A: Given data: The mass of the two satellites are m=49.1 kg The radius is r=7410 km The mass of the…
Q: A space platform is in a circular orbit about the earth at an altitude of 300 km. As the platform…
A: Given data: The altitude of the space platform is hA=300 km. The velocity of the satellite relative…
Q: A disk with velocity v= 10m/s, mass m=4 kg, and radius r=.3 m. Find the total kinetic energy.
A: The total kinetic energy is the sum of the translation kinetic energy and rotational kinetic energy.…
Q: In 2014, the Rosetta space probe reached the comet Churyumov– Gerasimenko. Although the comet’s core…
A:
Q: A uniform solid sphere of radius R = 3.5 km produces a gravitational acceleration of ag on its…
A:
Q: A communications satellite is launched into circular orbit around the Earth, at an altitude h. The…
A: a) Write the equation of Kepler’s third law.
Q: A satellite has a mass of 5850 kg and is in a circular orbit 4.10 × 105 m above the surface of a…
A: Satelite mass (m) = 5850kgOrbital radius (r) = 4.10 x 103 m +4.15 x 106mGravitational constant (G) =…
Q: Zero, a hypothetical planet, has a mass of 4.5 x 1023 kg, a radius of 3.2 x 106 m, and no…
A: The Gravitational Force is a Conservative Force, therefore the total energy E will be conserved. We…
Q: A disk with velocity v= 10m/s, mass m=5 kg, and radius r=2 m. Find the total kinetic energy.
A: We know that for a disc: Inertia(I) is as below. value of the rotational kinetic energy is: value…
Q: Assume a planet is a uniform sphere of radius R that (somehow) has a narrow radial tunnel through…
A:
Q: Suppose the 50 turn coil in the figure below lies in the plane of the page and originally has an…
A:
Q: Planet X is a sphere where a 0.5 kg block weighs 36 N when sitting on the surface. If an object is…
A:
Q: a) Find the total mechanical energy EA+ EB of the two satellites + Earth system before the…
A: a) The total energy of the two satellites plus the Earth system can be represented as, Here, E, K,…
Step by step
Solved in 3 steps with 6 images
- You are a visitor aboard the New International Space Station, which is in a circular orbit around the Earth with an orbital speed of vo = 2.72 km/s. The station is equipped with a high velocity projectile launcher, which can be used to launch small projectiles in various directions at high speeds. Most of the time, the projectiles either enter new orbits around the Earth or eventually fall down and hit the Earth. However, as you know from your physics courses at the Academy, projectiles launched with a sufficiently great initial speed can travel away from the Earth indefinitely, always slowing down but never falling back to Earth. With what minimum total speed, relative to the Earth, would projectiles need to be launched from the station in order to "escape" in this way? For reference, recall that the radius of the Earth is RE = 6370000 m, the mass of the Earth is MẸ = 5.98 × 1024 kg, the acceleration due to gravity on the surface of the Earth is g = 9.81 m/s and the universal…Two Earth satellites, A and B, each of mass m, are to be launched into circular orbits about Earth's center. Satellite A is to orbit at an altitude of 5390 km. Satellite B is to orbit at an altitude of 22500 km. The radius of Earth REis 6370 km. (a) What is the ratio of the potential energy of satellite B to that of satellite A, in orbit? (b) What is the ratio of the kinetic energy of satellite B to that of satellite A, in orbit? (c) Which satellite (answer A or B) has the greater total energy if each has a mass of 11.7 kg? (d) By how much?In the figure, two satellites, A and B, both of mass m = 36.1 kg, move in the same circular orbit of radius r = 7240 km around Earth (mass ME = 5.98×1024 kg) but in opposite senses of rotation and therefore on a collision course. (a) Find the total mechanical energy Е+ ЕÅ of the two satellites + Earth system before the collision. (b) If the collision is completely inelastic so that the wreckage remains as one piece of tangled material (mass = 2m), find the total mechanical energy immediately after the collision. (c) Just after the collision, is the wreckage falling directly toward Earth's center or orbiting around Earth? (a) Number Units (b) Number (c) Units A B Earth
- A binary-star system contains a visible star and a black hole moving around their center of mass in circular orbits with radii r1 and r2 , respectively. The visible star has an orbital speed of v=5.36x105 ms-1 and a mass of m1 =5Ms ,where Ms= 1.98x1030kg is the mass of our Sun. Moreover, the orbital period of the visible star is T = 30 hours.(a) What is the radius r1 of the orbit of the visible star?(b) Calculate the mass m2 of the black hole in terms of MS . [Hint: One root of the equation x3 = 20a(5a+x)2 , where a is a constant, is x = 28a .]SSM (a) What is the escape speed on a spherical asteroid whose radius is 500 km and whose gravitational acceleration at the surface is 3.0 m/s2? (b) How far from the surface will a particle go if it leaves the asteroid’s surface with a radial speed of 1000 m/s? (c) With what speed will an object hit the asteroid if it is dropped from 1000 km above the surface?Zero, a hypothetical planet, has a mass of 4.7 x 1023 kg, a radius of 3.2 x 106 m, and no atmosphere. A 10 kg space probe is to be launched vertically from its surface. (a) If the probe is launched with an initial kinetic energy of 5.0 x 107 J, what will be its kinetic energy when it is 4.0 x 106 m from the center of Zero? (b) If the probe is to achieve a maximum distance of 8.0 x 106 m from the center of Zero, with what initial kinetic energy must it be launched from the surface of Zero? (a) Number: i Units: (b) Number: i Units:
- (a) Calculate the work (in MJ) necessary to bring a 105 kg object to a height of 1004 km above the surface of the Earth. MJ (b) Calculate the extra work (in J) needed to launch the object into circular orbit at this height.A satellite describes an elliptic orbit of minimum altitude 606 km above the surface of the earth. The semimajor and semiminor axes are 17 440 km and 13 950 km, respectively. Knowing that the speed of the satellite at point C is 4.78 km/s, determine (a) the speed at point A, the perigee, (b) the speed at point B, the apogee.