Mr. Spock was floating at distance of 2.25 x10 m from earth, suddenly an unidentified spacecraft warps at a distance of 4000 km from him. Unable to ask for any assistance, would an 82-kg Mr. Spock gravitate towards earth or the unidentified spacccraft? The spacecraft was analyzed to be of m = 9.30 x1022 kg.
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- Three uniform spheres of masses m₁ = 3.00 kg, m₂ = 4.00 kg, and m3 = 5.00 kg are placed at the corners of a right triangle (see figure below). Calculate the resultant gravitational force on the object of mass m₂, m2 assuming the spheres are isolated from the rest of the Universe. Î + × 10-11 N y (0, 3.00) m m (-4.00, 0) m 12 Mg F 32 Ο m2 xAt what rate must a cylindrical spaceship rotate if occupants are to experience simulated gravity of 0.52 gg? Assume the spaceship's diameter is 29 mm , and give your answer as the time needed for one revolution (see the figure (Figure 1)). Express your answer using three significant figures and include the appropriate units.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.
- (a) Imagine that a space probe could be fired as a projectile from the Earth's surface with an initial speed of 5.96 x 10“ m/s relative to the Sun. What would its speed be when it is very far from the Earth (in m/s)? Ignore atmospheric friction, the effects of other planets, and the rotation of the Earth. (Consider the mass of the Sun in your calculations.) 354790 Your response differs from the correct answer by more than 100%. m/s (b) What If? The speed provided in part (a) is very difficult to achieve technologically. Often, Jupiter is used as a "gravitational slingshot" to increase the speed of a probe to the escape speed from the solar system, which is 1.85 x 10“ m/s from a point on Jupiter's orbit around the Sun (if Jupiter is not nearby). If the probe is launched from the Earth's surface at a speed of 4.10 × 10“ m/s relative to the Sun, what is the increase in speed needed from the gravitational slingshot at Jupiter for the space probe to escape the solar system (in m/s)? (Assume…A meteoroid is moving towards a planet. It has mass m = 0.54×109 kg and speed v1 = 4.7×107 m/s at distance R1 = 1.6×107 m from the center of the planet. The radius of the planet is R = 0.78×107 m. The mass of the planet is M = 5.6×1025kg. 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. Select from the variables below to write your expression. Note that all variables may not be required.α, β, θ, d, g, G, h, m, M, P, R, R1, t, v, v1 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.Two planets P₁ and P₂ orbit around a star S in circular orbits with speeds v₁ = 43.4 km/s, and v₂ = 57.0 km/s respectively. If the period of the first planet P₁ is 790 years what is the mass, in kg, of the star it orbits around? kg Determine the orbital period, in years, of P2. yr
- Two planets P, and P, orbit around a star S in circular orbits with speeds v, = 46.4 km/s, and v, = 57.4 km/s respectivel (a) If the period of the first planet P, is 710 years what is the mass, in kg, of the star it orbits around? kg (b) Determine the orbital period, in years, of P2. yrA 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.A binary-star system contains a visible star and a black hole moving around their center of mass in circular orbits with radii r1 and r2 , respectively. The visible star has an orbital speed of v=5.36x105 ms-1 and a mass of m1 =5Ms ,where Ms= 1.98x1030kg is the mass of our Sun. Moreover, the orbital period of the visible star is T = 30 hours.(a) What is the radius r1 of the orbit of the visible star?(b) Calculate the mass m2 of the black hole in terms of MS . [Hint: One root of the equation x3 = 20a(5a+x)2 , where a is a constant, is x = 28a .]
- Our solar system is roughly 2.2 x 1020 m away from the center of the Milky Way galaxy, and the system is moving at roughly 231.4 km/s around the galaxy's center. Since most of the galaxy's mass is near its center (and we are on an outer arm of this spiral galaxy), let's model the galaxy has a spherical mass distribution (like a single, giant star that our system is orbiting around). What is the mass of the galaxy (according to our rough, spherical model)? Obviously, this will be a VERY big answer, and so enter in your answer to the order of 1040 kg. In other words, calculate the answer, and then divide by 1040 and then enter in the result. BTW - by assuming that all mass in the galaxy is made up of stars that are about the same mass as our sun, it isn't too hard to then estimate how many stars are in the galaxy!). As an another aside, some measurements and observations that we have taken in Astronomy suggests that in reality, stars only make up a fraction of the total massCurrent Attempt in Progress Three dimensions. Three point particles are fixed in place in an xyz coordinate system. Particle A, at the origin, has mass ma. Particle B, at xyz coordinates (2.00d, 2.00d, 2.00d), has mass 4.00ma, and particle C, at coordinates (-3.00d, 2.00d, -3.00d), has mass 4.00mA. A fourth particle D, with mass 3.00ma, is to be placed near the other particles. If distance d = 4.20 m, at what (a) x, (b) y, and (c) z coordinate should D be placed so that the net gravitational force on A from B, C, and D is zero? %3D (a) Number i Units (b) Number Units (c) Number Units > >15. A pilot of mass 75 k plane is flying man normal? the she nears it feels four times heav diagram. 41.6657 FC V-1.54.10² 9.d (= 75 radius = 150 1.2 m 59m/ radiusis 54m T 3.6 kmph tmps 39 16. A ball of mass 4.0 kg is attached to the end of a 1.2 m long string and whirled around as shown at a velocity of 3.4 m/s. If the ball is rotated in a horizontal circle what angle does the string make with the horizontal? 0 r R 3g r= 2 V FTsino 2 Fg 41.66/2 3x9.8 FT F cose