Curiosity lands on Mars Early Monday morning (August 6, 2012), the Mars rover named Curiosity successfully landed on the surface of Mars. The rover launched on November 26 th, 2011 and traveled for 8 ½ months to arrive on Mars. We Earthlings have been trying to reach Mars since 1960. Some of the spacecraft sent were intended to fly past Mars and take photos. Some were meant to orbit Mars, and some had landers that were intended to reach the surface. But all of these attempts weren t successful 1. So, the scientists at NASA were ecstatic when Curiosity landed successfully. Mission type Total attempts Partial success Flyby 11 5 22 9 2 Lander 10 3 Rover 6 4 1 Sample return 1 Total 50 21 3 1. What percent of our attempts to reach Mars were totally successful? 2. What percent of our attempts to reach Mars were totally or partially successful? It is a long way to Mars 2 (This trip was 352 million miles long) and it took Curiosity 8 and ½ months to get there. That is a long time for the NASA scientists to hold their breaths. 3. How fast must the Curiosity rocket have been going to get to Mars in 8.5 months?
When Curiosity landed it took NASA about 14 minutes to receive the radio transmission from Curiosity that it had landed. Radio transmission through space travel at the speed of light = 300,000 kilometers per second or 186,000 miles per second. 4. Show how the scientists must have calculated that it would take about 14 minutes for the radio transmission to travel from Mars to Earth. (At the time of landing Mars was only 154 million miles (247,800,000 kilometers) away from Earth.) Deceleration The way that this rover was brought down to the surface of Mars was a totally new method of landing. They called it a sky crane landing. You can see in the animation of its landing at Yummymath.com. Amazingly, the spacecraft was slowed from 13,200 miles per hour (21,243 kilometers per hour) to about 1.7 miles per hour (0.75 m/sec) in 7 minutes. That seemed like very fast deceleration to me. I wondered how deceleration is measured and how Curiosity s deceleration compared with deceleration that I ve experienced like a car stopping. I found that to measure deceleration you divided the change of speed by the amount of time that it took to change that speed. Example: An airplane might change its speed from 300 mph to 60 mph in 30 seconds, before it touched down on the runway. To figure out the deceleration rate of my airplane landing, I need to change all of these measurements to the same units. So, I need to change miles per hour to feet per second. 1 mile is the same as 5,280 feet and 1 hour is the same as 3,600 seconds. 1 mile 1 hour = 5,280 feet 1.47 So, to convert from miles per hour to feet per second I should 3,600 seconds simply multiply my miles per hour rate by 1.47. 300 miles per hour x 1.47 should give me the feet per second equivalent to 300 miles per hour. 5. 300 miles per hour = how many feet per second? 6. 60 miles per hour = how many feet per second? Again, to calculate deceleration you need to divide the change in speed by the time that the change requires. Deceleration is measured in feet per second divided by seconds. The unit for deceleration is feet per second per second or feet per second squared.
As an example I ve calculated the deceleration required to slow my Toyota Camry from 60 mph to 0 mph in 15 seconds. 60 miles per hour = 60 x 1.47 = 88.2 feet per second. 0 miles per hour = 0 feet per second The speed reduction is 88.2 -- 0 = 88.2 feet per second. So, the rate of deceleration is 88.2 feet per second /15 seconds = 5.88 feet per second per second. Online I found that my Toyota Camry could brake at 24.2 feet per second per second. So, I guess I could stop my car faster than in 15 seconds if I tried. Boy, that would be scary. 7. What was the deceleration rate of the airplane landing mentioned in problems 5 and 6? Curiosity slowed from 13,200 miles/hour to 1.7 miles per hour (0.75 m/sec) during its seven minute descent. 8. What was the deceleration rate of Curiosity? 1 Mission Launch Termination Elements Result Mars 1M No.1 10 October 1960 10 October 1960 Flyby Launch failure Mars 1M No.2 14 October 1960 14 October 1960 Flyby Launch failure Mars 2MV-4 No.1 24 October 1962 24 October 1962 Flyby Broke up shortly after launch Mars 1 1 November 1962 21 March 1963 Flyby Some data collected, but lost contact before reaching Mars, flyby at approx. 193,000 km Mars 2MV-3 No.1 4 November 1962 19 January 1963 Lander Failed to leave Earth's orbit Mariner 3 5 November 1964 5 November 1964 Flyby Failure during launch ruined trajectory Mariner 4 28 November 1964 21 December 1967 Flyby (21 images returned) Zond 2 30 November 1964 May 1965 Flyby Communication lost three months before reaching Mars Mariner 6 25 February 1969 August 1969 Flyby Mariner 7 27 March 1969 August 1969 Flyby Mars 2M No.521 27 March 1969 27 March 1969 Launch failure Mars 2M No.522 2 April 1969 2 April 1969 Launch failure Mariner 8 8 May 1971 8 May 1971 Launch failure Kosmos 419 10 May 1971 12 May 1971 Launch failure Mariner 9 30 May 1971 27 October 1972 (first successful orbit) Mars 2 19 May 1971 22 August 1972 27 November 1971 Lander, rover Crashed on surface of Mars 22 August 1972
2 December 1971 Lander, rover Partial success. First successful landing; landed softly but ceased transmission within 15 seconds Mars 4 21 July 1973 10 February 1974 Could not enter orbit, made a close flyby Mars 5 25 July 1973 21 February 1974 Partial success. Entered orbit and returned data, but failed within 9 days Mars 6 5 August 1973 12 March 1974 Lander Partial success. Data returned during descent but not after landing on Mars Mars 7 9 August 1973 9 March 1974 Lander Landing probe separated prematurely; entered heliocentric orbit Viking 1 20 August 1975 17 August 1980 13 November 1982 Lander Viking 2 9 September 1975 25 July 1978 11 April 1980 Lander Phobos 1 7 July 1988 2 September 1988 Contact lost while en route to Mars Lander Not deployed Phobos 2 12 July 1988 Partial success: entered orbit and 27 March 1989 returned some data. Contact lost just before deployment of landers Landers Not deployed Mars Observer 25 September 1992 21 August 1993 Lost contact just before arrival Mars Global Surveyor 7 November 1996 5 November 2006 Mars 96 16 November 1996 17 November 1996, lander, Launch failure penetrator Mars Pathfinder 4 December 1996 27 September 1997 Lander, rover Nozomi (Planet- Complications while en route; 3 July 1998 9 December 2003 B) Never entered orbit Mars Climate Crashed on surface due to metricimperial mix-up 11 December 1998 23 September 1999 Mars Polar Lander Crash-landed on surface due to Lander 3 January 1999 3 December 1999 improper hardware testing Deep Space 2 Hard landers 2001 Mars 7 April 2001 Odyssey Mars Express 2 June 2003 Beagle 2 6 February 2004 Lander, rover Landing failure; fate unknown. MER-A Spirit 10 June 2003 22 March 2011 Rover MER-B 7 July 2003 Opportunity Rover Rosetta 2 March 2004 Mars Reconnaissance 12 August 2005 Gravity assist en route to comet 67P/Churyum ov- Gerasimenko Phoenix 4 August 2007 10 November 2008 Lander Gravity assist Dawn 27 September 2007 to Vesta
Fobos-Grunt 8 November 2011 8 November 2011 Yinghuo-1 MSL Curiosity 26 November 2011 Phobos lander, sample return 8 November 2011 Rover Failed to leave Earth orbit. Rescue attempts unsuccessful 2 The distance to Mars varies since both planets have elliptical orbits and they do not require the same amount of time to orbit the Sun. So, Mars is closest to Earth at about 36 million miles (56 million km) and furthest from Earth at about 250 million miles (401 million kilometers). Source: http://thelede.blogs.nytimes.com/2012/08/05/curiosity-is-set-to-land-on-mars/ http://www.latimes.com/news/nation/nationnow/la-mars-exploration-pictures-20120803,0,5704041.photogallery http://en.wikipedia.org/wiki/exploration_of_mars Brought to you by Yummymath.com