The amount of energy needed to increase the radius of orbit of a 500-kg satellite from its original orbit of radius 10 000 km can be modelled by the function E =2×101° n10r-10 000 where E is the energy, in Joules, and r is the new radius, in kilometers.
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- 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 = = muesc - GmM/r=0 Vesc = √2GM/r where G is Newton's constant of gravitation, M is the mass of the object from which the escape is happening, and r 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 of its gravity, 1. In the atmosphere of…The kinetic energy (T) of an object with mass m traveling at a speed v is defined as T = \frac{1}{2}mv^2T=21mv2. What is the kinetic energy (in J) of an object of mass 41 g traveling a velocity of 37 miles per hour? (1 mile = 1.609 km) Round your answer to the tenths (0.1) place.You have a super high-tech spacecraft travelling through space that gets caught in a circular orbit around a mysterious object of mass 10 times that of the Sun and a radius of 30km. Your team decides to observe the behavior of this object but due to the heat that it's giving off, it is required that your satellite obtain a circular orbit of at least r = 5.3e5km to be considered 'safe'. You are currently in a circular orbit with r = 4.1e5km. What is the minimum delta-v required to reach the safe orbit
- Find the escape velocity ve for an object of mass m that is initially at a distance R from the center of a planet of mass M. Assume that R≥Rplanet, the radius of the planet, and ignore air resistance. Express the escape velocity in terms of R, M, m, and G, the universal gravitational constant.In this problem we will observe how the momentum of an electron changes as its velocity approaches the speed of light. The mass of an electron is 9.109 × 10-31 kg. Part (a) First, what is the momentum of an electron which is moving at the speed of a car on a highway, say 29 m/s, in kilogram meters per second?The International Space Station, which has a mass of 4.94×105 kg, orbits 258 miles above the Earth's surface, and completes one orbit every 94.3 minutes. What is the kinetic energy of the International Space Station in units of GJ (109 Joules)? (Note: don't forget to take into account the radius of the Earth!) Enter answer here GJ
- The estimated mass and radius of Planet X are used to calculate the minimum escape speed, Ve, for an object launched from the surface of the planet. If the actual mass and/or radius of the planet are slightly different from the estimated values, how will the actual escape speed Va for the surface of Planet X compare to Ve ? v_a v_c if the actual mass is less and the actual radius is greater than their estimated values. v_a > v_c if the actual mass is greater and the actual radius is less than their estimated values. v_a = v_c regardless of any difference in mass or radius. v_a < v_c if the actual mass is greater and the actual radius is the same as their estimated values.To complete this exercise, you need to know that the circumference of a circle is proportional to its radius, and that the constant of proportionality is 2π. You do not need to know either the radius of the Moon’s orbit or the radius of Earth. For purposes of this exercise, we assume that the Moon’s orbit around Earth is circular. In one trip around Earth, the Moon travels approximately 2.4 million kilometers. Another satellite orbits Earth (in a circular orbit) at a distance from Earth that is 1/4 that of the Moon. How far does this satellite travel in one trip around Earth? (Use decimal notation. Give your answer to one decimal place.) A rope is tied around the equator of Earth. A second rope circles Earth and is suspended 77 feet above the equator. How much longer is the second rope than the first?Let G be the universal gravitational constant and mp be the mass of the planet a satellite is orbiting. Which equation could be used to find the velocity of the satellite if it is placed in a low Earth orbit? Let G be the universal gravitational constant and mp be the mass of the planet a satellite is orbiting. Which equation could be used to find the velocity of the satellite if it is placed in a low Earth orbit? Gue (13,522 km| Gm (7,324km| Gm (42,164 kI / Gue (48,115 km|'
- A satellite m = 500 kg orbits the earth at a distance d = 225km above the of the planetThe radius of the earth r_{e} = 638 * 10 ^ 6 * m and the gravitational constant G = 6.67 * 10 ^ - 11 * N * m ^ 2 / k * g ^ 2 and the Earth's mass m_{e} = 5.98 * 10 ^ 24 * kg What the speed of the satellite in m/sD Gm₁m₂ Fg KE = mv², Ug = - 2πr , ac = =²₁, v = ²7₁ T Gm₁m₂ GM g = G, Vesc = 2GM R , E = KE + Ug, G = 6.674 x 10-¹1 Nm²/kg² Problem 1: You are the science officer on a visit to a distant solar system. Prior to landing on a planet you measure its radius to be 9 x 106 m and its rotation period to be 22.3 hours. You have previously determined that the planet orbits 2.2 x 10¹¹ m from its star with a period of 402 days (3.473 x 107 sec). Once on the surface you find that the free-fall acceleration is 12.2 m/sec². a) What is the mass of the planet? Answer: 1.5 x 1025 kg. b) What is the mass of the star? Answer: 5.2 x 1030 kg.An earth-like planet with a mass of 6.00×1024 kg has a space station of mass 4.60×104 kg orbiting it at a distance of 5.00×105 km. What is the gravitational potential energy between the space station and the planet? (We can simplify the Gravitational Constant G to 6.7x10-11 Nm2/kg) (calculate in J)