A) Find an expression for the speed v of the mass at point A in terms of R, m and G (B) Find an expression for the time period T of rotation of the planets in terms of R, m and G.
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A) Find an expression for the speed v of the mass at point A in terms of R, m and G
(B) Find an expression for the time period T of rotation of the planets in terms of R, m and G.
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- A meteoroid is moving towards a planet. It has mass m = 0.18×109 kg and speed v1 = 3.8×107 m/s at distance R1 = 1.6×107 m from the center of the planet. The radius of the planet is R = 0.26×107 m. The mass of the planet is M = 10×1025 kg. There is no air around the planet. a)Enter an expression for the total energy E of the meteoroid at R, the surface of the planet, in terms of defined quantities and v, the meteoroid’s speed when it reaches the planet’s surface. b)Enter an expression for v, the meteoroid’s speed at the planet’s surface, in terms of G, M, v1, R1, and R. c)Calculate the value of v in meters per second.The radius Rh of a black hole is the radius of a mathematical sphere, called the event horizon, that is centered on the black hole. Information from events inside the event horizon cannot reach the outside world. According to Einstein's general theory of relativity, Rh = 2GM/c2, where M is the mass of the black hole and c is the speed of light. Suppose that you wish to study a black hole near it, at a radial distance of 48Rh. However, you do not want the difference in gravitational acceleration between your feet and your head to exceed 10 m/s2 when you are feet down (or head down) toward the black hole. (a) Take your height to be 1.5 m. What is the limit to the mass of the black hole you can tolerate at the given radial distance? Give the ratio of this mass to the mass MS of our Sun. (b) Is the ratio an upper limit estimate or a lower limit estimate?The following questions relate to other Moons in our solar system. a. Europa is a Galilean satellite of Jupiter, where there is most probably a liquid water ocean underneath a thick cover of ice due to internal heating caused by the interaction with Jupiter and the other Galilean moons . The orbital period of Europa is P = 3.551 days; the semimajor axis of its orbit is a = 670 900km. Given this information, find the mass of Jupiter. b. Deimos is the outer moon of Mars. The orbital period of Deimos is P = 1.263 days; the semimajor axis of its orbit is a = 23 463.2km. Find the mass of Mars.
- How fast is a planet's Roran at the size and mass of the Earth, so that the object lying on the equator appears weightless? Find the planet's periodic time in minutes?It can: ME= 5.94×1024 kg RE= 6.38×106 m G=6.67×10-11 N.m2/kg2C) ESA wants to send a satellite to Jupiter to investigate its internal structure and origin by measuring the atmospheric composition and temperature. The spacecraft will leave Earth from a parking orbit of radius 6578 km and arrive at Jupiter in a parking orbit of radius 75782 km. What is the total velocity change required to do this mission? How long would it take for the satellite to arrive at Jupiter?In the year 25 000 the Earth is 1.42x101 m away from the sun and in a circular orbit, but a year remains 365 days long. Part A Calculate the mass of the sun in the year 25 000. ΑΣΦ ? msun = kg
- What is the velocity of Jupiter if an object on the equator of Jupiter would travel approximately 280,000 miles in about 10 hours?Find an expression for the kinetic energy of a satellite of mass m in an orbit of radius r about a planet of mass M . Express your answer in terms of the variables m, r, M, and appropriate constants.The center of a moon of mass m is a distance D from the center of a planet of mass M. At some distance x from the center of the planet, along a line connecting the centers of planet and moon, the net force on an object will be zero. Derive an expression for x.
- a.) Find the net force on the Moon (mM=7.35×1022kg)(mM=7.35×1022kg) due to the gravitational attraction of both the Earth (mE=5.98×1024kg)(mE=5.98×1024kg) and the Sun (mS=1.99×1030kg)(mS=1.99×1030kg), assuming they are at right angles to each other (Figure 1). Express your answer to three significant figures and include the appropriate units. Fnet= __________ ____________ b.) Determine the direction of the net force. Express your answer to three significant figures and include the appropriate units. θ= ______________ ___________Find an expression for the square of the orbital period. Express your answer in terms of G, M, R, and π. The potential energy U of an object of mass m that is separated by a distance R from an object of mass M is given by U=−G*Mm/R. What is the kinetic energy K of the satellite? Express your answer in terms of the potential energy U.Geosynchronous satellite moves in a circular orbit around the Earth and completes one circle in the same time T during which the Earth completes one revolution around its own axis. The satellite has mass m and the Earth has mass M and radius R. In order to be geosynchronous, the satellite must be at a certain height h above the Earth’s surface. a) Derive an expression for h in terms of m, M, R, T and constants. b) Calculate the numerical value for h in meters.