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- The Moon and Earth rotate about their common center of mass, which is located about 4700 km from the center of Earth. (This is 1690 km below the sufrace.) (a) Calculate the acceleration due to the Moon’s gravity at that point. (b) Calculate the centripetal accelereation of he center of Earth a sit rotates about that point once each lunar month (bout 27.3 d) and compare it with the acceleration found in part (a). Comment on whether or not they are equal and why they should or should not be.What is the gravitational acceleration close to the surface of a planet with a mass of 2ME and radius of 2RE where ME, and RE are the mass and radius of Earth, respectively? Answer as a multiple of g, the magnitude of the gravitational acceleration near Earths surface. (See Section 7.5.)In Example 2.6, we considered a simple model for a rocket launched from the surface of the Earth. A better expression for the rockets position measured from the center of the Earth is given by y(t)=(R3/2+3g2Rt)2/3j where R is the radius of the Earth (6.38 106 m) and g is the constant acceleration of an object in free fall near the Earths surface (9.81 m/s2). a. Derive expressions for vy(t) and ay(t). b. Plot y(t), vy(t), and ay(t). (A spreadsheet program would be helpful.) c. When will the rocket be at y=4R? d. What are vy and ay when y=4R?
- Two ocean liners, each with a mass of 40 000 metric tons, are moving on parallel courses 100 m apart. What is the magnitude of the acceleration of one of the liners toward the other due to their mutual gravitational attraction? Model the ships as particles.Model the Moons orbit around the Earth as an ellipse with the Earth at one focus. The Moons farthest distance (apogee) from the center of the Earth is rA = 4.05 108 m, and its closest distance (perigee) is rP = 3.63 108 m. a. Calculate the semimajor axis of the Moons orbit. b. How far is the Earth from the center of the Moons elliptical orbit? c. Use a scale such as 1 cm 108 m to sketch the EarthMoon system at apogee and at perigee and the Moons orbit. (The semiminor axis of the Moons orbit is roughly b = 3.84 108 m.)Unreasonable Results (a) Based on Kepler's laws and information on the orbital characteristics of the Moon, calculate the orbital radius for an Earth satellite having a period of 1.00 h. (b) What is unreasonable about this result? (c) What is unreasonable or inconsistent about the premise of a 1.00 h orbit?
- 4.) The sun, Earth, and Jupiter are aligned in a straight line. Using the average distances from table 11.1 determine the following: a.) what is the distance between Earth and Jupiter in uniters of metres? (show all work) b.) what is the gravitational attraction between Earth and Jupiter in units of Newton's? (show all work) Object Avg. Radius (m) Mass (kg) Mean sun to planet distance (m) Sun 6.96 x 108 1.99 x 1030 --- Earth 6.38 x 106 5.97 x 1024 1.50 x 1011 Jupiter 7.15 x 107 1.90 x 1027 7.78 x 10112-D star cluster puzzle Find the net gravitational force on each star for each star cluster Let m=mass of the star = 1.99 x 10^30 kg, l=earth to star distance=149.6 x 10^6 km, G=6.67 x10^-11 N m^2/kg^2. Note that the masses of each star are the same. Also, it is advised to use vectors and components. And you can just find the gravitational net force of one of the stars in the shape I need the answers for the following: 3) Pentagon 4) Hexagon 5) Regular heptagon 6) Regular OctagonAn ultracentrifuge accelerates uniformly from rest to 100,000 rpm in 2.0 min. If this ultracentrifuge accelerates 2.0 seconds starting from rest, what is the magnitude of the centripetal acceleration in unit of gravitational acceleration g for your sample sitting at 6.0 cm from the center axis? Use g = 9.8 m/s2. Hint: compute the centripetal acceleration in unit of m/s2 first, then divided by g will be your answer. For example, if your centripetal acceleration is 19.6 m/s2, your answer measured in unit of g is 2.0.
- Using SI units. Determine the gravitational force acting between two spheres that are touching each other. The mass of each sphere is 200 kg and the radius is 300 mm. Give your answer in micro-netwons (µN) and to three significant figures.In this problem you will measure the gravitational constant in a series of “observational experiments,” making use of Newton’s law of gravitation and second law of motion as well as Kepler’s third law of planetary motion a)Since measuring the centripetal acceleration of an orbiting body is rather difficult, an alternative approach is to use the body’s rotational period instead. Enter an expression for the gravitational constant, in terms of the distance between Earth and the moon, RME, Earth’s mass,ME, and the moon’s period of rotation around Earth, T. b)Using the expression you entered in part (b) and taking the rotational period of the moon to be T = 27.1 days, what value would Newton have calculated for the gravitation constant, in units of N⋅m2/kg2? Take ME = 5.95×1024 kg and RME = 3.86×108 m. c) Suppose a rocket is launched as described in part (d) with an initial speed of vi = 494 m/s and attains a peak altitude of H = 12.7 km above the surface of Earth. Taking ME = 5.95×1024 kg…What is the magnitude of the gravitational acceleration at a height of two earth radius (2RE) above earth surface? Take gravitational acceleration near Earth surface as 9.81 m/s2. Express your answer in m/s2 and enter numerical value only, no units