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If the escape velocity is the minimum speed needed to leave an objects gravity, then briefly discuss what it would mean for an object's escape velocity to be greater than the
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- How fast would a 6.0 m-long sports car have to be going past you in order for it to appear only 5.5 m long?What happens to the density of an object as its speed increases, as measured by an Earth observer?Since 1995, hundreds of extrasolar planets have been discovered. There is the exciting possibility that there is life on one or more of these planets. To support life similar to that on the Earth, the planet must have liquid water. For an Earth-like planet orbiting a star like the Sun, this requirement means that the planet must be within a habitable zone of 0.9 AU to 1.4 AU from the star. The semimajor axis of an extrasolar planet is inferred from its period. What range in periods corresponds to the habitable zone for an Earth-like Planet orbiting a Sun-like star?
- Compute directly the gravitational force on a unit mass at a point exterior to a homogeneous sphere of matter.A spacecraft in the shape of a long cylinder has a length of 100 m, and its mass with occupants is 1 000 kg. Ii has strayed too close to a black hole having a mass 100 times that of the Sun (Fig. P11.11). The nose of the spacecraft points toward the black hole, and the distance between the nose and the center of the black hole is 10.0 km. (a) Determine the total force on the spacecraft. (b) What is the difference in the gravitational fields acting on the occupants in the nose of the ship and on those in the rear of the ship, farthest from the black hole? (This difference in accelerations grows rapidly as the ship approaches the black hole. It puts the body of the ship under extreme tension and eventually tears it apart.)An astronaut has a heartbeat rate of 66 beats per minute as measured during his physical exam on Earth. The heartbeat rate of the astronaut is measured when he is in a spaceship traveling at 0.5c with respect to Earth by an observer (A) in the ship and by an observer (B) on Earth. (a) Describe an experimental method by which observer B on Earth will able to determine the heartbeat rate of the astronaut when the astronaut is in the spaceship. (b) What will be the heartbeat rate(s) of the astronaut reported by observers A and B?
- The escape velocity from a massive object is the speed needed to reach an infinite distance from it and have just slowed to a stop, that is, to have just enough kinetic energy to climb out of the gravitational potential well and have none left. You can find the escape velocity by equating the total kinetic and gravitational potential energy to zero E=12mv2esc−GmM/r=0E=12mvesc2−GmM/r=0 vesc=2GM/r−−−−−−√vesc=2GM/r where GG is Newton's constant of gravitation, MM is the mass of the object from which the escape is happening, and rr is its radius. This is physics you have seen in the first part of the course, and you should be able to use it to find an escape velocity from any planet or satellite. For the Earth, for example the escape velocity is about 11.2 km/s, and for the Moon it is 2.38 km/s. A very important point about escape velocity: it does not depend on what is escaping. A spaceship or a molecule must have this velocity or more away from the center of the planet to be free…A space probe of mass 3.9 x 103 kg is orbiting a star of mass 3.6 x 1030 kg in a circular orbit at a distance of 1.7 x 1011 m from its center. Calculate the minimum energy, in units of 109 J, required to transfer the probe to a circular orbit 5.5 x 1011 m from the star. Use G = 6.7 x 10-11 N m2/ kg2. (Please answer to the fourth decimal place - i.e 14.3225)Two 0.60-kgkg basketballs, each with a radius of 19 cmcm , are just touching a) How much energy is required to change the separation between the centers of the basketballs to 1.0 mm ? (Ignore any other gravitational interactions.) b) How much energy is required to change the separation between the centers of the basketballs to 13 mm ? (Ignore any other gravitational interactions.)
