Problem 7. Use Kepler's third law (and the reduced mass) to derive the time it will take two baseballs, initially at rest a meter apart in deep space, to hit each other due to gravitational attraction. The mass of a baseball is 145 grams. Ignore the diameter of the baseballs; i.e. assume they are point particles.
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- Three uniform spheres of masses m1 = 3.00 kg, m2 = 4.00 kg, and m3 = 6.50 kg are placed at the corners of a right triangle (see figure below). Calculate the resultant gravitational force on the object of mass m2, assuming the spheres are isolated from the rest of the Universe.Three uniform spheres of masses m1 = 3.00 kg, m2 = 4.00 kg, and m3 = 6.50 kg are placed at the corners of a right triangle (see figure below). Calculate the resultant gravitational force on the object of mass m2, assuming the spheres are isolated from the rest of the Universe.Nothing can escape the event horizon of a black hole, not even light. You can think of the event horizon as being the distance from a black hole at which the escape speed is the speed of light, 3.00 ×× 1088 m/sm/s, making all escape impossible. What is the radius of the event horizon for a black hole with a mass 7.5 times the mass of the sun? This distance is called the Schwarzschild radius.?
- Three uniform spheres of masses m1 = 2.50 kg, m2 = 4.00 kg, and m3 = 7.50 kg are placed at the corners of a right triangle (see figure below). Calculate the resultant gravitational force on the object of mass m2, assuming the spheres are isolated from the rest of the Universe. in terms of I hat and j hat. ( î + ĵ )x10−11) Several planets possess nearly circular surrounding rings, perhaps composed of material that failed to form a satellite. In addition, many galaxies contain ringlike structures. Consider a homogeneous ring of mass M and radius R. a) What gravitational attraction does it exert on a particle of mass m located a distance x from the center of the ring along its axis? b) Suppose the particle falls from rest as a result of the attraction of the ring of matter. Find an expression for the speed with which it passes through the center of the ring. (a: see notes from class, b: Use the definition of potential energy.)Nothing can escape the event horizon of a black hole, not even light. You can think of the event horizon as being the distance from a black hole at which the escape speed is the speed of light, 3.00×10^8 m/s, making all escape impossible. What is the radius of the event horizon for a black hole with a mass 3.5 times the mass of the sun?
- A star near the visible edge of a galaxy travels in a uniform circular orbit. It is 48,300 ly (light-years) from the galactic center and has a speed of 275 km/s. Estimate the total mass of the galaxy based on the motion of the star. Gravitational constant is 6.674×10−11 m3/(kg·s2) and mass of the Sun Ms=1.99 × 1030 kg. dont provide hand written solution2. Integrate the equations of motion for a spherical pendulum, i.e., a particle of mass m moving on the surface of a sphere of radius / in a gravitational field, with Lagrangian L = ml² -(0² + psin² 0) + mglcos 0. 2 Hint: Merely set up the integrals, do not evaluate them. You should obtain two integrals w.r.t. de: one determining t and another determining p. Express the first integral in terms of E,Ueff, m, and l. Express the second integral in terms of E,U eff, m, l, and M₂.A satellite of mass 200 kg is launched from a site on Earth’s equator into an orbit 200 km above the surface of Earth. a. What is the satellite’s speed before it’s launched (in m/s)? (Hopefully, it’s moving along with the surface of the Earth as the Earth rotates.) b. What is the satellite’s speed in its orbit (in m/s)? (Remember there is only onespeed a satellite can have in order to maintain a stable circular orbit with agiven radius.) c. Assuming a circular orbit, what is the orbital period of this satellite? (In other words, how long (in hours) does it take for the satellite to complete one orbit?) d. What is the minimum energy (work) necessary to place the satellite in orbit,assuming no air friction? (Remember, work is the amount of energy added tothe system, and the total energy of the system is a combination of kinetic andgravitational potential energies.)
- Considering both special relativity and gravity, how much does Alice age if Julie ages 1 year?Let's say we have a M1 and M2. Let's just say. Let's examine this hypothetical situation. The first mass would be 1.50 kg and the second mass would be 2.00 kg. These two masses would then be separated by a length or we should say a distance of this L = 2.50 m. Let's say we want to place a third mass (immaterial mass) in the middle of the two masses, such that there would be no net force. Find this specific place where this would occur, and to make it easy, find the distance from the first mass towards this third massTwo objects, m1 and m2 are gravitationally attracted to one another. However, m1 is 500 times more massive than m2. Which mass experiences the greater gravitational attractive pull force? A) mass m1 experiences a greater attractive force from m2 B) mass m2 experiences a greater attractive force from m1 C) both masses experience equal but opposite attractive forces D) the problem statement does not provide enough information to be solved