A rocket is launched from the surface of a planet with mass 9.1 x 1024 kg and radius 3.2 x 106 m at its escape speed. Calculate the speed of the rocket when it is three times as far from the center of the planet as it was at launch, in m/s. Use G = 6.7 x 10-11 N m2/ kg2. (Please answer to the fourth decimal place - i.e 14.3225)
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(Please answer to the fourth decimal place - i.e 14.3225)
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- 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 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 and Ri = 6.41×106 m, what is the measured value of the gravitational constant, in units of N⋅m2/kg2?A planet orbiting a distant star has radius 3.54×106 mm. The escape speed for an object launched from this planet's surface is 7.65×103 m/sm/s. What is the acceleration due to gravity at the surface of the planet? Express your answer with the appropriate units.Exoplanet Taphao Keow is a Jupiter-sized planet orbiting another star. It has a mass of approximately 1×10+27[kg]. Its actual radius is not currently known, but we do know that the radius of Jupiter is 7×107[m]. Question: If Taphao Keow had a radius that was the same radius as Jupiter, what would it's local surface gravitational acceleration be? O 266 [m/s2] 124 [m/s²] 70 [m/s²] O 24 [m/s²] O 14 [m/s²] It would have a gravitational acceleration far larger than any of the other answers (many orders of magnitude larger) It would have a gravitational acceleration far smaller than any of the other answers (many orders of magnitude larger)
- Fg KE = mv², Ug Gm₂mz r2 == 2 ac -2²₁v=2²7₁9= = 27, g = GM, Vesc = = Gm₁m₂ T 2GM VR E = KE + Ug, G = 6.674 x 10-¹1 N. m²/kg² }A 4.4 kg mass weighs 35.64 N on the surfaceof a planet similar to Earth. The radius ofthis planet is roughly 6 × 10^6 m.Calculate the mass of of this planet. Thevalue of the universal gravitational constantis 6.67259 × 10^−11 N · m^2/kg^2.Answer in units of kg. Calculate the average density of this planet.Answer in units of kg/m^3.Consider a spherical shell constructed from a material of density 6.1 x 103 kg/m3. The inner radius of the shell is 4.9 x 106 m from the center, and the outer radius of the shell is 9.2 x 106 m from the center. Calculate the magnitude of the gravitational field 13.1 x 106 m from the center of the shell, in N/kg. Use G = 6.7 x 10-11 N m2 / kg2. (Please answer to the fourth decimal place - i.e 14.3225)
- HINT M. kg (a) Find the magnitude of the gravitational force (in N) between a planet with mass 6.50 x 1024 and its moon, with mass 2.55 x 10 kg, if the average distance between their centers is d= 2.90 x 108 m. %3D N (b) What is the moon's acceleration (in m/s2) toward the planet? (Enter the magnitude.) m/s? (c) What is the planet's acceleration (in m/s²) toward the moon? (Enter the magnitude.) m/s2What is the escape speed from a planet of mass M = 3.1 x 1023 kg and radius R = 2.6 x 106 m? Write the answer in terms of km/s.(a) Find the magnitude of the gravitational force (in N) between a planet with mass 8.25 ✕ 1024 kg and its moon, with mass 2.20 ✕ 1022 kg, if the average distance between their centers is 2.20 ✕ 108 m. ___N (b) What is the moon's acceleration (in m/s2) toward the planet? (Enter the magnitude.) ___m/s2 (c) What is the planet's acceleration (in m/s2) toward the moon? (Enter the magnitude.) ___m/s2
- Weight w are fired from a giant cannon made by a shooting club. In early tests of the cannon, pointed straight up, the people want to shoot a projectile to an altitude of 1.5RE, where RE is the radius of the earth. Dismiss the effects of air resistance and the rotation of the earth. (Note: g = GME/RE2, where G is Newton’s gravitational constant, ME is the mass of the earth and RE is the radius of the earth.) What must the muzzle speed of the projectile be for it to get this high? What is the speed of the projectile when it returns to the surface of the earth (just before hitting the ground)?An asteroid has a mass of 3.66 × 10kg and a radius of 8.2 × 10m. If a 25 kg mass is dropped from 10 m above the “ground” of the asteroid, how long will it take the mass to fall to the ground?Please don't provide handwritten solution .....