Which takes more fuel: a voyage from the earth to the moon or from the moon to the earth? Explain.
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Which takes more fuel: a voyage from the earth to the moon or
from the moon to the earth? Explain.
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- A spaceship with m = 1.00 ✕ 104 kg is in a circular orbit around the Earth, h = 800 km above its surface. The ship's captain fires the engines in a direction tangent to the orbit, and the spaceship assumes an elliptical orbit around the Earth with an apogee of d = 3.00 ✕ 104 km, measured from the Earth's center. How much energy (in J) must be used from the fuel to achieve this orbit? (Assume that all the fuel energy goes into increasing the orbital energy and that the perigee distance is equal to the initial radius.)A satellite moves in a circular orbit around Earth at a speed of 5206 m/s. (a) Determine the satellite's altitude above the surface of Earth. m (b) Determine the period of the satellite's orbit.A space probe is in orbit around Mars at an altitude of 1200 km. To move to a higher orbit, small rocket engines are used to provide the energy required.(a) Compare the kinetic energy of the space probe in the lower and higher orbit.(b) Explain why energy is required to move the space probe from a lower to a higher orbit. In your answer refer to the total energy of the satellite.
- A spacecraft is launched from Cape Canaveral to a 28.5° inclined circular orbit of altitude h = 400 km. We want to reach the ISS, which orbit has the same altitude but is inclined at 51.6°. Explain what solutions are possible for this operation, and determine (using calculations) which is the most economical.(a) What is the escape speed on a spherical asteroid whose radius is 274 km and whose gravitational acceleration at the surface is 0.444 m/s2? (b) How far from the surface will a particle go if it leaves the asteroid's surface with a radial speed of 311 m/s? (c) With what speed will an object hit the asteroid if it is dropped from 289.4 km above the surface?If you are going to launch a 10,000 kg spacecraft from Earth, (a) how much kinetic energy it must possess in order to escape the gravitational pull? (b) If the mass is reduced by 5,000 kg, how much kinetic energy is required?
- In a futuristic scenario, you are assigned the mission of making an enemy satellite that is in a circular orbit around Earth inoperative. You know you cannot destroy the satellite, as it is well protected against attack, but you can try to knock it out of its orbit so it will fly away and never return. What is the minimum amount of work ? applied to the satellite that is required to accomplish that? The satellite's mass and altitude are 975 kg and 259 km. Earth's mass and radius are 5.98×1024 kg and 6370 km.W = ? J(a) What is the escape speed on a spherical asteroid whose radius is 803 km and whose gravitational acceleration at the surface is 1.75 m/s2? (b) How far from the surface will a particle go if it leaves the asteroid's surface with a radial speed of 1330 m/s? (c) With what speed will an object hit the asteroid if it is dropped from 1811 km above the surface?Neglecting Earth's rotation, show that the energy needed to launch a satellite of mass m into circular orbit at altitude h above Earth's surface is: RE + 2h 2(RE +h) GMEM RE How much energy is required to launch a 10,000 kg satellite into a 200 km altitude circular orbit around the Earth?
- (a) A planet is in an elliptical orbit around a distant star. At its closest approach, the planet is 0.580 AU from the star and has a speed of 54.0 km/s. When the planet is at its farthest distance from the star of 37.0 AU, what is its speed (in km/s)? (1 AU is the average distance from the Earth to the Sun and is equal to 1.496 x 10¹¹ m. You may assume that other planets and smaller objects in the star system exert negligible forces on the planet.) km/s (b) What If? A comet is in a highly elliptical orbit around the same star. The comet's greatest distance from the star is 20,900 times larger than its closest distance to the star. The comet's speed at its greatest distance is 2.70 x 10-² km/s. What is the speed (in km/s) of the comet at its closest approach? km/sWonder Woman and Superman fly to an altitude of 1630 km, carrying between them a chest full of jewels that they intend to put into orbit around Earth. They want to make this tempting treasure inaccessible to their evil enemies who are trying to gain possession of it, yet keep it available for themselves for future use when they retire and settle down. But perhaps the time to retire is now! They accidentally drop the chest, which leaves their weary hands at rest, and discover that they are no longer capable of catching it as it falls into the Pacific Ocean. At what speed does the chest impact the surface of the water? Ignore air resistance, although in the real world it would make a world of difference. The radius and mass of Earth are 6370 km and 5.98×10^24 kg, respectively.A 1500 kg satellite is in a stable orbit at an altitude of 4.0 × 10 5 m above Earth's surface. What is the satellite's total energy in this orbit? (Mearth = 5.97x1024 kg) (rearth = 6.4x106 m)