Chapter 14 - Relativistic Limits of Space Flight

HOME PAGE Web Site Contents Mars Report Contents Mars Report Abstract CV for Dr. David Roffman Diplomas PhD Thesis PhD Thesis Powerpoint Mars PowerPoint MSL Weather Reports Base on Mars? Seasonal Pressure Altitude Calculations Seismic Activity on Mars? Perserverance Weather Data MSL Years 5-6 Winter MSL Year 5 FALL MSL Year 5 Summer MSL Year 5 Spring MSL Years 4-5 Winter MSL Year 4 FALL MSL Year 4 Summer Weather MSL Year 4 Spring Weather MSL Yr 3-4 Winter Weather MSL Fall Yr 3 Weather MSL Yr. 3 Summer Weather MSL Yr. 3 Spring Weather Martian plume March 25 2017 MSL Ultraviolet 3 YEARS OF MSL UV Desai, EDL, Parachutes & ExoMars Mars winter vs. summer temps Helo to Mars Sea at Utopia Planitia, Mars Tree Stump at MSL? Spherical life on Mars? Mars Report Abstract, 1-1.2 Mars Report Sec.2-2.1 Report 2.2-2.4 Report 2.5-2.5.2 Report 2.5.3-2.7 Report 3-4 Report 4.1-4.1.2 Report 5 to 6 Report  7-7.2.1 Report 8 Report 9 Report 10 Report 11 Global Dust Storm Report 12 Report  13-13.2 Report 13.3-13.5 Report 13.6 Report 14-15 Report 15.1 Report 15.2-15.3 Report 15.4-15.6.2 Report - Report Report 16-16.1 Report 17-20 Report References Rebuttal of REMS Report Running water on Mars MSL Year 0 Weather MSL Yr 2 Winter-Spring Weather MSL Yr 2 Summer Weather MSL Yr 2 Fall Weather MSL Yr 2-3 Winter Weather Adiabatics MSL Hi Temps MSL Low Temps Organic Chem found by MSL Oxygen in Mars Air MSL Day length & Temp Warm winter ground temps 155-Mile High Mars Plume Radiation Diurnal Air Temp Variation Mars Temps Fahrenheit Beagle found JPL/NASA Pressure Mistakes Enter MarsCorrect Sol 370, 1160 & 1161 Histories Mars-Radio-Show JPL Fudges Pressure Curves MSL Temp. ∆ Mast to Ground High & Low Pressures Normalized Mars soil 2% water Moving rock Mars MAVEN MSL Relative Humidity Claim Ashima Concedes Original MSL Weather Record Old MSL Weather Record MSL Summer Weather Pressure Estimate REMS Wind MSL Pressures REMS Reports Curiosity Geology CERN-2013-pics Daylight Math MSL Errors P1 MSL Errors P2 MSL-Chute-Flap MSL daylight Ashima Sols 15 to 111 Ashima Sol 112 to 226 Ashima Sol 227 on New Ashima Sols 270+ MSL Summer to Sol 316 Updated Secrets of Mars Weather Forecast Wind Booms MSL Credibility MSL Temp. Swings MSL Temperatures Sample Analysis at Mars (SAM) VL2 - MSL Ls Comparson Ashima MIT Mars GCM Dust Storm Nonsense Mars Slideshow Moving Sand & Martian Wind 3 DEC12 Press Conf. MSL Press Conf. 15NOV2012 Sol Numbering MSL Pressure Graph to Ls 218.8 MSL Sky Color Mars Sky Color DATA DEBATE! Zubrin's Letter Phoenix Vaisala Vaisala Pressure Sensors Phoenix &MSL Flawed MSL REMS Viking pressure sensors failed MSL landing site Mars Landings Phobos Grunt Martian Air Supersaturation Mars & CH4 Mars and MSL Time Viking Pressure Audit Links Mars Society 2008 Quant Finance Frontiers Home Front. Preface Frontiers Ch. 1 Frontiers Ch. 2 Antimatter Lightning Frontiers Ch. 3 Frontiers Ch. 4 Frontiers Ch. 5 Frontiers Ch. 6 Frontiers Ch. 7 Frontiers Ch. 8 Frontiers Ch. 9 Frontiers Ch 10 Frontiers Ch 11 Frontiers Ch 12 Frontiers Ch 13 Frontiers Ch 14 Frontiers Ch 15 Frontiers Ch 16 Frontiers Ch 17 Frontiers Ch 18 Frontiers Ch 19 Frontiers Ch 20 Frontiers Ch 21 Frontiers Ch 22 World Tour Spring-Break -13 Other Travels Asteroid Impact? ExoMars data Unit Issues Viking Pressures Tavis CADs Landing Long Scale Heights LS of Max/Min Pressures Tavis Report Tavis Failures Lander Altitude Martian Trees? Code Experiment Gedanken Report Mars Nuke? Martian Flares Mach Numbers MOLA (altitude) Original Mars Report Mariner 9 & Pressure Mars  Temps MSL Time MPF Pressure Blog Debates Spring Pendulum Plasma Model Reporting Errors Orbital Parameters Anderson Localization P. 1 Anderson Localization P. 2 Moving rock old Navigating Mars Mars Report Section Links Mars Report Figure Link Gillespie Lake rock outcrop MSL Sol 200 Anomaly Sol 1300&1301 Anomalies Gilbert Levin & Labeled Release Brine on Mars Ceres Lights Yr 1 Table 1 Missing data Mitchell Report Old Mars Report All MPF Temps ExoMars fails Did Spirit find past life? MSL ground temps go haywire OPACITY AT MSL Luminescence on Mars Dust Storms & Microorganisms 2018 Global Dust Storm Links to Sections of the Basic Report

 Notes by David A Roffman on Chapter 14 of


Chapter by Bruce N. Cassenti,

Associate Professor, Department of Engineering and Science,

Rensselaer Polytechnic Institute,  Hartford, Connecticut


    Einstein’s Special Theory of Relativity is a hallmark of physics, and is incredibly accurate.  Even though it is designed for inertial frames, it can still be applied to spacecraft if continuously altered.  A tenement of this theory is that the speed of light in a vacuum is constant for all inertial frames, regardless of the observer’s location. Maxwell’s equations are assumed to be perfectly accurate.  Also, physical laws do not break down in any inertial frame.  Time can be dilated if one reaches speeds close enough to that of light.  Specifically this describes time dilation due to relative motion, whereas general relativity time dilation is due to gravity. I am not an expert in the later, however I am quite familiar with the former.  A analogy that is likened to derivation of the relativistic factor is below.

           Consider a river that flows from up to down with a speed "v" as shown in Figures 1 and 2.  How long would it take to swim (at a velocity "v") up a distance "d" (that is, against the current) and back?  This is shown in Figure 1.  The time up is just d/(c-v) and the time back is d/(c+v).  The total time is therefore 2*d*c/(c2-v2).  If one were to swim across the river and back (a total distance of 2*d as in Figure 2) the total time would be 2*d/sqrt(c2-v2).  Take the first time over the second time.  One gets t1/t2 = c/sqrt(c2-v2).  Therefore t1 = t2/sqrt(1-v2/c2).  These two times to go the same distance are only equal if v = 0.  They are pretty much the same as long as v<<c.  Notice how if v is not equal to 0 it will always take longer for the swimmer to travel up and down than left and right.

    There are a number of paradoxes generated by special relativity, such as: the pole vaulter, twin, faster than light travel, and instant messaging. The pole vaulter paradox is one of sizes and causality. As a pole vaulter is traveling very fast, he enters a barn and burst through the front door. To an outside observer, it appears that the pole (which is longer than the length of the barn) is completely enclosed in the barn.  However, to the pole vaulter though, the barn appears half as long, and the back door opened before the front door. This seems illogical, but when considering that the light from the doors takes longer to reach people than the time for the doors to close, all is clarified. The closing of the front door is independent of the back doors opening (if the speed of light is the ultimate speed in existence).

   While the pole vaulter paradox may seem odd, the next one (the twin paradox) is the most commonly discussed. One twin waits on Earth, while the other travels on a relativistic space craft. Both twins will see each other’s clocks dilate at the same rate. Despite the slowdown of the clocks, each twin cannot think that the other has aged less. This situation is the paradox.

    As for faster than light travel, it is possible for a moving inertial frame that an event can precede its cause.  Many physicists like to take the easy way out by ruling out faster than light travel, rather than trying to find the “how to go this fast.”  Instant messaging is quite simply a loop concept of people receiving data that can go on forever.  It is very confusing, so a wave function collapse may help to explain it.  I rule out FTL in another write-up.

    With all of these paradoxes, special relativity may seem to be discredited, but the experimental evidence it almost flawless. The Michelson-Morley experiment splits a beam of light into two, and then recombines the beams.  Velocity doesn’t change at any point in this process. Relativistic particles and Doppler shifts also have helped to support special relativity. Cerenkov radiation occurs when something moves faster through a substance than light would. A light boom follows, releasing radiation perpendicular to the applied object.  This radiation is consistent with the theory.

    Searches for faster than light particles (Tachyons) have not yet been proven successful.  If they were real, they would not have the time properties expected. 

     Relativistic rockets are the next subject, and with an acceleration of 1g, it is quite possible for a human to circumnavigate the universe in one working lifetime.  In terms of the photon rocket, it is possible to build, but would be incredibly difficult.  A last note is that special relativity doesn’t allow for faster than light travel.


Fraction of light speed

Amount of time that passes in one year