Consider a satellite in an elliptical orbit (with eccentricity e, =0.6). At the perigee of this orbit, it increases its speed in the tangential direction by an amount a=1.6, so its new speed is now v2-1.6v1. What is the new orbit's eccentricity? x If the satellite wishes by this "tangential thrust" to enter a circular orbit, what must a be? x
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- Problem 1. Consider the Sun-Earth system with a center-to-center distance of 1.5x 101 m. Suppose that at some instance the Sun's velocity is zero and its location is at the origin. Ignoring all effects but that of the Earth, what will the Sun's velocity and position be after 1 day. Compute the same quantities for the Earth ignoring the fact the Earth is in a circular orbit (i.e., assume it to initially be at rest). Treat this as a 1D problem. Gr Ecrok FJ 2/A 2 57 (5.994 Xt0 49 5,21 10 Problem 2. Given only the distance between the Earth and Moon (REM = 3.84 x 108 m) and that between the Earth and the Sun (1 AU), determine the mass of the Earth and the mass of the Sun. How can we measure REM or RSE? M 1 142 1 k (PA 6x10-4 kg object is moving uniformly on a horizontal circular path of radius r = 6.3 m. a. Find the period, T, the time for one rotation if its speed is 5x104 m/s. b. Calculate its centripetal force.A bead of mass m slides without friction along a curved wire with shape z = f(r) where r = Vr2 + y², i.e. the distance from the z-axis. The wire is rotated around the z-axis at a constant angular velocity w. Gravity acts downward along the z-axis with a constant acceleration g. a) Using Newton's second law in an inertial frame, derive an expression for radius ro of a fixed circular orbit (i.e. a solution with r = ro = const.). What is the normal force the wire applies to the bead to keep it in a circular orbit? b) Show that the equation of motion for r(t) (general equation not the circular motion) is F(1 + f'(r)²) + i² f'(r)f"(r) + gf'(r) – w?r = 0. Using this verify your answer to part (a). c) Consider small displacements from the circular orbit, r = ro+e(t). Derive a condition on the function f(r) such that a circular orbit at r = ro is stable. d) Find the force on the bead in the o direction, i.e. perpendicular to the plane of wire. The angular velocity is w = . Obtain the answer…
- An astronaut orbiting the Earth is preparing to dock with a Westar VI satellite. The satellite is in a circular orbit 700 km above the Earth's surface, where the free-fall acceleration is 8.28 m/s2. Take the radius of the Earth as 6400 km. Determine the speed of the satellite. x m/s Determine the time interval required to complete one orbit around the Earth, which is the period of the satellite. X minAn astronaut orbiting the Earth is preparing to dock with a Westar VI satellite. The satellite is in a circular orbit 500 km above the Earth's surface, where the free-fall acceleration is 8.28 m/s2. Take the radius of the Earth as 6400 km. Determine the speed of the satellite. Determine the time interval required to complete one orbit around the Earth, which is the period of the satellite.A geosynchronous Earth satellite is one that has an orbital period of precisely 1 day. Such orbits are useful for communication and weather observation because the satellite remains above the same point on Earth (provided it orbits in the equatorial plane in the same direction as Earth’s rotation). Calculate the radius of such an orbit based on the data for Earth in Appendix D.
- You are a visitor aboard the New International Space Station, which is in a circular orbit around the Earth with an orbital speed of ?o=2.45 km/s�o=2.45 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 ?E=6370000 m�E=6370000 m, the mass of the Earth is ?E=5.98×1024 kg�E=5.98×1024 kg , the acceleration due to gravity on the surface of the Earth is ?=9.81…You are the science officer on a visit to a distant solar system. Prior to landing on a planet you measure its diameter to be 1.50×107 m and its rotation period to be 22.3 hours. You have previously determined that the planet orbits 2.50×1011 m from its star with a period of 402 earth days. Once on the surface you find that the free-fall acceleration is 13.1m/s2. What is the mass of the planet? Express your answer with the appropriate units. What is the mass of the star? Express your answer with the appropriate units.Many spacecraft have visited Mars over the years. Mars is smaller than the earth and has correspondingly weaker surface gravity. On Mars, the free-fall acceleration is only 3.8 m/s2 What is the orbital period of a spacecraft in a low orbit near the surface of Mars? The radius of Mars is 3.4×10^6m..
- A satellite with mass m, 102 kg orbits the Earth at a height of h = 503 km above the Earth's surface. The mass of the Earth is ME = 5.97 × 1024 kg and radius of the Earth is RE = 6.38 × 10° m. What is the magnitude of force that the Earth exerts on the satellite? F N Part 3) What is the orbital period of the satellite? T SNASA uses a machine often called the "vomit comet" to mimic the effects of low gravity in space during astronaut training. The machine moves in circular arcs at a speed of v = 214 m/s. What is the radius the pilot must fly to create weightlessness as they go around the top of the circular arc? Give your answer in meters.A 615-kg satellite is in a circular orbit about Earth at a height above Earth equal to Earth's mean radius. (a) Find the satellite's orbital speed. m/s (b) Find the period of its revolution. h (c) Find the gravitational force acting on it. N