How about visiting another world

The Mars Pathfinder robotic Rover, Sojourner, was the first vehicle landed to explore another planet. That happened July 4th, 1997. Until today, four rovers have successfully been operated on the surface of our red neighbour planet. March 10th, 2016, the Mars Reconnaissance Orbiter had kept a close eye at Mars for ten years.

March 14th, 2016, the ExoMars spacecraft left the Earth for Mars. After a seven month journey, on October 16th, the TGO, Trace Gas Orbiter, and the Schiaparelli lander will separate. The TGO will, like five other space crafts, orbit the red planet. Schiaparelli is an entry-descent-and-landing technology demonstrator module. In other words – It’s a technological test for further missions. Landing on a planet is a tricky business. Ask NASA!

ExoMars 2016 Schiaparelli descent sequence. credit: ESA/ATG medialab http://www.esa.int/spaceinimages/Images/2016/02/ExoMars_2016_Schiaparelli_descent_sequence_16_9

ExoMars 2016 Schiaparelli descent sequence. Credit: ESA/ATG medialab

Now, that goes for a planet next to us. How about further away from us? Pluto?

July 14th, NASA’s New Horizons made its “Pluto flyby”. The journey started 9½ years earlier, January 19th, 2006. Why spend that much time to get to Pluto, and then just pass the dwarf planet? Well, New Horizons is so far the fastest spacecraft leaving the Earth at a speed of more than 16 km/s. It passed Pluto at a speed of 13.78 km/s. The energy from the Sun is not enough to power any kind of spacecraft at a distance of 30

The energy from the Sun is not enough to power any kind of spacecraft at a distance of 30 AU. Instead, New Horizons is powered by plutonium-238 oxide pellets. That will keep its instrument going for another 14 years. Still, you can’t slow a spacecraft down using nuclear power if you don’t blow pieces of it in the opposite direction. Newton had that figured out in the 17th century. To keep a satellite in orbit, 200 km above the surface of Pluto, its orbital speed has to be less than one kilometer per second. To decelerate over 400kg New Horizons about 13 km/s you need as much energy as accelerating it 13000 m/s. To plan the journey in a way that the spacecraft would reach Pluto at just the right speed to “fall into orbit” would require a lot of patience.

Image converted using ifftoany

New Horizons gained speed using the gas giant Jupiter’s gravitation. Credit: Johns Hopkins University Applied Physics Laboratory/Southwest Research Institute (JHUAPL/SwRI)

Since 1972, no human has been further out from the planet than the International Space Station – about 400 km above Earth’s surface. Safety is an issue. As soon as a human leave the Earth on a spacecraft the crucial task of the mission shifts to bringing that person safely back to Earth. How safe would it be to visit another body in space?

Well, we did actually go to the moon! Or more correctly – a dozen men have walked on the surface of the only moon we have. And – They returned! – With rock samples. Since that, we have learned a lot and have done great in improving our engineering capability. We could actually send a manned expedition to Mars. The landing would be quite safe. But it would be a one-way journey.

There are in fact plans to build a village on the Moon. It has been proven that it is possible to leave the Moon and return safely to the Earth so that part of the mission seems to be ok. ESA’s director general Jan Wörner has said: “There are multiple usages for multiple users but on a single place.” The moon could become a superb testing ground.

Escape1The start of the journey back home is challenging. To escape the gravity of a massive body you need to gain enough speed – escape velocity. That’s the speed where the kinetic energy equals the gravitational potential energy.

escape2By doing some algebra, we can extract a clean formula where “G” is the gravitational constant 6,67·10−11N·m²/kg², “M” is the massive body and “r” is the radius of the massive body. Notice that the mass of the spacecraft is of no interest.

Inserting the data of the Moon, Pluto, and Mars into the equation, we see that the escape velocity leaving the Moon is 1340 m/s, leaving Pluto would require a speed of 1210 m/s and to leave Mars we need to exceed a speed of 5015 m/s. Does that mean that, if we could solve the deceleration problem, we could use the technology we already used on the Moon 45 years ago to plan a round trip to Pluto?

Apollo-12-LM


JanJan teaches mathematics and interdisciplinary science to pupils 13-16 years of age at Sursik School, Pedersöre, Finland. Space-related science often gives some sort of answer to the question “Why?”, a question quite common in math class. It also triggers curiosity, one key component in progress.

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