Calculate the ratio of Mercury's orbital speed at perihelion to its speed at aphelion.
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- On February 15, 2013, Asteroid 2012 DA14 passed within 17,200 miles [mi] of the surface of the Earth at a relative speed of 7.8 kilometers per second [km/s]. This is considerably closer than the orbit of geosynchronous satellites (26,200 miles). This is the closest recorded approach of an object this large. The asteroid 2012 DA14 was estimated to have a diameter of 30 meters [m] and a specific gravity of 3. If 2012 DA14 had hit the Earth, what is the total amount of energy that would have been released (i.e., what was the kinetic energy of the asteroid)? Express your answer in megatons [Mton]. One megaton is the energy released by one million metric tons of TNT explosive. A metric ton equals 1,000 kilograms [kg], and the explosive energy of TNT is 4,184 joules per gram [J/g].An earth-like planet with a mass of 6.00×1024 kg has a space station of mass 4.60×104 kg orbiting it at a distance of 5.00×105 km. What is the gravitational potential energy between the space station and the planet? (We can simplify the Gravitational Constant G to 6.7x10-11 Nm2/kg) (calculate in J)What are the speed and period of a satellite in an 85.00 km altitude lunar orbit? (what is Rmoon?) (mu_moon = 4903 km^3/s^2; v = 1.640 km/s)
- Please asapLet’s imagine that you have an idea for an experiment to fly on NASA’s “Vomit Comet.” (What’s special about this plane? It flies in parabolic paths (aka freefall) which result in near weightlessness. This means that you can ignore the effects of gravity when plan your experiment.) You want to mimic the orbital motion of the planets but by using electrostatic force rather than gravitational. And, instead of a planet, you will be orbiting a droplet of water that is 0.5mm in radius and has an deficit of 1.5 x 106 electrons. The droplet is to orbit around a small (1cm radius) sphere. If you want the droplet to move with an orbital radius of 14cm and period of one minute, what should the charge be on the central sphere? BTW The density of water is 997 kg/m3.A satellite is orbiting the earth in low orbit (160 km above the surface of the earth). If the universal gravitational constant is 6.67 x 10^-11 m^3/kg x s^2 the mass of the earth is 5.972 x 10^24 kg and the radius of the earth is 6371 km, what speed must the satellite travel in order to maintain the low earth orbit?