1300 mi A. 1400 mi
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A space vehicle is in a circular orbit with a 1400-mi radius around the moon. To transfer to a smaller orbit with a 1300-mi radius, the vehicle is first placed in an elliptic path AB by reducing its speed by 86 ft/s as it passes through A. Knowing that the mass of the moon is 5.03 x 10 21 Ib.s2/ft, determine (a) the speed of the vehicle as it approaches B on the elliptic path, (b) the amount by which its speed should be reduced as it approaches B to insert it into the smaller circular orbit.
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- Problem 1. A planet with a mass of 7.00x10" kg is in a circular orbit around a star with a mass of 2.00 x10" kg. The planet has an orbital radius of 9.00x10º m. (a) What is the orbital velocity of the planet? (b) What is the period of the planet's orbit? (c) What is the total mechanical energy of the planet? 10A uniform solid sphere of radius R = 3.5 km produces a gravitational acceleration of ag on its surface. At what distance from the sphere's center are there points (a) inside and (b) outside the sphere where the gravitational acceleration is ag/7? (a) Number i (b) Number Units UnitsA satellite is revolving round the earth at a distance of 182 km from the surface of the earth. The radius of the earth is 6371 km and g is 9.81 ms-2. Calculate the orbital velocity of the satellite.
- A communications satellite is launched into circular orbit around the Earth, at an altitude h. The satellite's mass is m, and it was launched from Earth's surface. (Use the following as necessary: Refor the radius of the Earth, Me for the mass of the Earth, G for the gravitational constant, m, and h.) (a) How long does the satellite take to complete one circular orbit? T= (b) What is the satellite's speed? V satellite (c) What is the minimum energy input necessary to place this satellite in orbit? Ignore air resistance but include the effect of the planet's daily rotation. (Use the following as necessary: RE, ME, G, m, h, and Te for the period of Earth's rotation.) AE minA planet orbits a star, in a year of length 4.46 x 107 s, in a nearly circular orbit of radius 2.46 x 1011 m. With respect to the star, determine (a) the angular speed of the planet, (b) the tangential speed of the planet, and (c) the magnitude of the planet's centripetal acceleration.(a) What linear speed must an Earth satellite have to be in a circular orbit at an altitude of 182 km? m/s (b) What is the period of revolution? min
- An asteroid, whose mass is 2.7 × 10-4 times the mass of Earth, revolves in a circular orbit around the Sun at a distance that is 1.6 times the Earth's distance from the Sun. (a) Calculate the period of revolution of the asteroid in years. (b) What is the ratio of the kinetic energy of the asteroid to the kinetic energy of Earth?An asteroid, whose mass is 1.9 × 10-4 times the mass of Earth, revolves in a circular orbit around the Sun at a distance that is 3.2 times the Earth's distance from the Sun. (a) Calculate the period of revolution of the asteroid in years. (b) What is the ratio of the kinetic energy of the asteroid to the kinetic energy of Earth?A planet orbits a star, in a year of length 2.88 x 107 s, in a nearly circular orbit of radius 1.85 x 10¹¹ m. With respect to the star, determine (a) the angular speed of the planet, (b) the tangential speed of the planet, and (c) the magnitude of the planet's centripetal acceleration.
- A satellite, with a mass of M=7.30x10^22 kg, moves in a circular orbit of radius R=3.80x10^09 meters. The satellite makes an entire rotation about the planet in 26.4 days. The planet attracts the satellite with a force of how many newtons?Current Attempt in Progress One model for a certain planet has a core of radius R and mass M surrounded by an outer shell of inner radius R, outer radius 2R, and mass 4M. If M-2.97 x 1024 kg and R-8.31 x 10 m, what is the gravitational acceleration of a particle at points (a) R and (b) 3R from the center of the planet? (a) Number (b) Number Units UnitsYou 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…