A 5.0 m diameter solid aluminum sphere is launched into space from the surface of the earth. By how many um does its diameter increase?
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- Jupiter's moon Io has active volcanoes (in fact, it is the most volcanically active body in the solar system) that eject material as high as 500 km (or even higher) above the surface. Io has a mass of 8.93×1022kg and a radius of 1821 km How high would this material go on earth if it were ejected with the same speed as on Io? (REarth = 6370 km, mEartg=5.96×1024kg) NOTE: Your answer suggests that you have assumed constant gravitational acceleration over the whole height of the ejected debris. Note that the gravitational field changes quite significantly over this height.A 10 kg object sits on the earth’s surface. What is the force of gravity between the object andthe earth? (mass of the earth = 5.97 x 1024 kg, radius of the earth = 6.37 x 106 m)An astronaut lands on a new, recently discovered planet in a different star system. The astronaut measures the acceleration due to gravity on the planet to be 12m/s2, and the mass of the planet is measured to be 7.5E23kg. What is the radius of the new planet?
- In 2014, the Rosetta space probe reached the comet Churyumov– Gerasimenko. Although the comet’s core is actually far from spherical, in this problem we’ll model it as a sphere with a mass of 1.0 x 1013 kg and a radius of 1.6 km. If a rock were dropped from a height of 1.0 m above the comet’s surface, how long would it take to hit the surface?A woman whose weight is 680 N on the Earth’s surface is in a spacecraft at an altitude above the Earth's surface equal to the radius of the Earth. Her approximate weight (in newtons) in the spacecraft isYou have a super high-tech spacecraft travelling through space that gets caught in a circular orbit around a mysterious object of mass 10 times that of the Sun and a radius of 30km. Your team decides to observe the behavior of this object but due to the heat that it's giving off, it is required that your satellite obtain a circular orbit of at least r = 5.3e5km to be considered 'safe'. You are currently in a circular orbit with r = 4.1e5km. What is the minimum delta-v required to reach the safe orbit
- 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 satellite m = 500 kg orbits the earth at a distance d = 199 km, above the surface of the planet. The radius of the earth is re=6.38×106 m and the gravitational constant G =6.67×10-11 N m2/kg2 and the Earth's mass is me=5.98×1024 kg. What is the speed of the satellite in m/s?
- 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 gravitational potential energy PE1 of the meteoroid at R1 in terms of defined quantities and the gravitational constant G. Assume the potential energy is zero at infinity. b) Calculate the value of PE1, in joules. c)Enter an expression for the total energy E1 of the meteoroid at R1 in terms of defined quantities.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.Suppose we drill a hole through the Earth along its diameter and drop a small mass m down the hole. Assume that the Earth is not rotating and has a uniform density throughout its volume. The Earth’s mass is ME and its radius is RE. Let r be the distance from the falling object to the center of the Earth. Derive an expression for the gravitational force on the small mass as a function of r when it is moving inside the Earth. Derive an expression for the gravitational force on the small mass as a function of r when it is outside the Earth. On the graph below, plot the gravitational force on the small mass as a function of its distance r from the center of the Earth. Determine the work done by the gravitational force on the mass as it moves from the surface to the center. What is the speed of the mass at the center of the Earth if the Earth has a given density Determine the time it takes the mass to move from the surface to the center of the Earth.