An average-sized asteroid located 2.0 ✕ 107 km from Earth with mass 2.5 ✕ 1013 kg is detected headed directly toward Earth with speed of 8.0 km/s. What will its speed be (in km/s) just before it hits our atmosphere
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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.Jupiter’s moon Io has active volcanoes (in fact, it is the most volcanically active object in the solar system) that eject material as high as 500 km (or even higher) above the surface. Io has a mass of 8.93 * 10^22 kg and a radius of 1821 km. For this calculation, ignore any variation in gravity over the 500 km range of the debris. How high would this material go on earth if it were ejected with the same speed as on Io?5) Two neutron stars are separated by a distance of 2.98x10^(10)m. Both have a mass of 3.17x10^(30)kg and a radius of 253000m. They are initially at relative rest. a) What is the speed of both when the distance between them is half the initial value? in m/s b) What is the speed of both when they are about to collide? in m/s
- (D Page view A Read aloud V Draw y Highlight Erase(a) Imagine that a space probe could be fired as a projectile from the Earth's surface with an initial speed of 5.78 × 10* m/s relative to the Sun. What would its speed be when it is very far from the Earth (in m/s)? Ignore atmospheric friction, the effects of other planets, and the rotation of the Earth. (Consider the mass of the Sun in your calculations.) 38107.8 m/s (b) What If? The speed provided in part (a) is very difficult to achieve technologically. Often, Jupiter is used as a "gravitational slingshot" to increase the speed of a probe to the escape speed from the solar system, which is 1.85 × 10“ m/s from a point on Jupiter's orbit around the Sun (if Jupiter is not nearby). If the probe is launched from the Earth's surface at a speed of 4.10 x 104 m/s relative to the Sun, what is the increase in speed needed from the gravitational slingshot at Jupiter for the space probe to escape the solar system (in m/s)? (Assume that the Earth and the point on Jupiter's orbit lie along the…