H3 What the acceleration of each astronaut? Assume the acceleration were constan

Question

H3 What the acceleration of each astronaut? Assume the acceleration were constant. Estimate how long would it take before Sandra and George meet. Treat them like point masses. (Careful, they BOTH accelerate so the total distance they both move must be 20.0m). Give your answer in standard time units of years, months, days, hours, and minutes, Would the actual time be more than or less than this? Explain. It takes the moon about T = 27.3 days to orbit the Earth. Compute the distance from the center of the Earth to the moon? What is this in terms of earth's Radius (R_E)? In 2153, the Arc corporation builds the first ever "orbital train". A tube is built that loops around the world and evacuated (so air resistance won't slow the train.) Passengers board the train and it accelerates until travels so fast that ft lifts off the track and "orbits" the Earth. What is the operating speed of the orbital train? What is the period (how long to go around the Earth once?) Do passengers in the orbital train experience the sensation of weightlessness? What would be the operating speed of an orbital train on Mars? Compute the escape speed from Earth. The average speed of a gas molecule Is approximately v = Squareroot 3 RT/M, where R is the gas constant, T is the temperature In Kelvin, and M is the molar mass. Hydrogen atoms are quite small. At normal air temperatures, some hydrogen atoms travel at escape speed! This is why there is virtually no hydrogen gas in our atmosphere. The space station. In orbit about 200km above the Earth's surface, has a speed of about 8 km/s (about 5 mi/s). In light of the answer to part (a), does this make sense? What is the escape speed from Mars? Why Is there no almost no water vapor in the atmosphere of Mars? The mass of the space shuttle is approximately m = 2.0 x 10^6 kg. The shuttle orbited the earth at about 200km above the surface. It had an orbital speed approximately equal to "orbital train" in the previous problem. Using the orbital velocity, listed in the previous problem, compute the kinetic energy of the shuttle while In orbit.

Explanation / Answer

we know, Me = 5.98*10^24 kg

Re = 6.37*10^6 m

a)

orbital speed around the earth, vo = sqrt(G*Me/Re)

= sqrt(6.67*10^-11*5.98*10^24/(6.37*10^6))

= 7913 m/s

b) Yes.

c)

we know, Mm = 6.39*10^23 kg

Rm = 3.39*10^6 m

orbital speed around the earth, vo = sqrt(G*Me/Re)

= sqrt(6.67*10^-11*6.39*10^23/(3.39*10^6))

= 3546 m/s

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