R= 6370 km 42 140 km 300 km Intended B trajectory Actual trajectory
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A: Given Data R = 6.37×106M = 5.98×1024G = 6.67×10-11N.m2kg2
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A: Mass, m = 7.75×1022 kg Radius, R = 4.200×10³ km Distance, d = 2.270×105 km Time period, T = ?
A space platform is in a circular orbit about the earth at an altitude of 300 km. As the platform passes through A , a rocket carrying a communications satellite is launched from the platform with a relative velocity of magnitude 3.44 km/s in a direction tangent to the orbit of the platform. This was intended to place the rocket in an elliptic transfer orbit bringing it to point B , where the rocket would again be fired to place the satellite in a geosynchronous orbit of radius 42 140 km. After launching, it was discovered that the relative velocity imparted to the rocket was too large. Determine the angle y at which the rocket will cross the intended orbit at point C.
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- You 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…A satellite is in a circular orbit around the Earth at an altitude of 3.82 x 106 m. (a) Find the period of the orbit. (Hint: Modify Kepler's third law so it is suitable for objects orbiting the Earth rather than the Sun. The radius of the Earth is 6.38 x 106 m, and the mass of the Earth is 5.98 x 1024 kg.) h (b) Find the speed of the satellite. km/s (c) Find the acceleration of the satellite. m/s2 toward the center of the earthA satellite is in a circular orbit around the Earth at an altitude of 2.62 × 106 m. (a) Find the period of the orbit. (Hint: Modify Kepler's third law so it is suitable for objects orbiting the Earth rather than the Sun. The radius of the Earth is 6.38 x 106 m, and the mass of the Earth is 5.98 x 1024 kg.) h (b) Find the speed of the satellite. km/s (c) Find the acceleration of the satellite. m/s² toward the center of the earth
- SSM (a) What is the escape speed on a spherical asteroid whose radius is 500 km and whose gravitational acceleration at the surface is 3.0 m/s2? (b) How far from the surface will a particle go if it leaves the asteroid’s surface with a radial speed of 1000 m/s? (c) With what speed will an object hit the asteroid if it is dropped from 1000 km above the surface?A satellite describes an elliptic orbit of minimum altitude 606 km above the surface of the earth. The semimajor and semiminor axes are 17 440 km and 13 950 km, respectively. Knowing that the speed of the satellite at point C is 4.78 km/s, determine (a) the speed at point A, the perigee, (b) the speed at point B, the apogee.A satellite of mass m= 100 kg is in a circular orbit at a height h = R above the surface of the earth where R is the radius of the earth. Find (a) the acceleration due to gravity at any point on the path of the satellite, (b) the gravitational force on the satellite and (c) the centripetal force on the satellite.
- You are exploring a distant planet. When your spaceship is in a circular orbit at a distance of 630 km above the planet's surface, the ship's orbital speed is 5500 m/s. By observing the planet, you determine its radius to be 4.48×106m. You then land on the surface and, at a place where the ground is level, launch a small projectile with initial speed 12.6 m/s at an angle of 30.8∘ above the horizontal. If resistance due to the planet's atmosphere is negligible, what is the horizontal range of the projectile?An undiscovered planet, many light-years from Earth, has one moon, which has a nearly circular periodic orbit. If the distance from the center of the moon to the surface of the planet is 2.270 × 10³ km and the planet has a radius of 4.200 × 10³ km and a mass of 7.75 × 1022 kg, how long (in days) does it take the moon to make one revolution around the planet? The gravitational constant is 6.67 × 10-¹¹ N.m²/kg². T = X10 TOOLS daysA satellite is in a circular orbit around the Earth at an altitude of 3.42 x 106 m. (a) Find the period of the orbit. (Hint: Modify Kepler's third law so it is suitable for objects orbiting the Earth rather than the Sun. The radius of the Earth is 6.38 x 10° m, and the mass of the Earth is 5.98 x 1024 kg. (b) Find the speed of the satellite. km/s (c) Find the acceleration of the satellite. m/s? toward the center of the earth