Early Monday morning (August 6, 2012), the Mars rover named Curiosity successfully landed on the surface of Mars. The rover launched on November 26th, 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 successful1. So, the scientists at NASA were ecstatic when Curiosity landed successfully.
Mission type Total attempts Success Partial success Flyby 11 5 Orbiter 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 Mars2 (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 5,280 feet = ≈ 1.47 So, to convert from miles per hour to feet per second I should 1 hour 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 Some data collected, but lost Mars 1 1 November 1962 21 March 1963 Flyby 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 Failure during launch ruined Mariner 3 5 November 1964 5 November 1964 Flyby trajectory Mariner 4 28 November 1964 21 December 1967 Flyby Success (21 images returned) Communication lost three months Zond 2 30 November 1964 May 1965 Flyby before reaching Mars Mariner 6 25 February 1969 August 1969 Flyby Success Mariner 7 27 March 1969 August 1969 Flyby Success Mars 2M No.521 27 March 1969 27 March 1969 Orbiter Launch failure Mars 2M No.522 2 April 1969 2 April 1969 Orbiter Launch failure Mariner 8 8 May 1971 8 May 1971 Orbiter Launch failure Kosmos 419 10 May 1971 12 May 1971 Orbiter Launch failure Mariner 9 30 May 1971 27 October 1972 Orbiter Success (first successful orbit) 22 August 1972 Orbiter Success Mars 2 19 May 1971 27 November 1971 Lander, rover Crashed on surface of Mars 22 August 1972 Orbiter Success Partial success. First successful 2 December 1971 Lander, rover landing; landed softly but ceased transmission within 15 seconds Could not enter orbit, made a close Mars 4 21 July 1973 10 February 1974 Orbiter flyby Partial success. Entered orbit and Mars 5 25 July 1973 21 February 1974 Orbiter returned data, but failed within 9 days Partial success. Data returned Mars 6 5 August 1973 12 March 1974 Lander during descent but not after landing on Mars Landing probe separated Mars 7 9 August 1973 9 March 1974 Lander prematurely; entered heliocentric orbit 17 August 1980 Orbiter Success Viking 1 20 August 1975 13 November 1982 Lander Success 25 July 1978 Orbiter Success Viking 2 9 September 1975 11 April 1980 Lander Success 2 September 1988 Orbiter Contact lost while en route to Mars Phobos 1 7 July 1988 Lander Not deployed Partial success: entered orbit and 27 March 1989 Orbiter returned some data. Contact lost Phobos 2 12 July 1988 just before deployment of landers Landers Not deployed Mars Observer 25 September 1992 21 August 1993 Orbiter Lost contact just before arrival Mars Global 7 November 1996 5 November 2006 Orbiter Success Surveyor Orbiter, Mars 96 16 November 1996 17 November 1996 lander, Launch failure penetrator Mars Pathfinder 4 December 1996 27 September 1997 Lander, rover Success Nozomi (Planet- Complications while en route; 3 July 1998 9 December 2003 Orbiter B) Never entered orbit Mars Climate Crashed on surface due to metric- 11 December 1998 23 September 1999 Orbiter Orbiter imperial mix-up 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 Currently 7 April 2001 Orbiter Success Odyssey operational Currently Mars Express Orbiter Success 2 June 2003 operational Beagle 2 6 February 2004 Lander, rover Landing failure; fate unknown. MER-A Spirit 10 June 2003 22 March 2011 Rover Success MER-B Currently 7 July 2003 Rover Success Opportunity operational Gravity assist en route to Currently comet Rosetta 2 March 2004 Success operational 67P/Churyum ov- Gerasimenko Mars Currently Reconnaissance 12 August 2005 Orbiter Success operational Orbiter Phoenix 4 August 2007 10 November 2008 Lander Success Currently Gravity assist Dawn 27 September 2007 Success operational to Vesta Phobos Fobos-Grunt 8 November 2011 lander, Failed to leave Earth orbit. Rescue 8 November 2011 sample return attempts unsuccessful Yinghuo-1 8 November 2011 Orbiter Currently MSL Curiosity 26 November 2011 Rover Success operational
2The 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
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