Flight to Mars. To send a satellite from Earth to Mars, a rocket must accelerate
ID: 2219341 • Letter: F
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Flight to Mars. To send a satellite from Earth to Mars, a rocket must accelerate the satellite until it is in the correct elliptical orbit around the sun. The satellite does not travel to Mars under rocket power, because that would require more fuel than it could carry. It just moves on a Keplerian orbit under the influence of the sun's gravity. The satellite orbit must have perihelion r = 1 AU, and aphelion r = 1.52 AU. (A) What is the semimajor axis of the satellite's orbit? (B) Calculate the time for the satellite's journey. Express the result in days.Explanation / Answer
Good question, fun to answer. I'll answer thoroughly for you... First let me start with the Mars mission surface walk... (1) Okay.. the atmosphere is NOT similar to Earth. Our atmosphere is Nitrogen-Oxygen-Carbon Dioxide. Mars' is basically only CO2. It is impossible for us to breathe its atmosphere, you'd simply suffocate. (2) Further, the air temperature at the surface is only around 32 Fahrenheit at its warmest (literal surface temperature is around 80 F, but it's the air temperature that's important for us). Obviously, you'd suffer from cold, frostbite, and if you were exposed long enough, hypothermia and death. (3) Also, the air pressure at the surface is only 0.7% that of Earth. It wouldn't be completely this bad for you, but it would be fairly close... in the first 30 seconds after stepping out of your spaceship without a spacesuit, any fluid on the surface of your body would begin to boil due to lack of ambient pressure, this includes the saliva on your tongue and the moisture in your eyes. Your eardrums would most likely burst due to the pressure in your body trying to equalize with the low pressure outside. However, unlike what some science fiction films have suggested, your body would not explode (more like Arnold in "Total Recall"). After the first 15 seconds you would lose consciousness. If you held your breath you could potentially stay alive longer but you risk pulmonary trauma. If you didn't hold your breath you'd pass out sooner, but your lungs might have a better chance of avoiding permanent damage. The pressure in your veins would rise until your heart no longer had the capacity to pump blood, at which point you'd die. All of this means that if you get to Mars - be sure to wear a spacesuit. Now, on to actually getting to our neighboring planet in the first place. (1) The most important variable about how long it would take to travel to Mars is obvious - how fast are you going? (2) The minimum straight-line distance between Earth and Mars is 34,796,787 miles (56,000,000 km). (3) The Sun-observatory Helios 1, launched in 1976, holds the record for the fastest man-made object. It didn't use a rocket to get to that maximum speed, instead it used a simple boost rocket then a number of very complicated orbital maneuvers for "gravity slingshots" around the Solar System before it reached its highly elliptical orbit. It's still out there, maximum speed topping out at 153,800 mph (257,510 km/h). (4) So, figure that by the time we're going to Mars, we can somehow achieve a non-gravity boos speed of Helios 1, then we just apply the good old 7th grad "Distance = Rate * Time" we get a total travel time of only 9.4 days! However - you and I will never see non-gravity boost speeds like this in our lifetimes. Barely a fraction. In which case, continue to the next point. (5) Now that we're getting back to reality, if we were to try to go to Mars today, the best that we could realistically do - especially when you consider that we'd be sending a large manned ship, not just a SUV-size probe - is Earth escape velocity, 24,383mph (399,204 km/h). In which case, our travel time to Mars goes from a pleasant 9.4 days, to, rounding to a pleasant decimal, almost exactly 2 months. That's a lot of oxygen, and water, and food, human waste recycling/disposal, hygiene, time not to run out of National Geographic to pass the time, computers and machines not failing, and perhaps most importantly - keeping deadly cosmic rays from searing the little Mars-missioners to bits. Our astronauts can orbit Earth happily because they're still inside the protective magnetosphere, while obviously, Mars-bound explorers won't. (6) Unfortunately, we have to step back a second and look at our new timetable of a 2 month flight. The distance that I used to calculate travel time is based on a straight-line Earth-to-Mars passage. It doesn't work that way. You cannot fly around space - anywhere in the Solar System - in a straight line. Our entire system developed with a huge rotational motion (good for not falling into the Sun). If you've ever been 7 years old and put your finger on a spinning bar stool, and spun it around, you'll see that eventually, your finger will begin to move in curves (one expanding curve). This means that through orbital mechanics, our Mars mission has to be flung out into space (at escape velocity) so that they will actually be in front of Mars long the planet's orbit. Mars will "catch up" to them, at which point they can fire thrusters to enter into a holding orbit around the Red Planet. They need to get "caught up," because we don't have the technology to chase down the planet - we let it come to us. (7) Now we're using real orbital motion to get into place, it will take between 7 and 8 months to get into position to "get caught" by Mars at our absolute minimum orbital distance (which, unfortunately, doesn't happen very often, due to the differen
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