The Viking spacecraft arrived at Mars in the summer of 1976 and passed through superior conjunction on November 25, as Mars passed directly behind the Sun as seen from Earth. This provided researchers the opportunity to use the spacecraft in an experiment to test general relativity.
This image shows the surface of Mars looking across the Viking 2 Lander. (Source: NASA)
After completing the primary missions, the Viking continuation mission objectives included a radio science solar conjunction relativity experiment. Scientists began an experiment that used the landers and orbiters as transponders, sending radio signals to the lander on Mars and instructing the lander to the return signals. The round-trip travel times of the radio signals going from Earth to the Viking landers and orbiters were measured.
Using dual-band, one-way ranging allowed estimation of the contribution of the solar-corona plasma to the echo delays obtained from ranging to the spacecraft.
The data confirmed the Shapiro time delay effect, which states that radar signals passing near a massive object take slightly longer to travel to a target and longer to return than they would if the mass of the object were not present.
Published by Albert Einstein in 1916, the general theory of relativity predicted that the round-trip or echo delays of light signals traveling between the Earth and Mars would be increased by the direct effect of solar gravity. The theory included gravitational time dilation, where time passes differently in regions of different gravitational potential.
NASA has continued to test general relativity, most recently with the Cassini space probe (see a NASA artist rending of its testing at right) and Gravity Probe B, which also confirmed the theory.
For more moments in tech history, see this blog. EDN strives to be historically accurate with these postings. Should you see an error, please notify us.
Editor’s note: This article was originally posted on November 25, 2013 and edited on November 25, 2019.
Gravity On Mars: Help Or Hindrance In Colonization?
23rd Nov 2023
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Gravity is a fundamental characteristic of planets and other celestial bodies that has a significant impact on life and physical phenomena. In the next decade, humanity is going to colonize the Moon, and after that, the Red Planet. In this article, we will explore gravity on Mars and its impact on humans. But first, let’s define the concept itself.
What Is Gravity?
Gravity (from the Latin gravis, “heavy”) is the universal fundamental interaction between material bodies with mass. In other words, any matter has a gravitational attraction that is proportional to its mass and distance to it. The greater the mass of an object and the closer it is, the greater its gravitational force.
Since the Earth is the most massive object near us (1.317e+25 pounds), all bodies and objects are attracted to it. For example, apples fall to the ground instead of getting attracted to a person’s head. The apple that fell on Newton’s head still fell to the ground later. The gravitational force with which the Earth attracts other bodies to itself is called gravity. The force of gravity is measured by the formula: F = m ⋅ g, where ‘m’ is the mass of the body, and ‘g’ is the gravitational acceleration — a uniformly accelerated motion that all bodies acquire in a vacuum under the influence of gravity near the surface, regardless of their mass.
Free fall acceleration on the Earth’s surface is a constant value that equals 9.8 m/s². This means that when a body is in a free fall, its speed changes by 9.8 m/s in one second. If a body moves vertically upward, its speed decreases by 9.8 m/s in 1 second. If the body moves vertically downward, then the speed increases by 9.8 m/s in 1 second. The gravitational acceleration experienced on the surface of an astronomical or other object is also called surface gravity. So, let’s learn what the surface gravity of Mars is.
How Does Gravity On Mars Compare To Earth, Moon And Venus?
How to calculate your weight on other planets.
If we take g on Earth as 100%, then on Venus, the surface gravity will be 91%, on the Moon — 16.6%, and on Mars — 38%. That is, if you weigh, say, 200 pounds on Earth, then on Venus you would weigh 182 pounds, on Mars — 76 pounds, and on the Moon only — 38! Remember how easily the Apollo astronauts jumped on the Moon even though their spacesuits weighed 130 pounds!
Why Is Mars’ Gravity So Low?
Gravity on different planets and moons depends on their mass and radius square. The greater the mass of the planet and the closer you are to its centre, the stronger the gravity and vice versa. Astronomical objects have different masses and radii, so their g value is also different.
The mass of Mars is approximately 0.107 that of Earth, or approximately 1.523 x 10^23 pounds. The radius of Mars is 2,106 miles, which is almost half that of Earth (3,959 miles). That’s why Mars’s surface gravity is so low.
Would You Fall Faster On Mars?
Since the acceleration of gravity on Mars is almost three times less than on Earth, you might think that you will fall to the Red Planet much more slowly because the gravity of Mars will not pull you as strongly as the Earth’s gravity. But let’s recall that the acceleration of gravity is calculated for bodies in a vacuum and does not take into account the height of the fall and… air resistance. The density of the Martian atmosphere is only 20 grams per cubic meter, which is 61 times less than the density of the Earth’s atmosphere (1.225 kilograms per cubic meter). In other words, the atmospheric resistance on Mars is so low that your final fall speed will be over five times higher than on Earth. Future colonists will need to carefully consider the design of the ship so that it does not crash on the surface at landing.
Is There Enough Gravity On Mars To Walk?
Yes. Even though on Mars, you will weigh almost three times less than on Earth, this disadvantage will be compensated by the spacesuit weight. Neil Armstrong and Buzz Aldrin walked on the Moon with ease, even though there was even less gravity there. In general, you don’t need to be afraid. You’ll have your feet firmly planted on the Red Planet’s surface, and the only thing you’ll need to watch out for is where you step.
Could I Run Faster On Mars?
Running on Mars. Credit: adme.media
In theory — yes, but there are some other factors to consider. On Earth, marathon speed is 6 miles, and the maximum speed that professional runners can achieve is 27 miles! If we compare gravity on Mars and Earth, then these indicators can be multiplied by 2.7 times. However, on Mars, you won’t be able to run in shorts, a T-shirt, and Nike Air Jordans! There, you will have a heavy spacesuit and boots, protecting you from the harsh conditions of the Martian atmosphere and landscape.
As soon as you step on the surface of the Red Planet, you will see it for yourself! The surface is covered with rust-coloured dust. The dust layer thickness may vary in different places, but on average, it is about two metres! The same fine dust flies in the air, occasionally creating dust storms, the most powerful of which can even be seen from Earth. Let’s agree, this can make running so much more difficult.
Is Mars Gravity Survivable?
Mars colony, concept Credit: Getty Images/e71lena
Let’s imagine that we landed safely and even managed to walk on the surface of the Red Planet. Can you survive on Mars in low gravity? Of course, it won’t kill you instantly, but it can have long-term health effects such as bone loss, muscle atrophy, cardiovascular problems, vision problems, and swelling. Astronauts face most of these problems after a long stay on the ISS, and yet, the gravity there is only 12% lower than Earth’s. By the way, read how space medicine fights low-gravity disease.
All in all, to survive on Mars, you will have to try very hard. Astronauts going to Mars will have to exercise regularly and take extra measures to maintain their physical health; technicians and engineers will have to develop special spacesuits that minimize the effect Mars gravity has on humans, as well as create residential complexes with life support systems that replicate terrestrial living conditions to a maximum.
Conclusion
So, we found out that Mars’s gravity is lower than Earth’s, but it allows people to survive and carry out basic vital activities. But there are a couple of nuances. Studying the effects of low gravity on human health and capabilities is an important goal for future missions to Mars and long-term housing on this planet.
Sources:
Kenneth L. Nordtvedt, Alan H. Cook, James E. Faller. “Gravity | Definition, Physics, & Facts”https://www.britannica.com/science/gravity-physics
NASA science. Mars facts.https://mars.nasa.gov/all-about-mars/facts
Here’s How Fast You Could Run on Other Planetshttps://brightside.me/articles/heres-how-fast-you-could-run-on-other-planets-813714/
Chris Denzel. “Gravitational Factors of Our Eight Planets” 2020https://sciencing.com/gravitational-factors-eight-planets-8439815.html
por II Shapiro · 1977 · Mencionado por 117 — Measurements of the round-trip time of flight of radio signals transmitted from the earth to the Viking spacecraft are being analyzed to test the predictions ...
22 oct 2024 — The predicted general relativistic effect of solar gravity on the round-trip times of electromagnetic signals traveling between earth and Mars ...
por RD Reasenberg · 1979 · Mencionado por 742 — Abstract. Analysis of 14 months of data obtained from radio ranging to the Viking spacecraft verified, to an estimated accuracy of 0.1%, the prediction of ...
por RD Reasenberg · 1982 · Mencionado por 4 — The predicted general relativistic effect of solar gravity on the round-trip times of electromagnetic signals traveling between Earth and Mars has been ...
por RD Reasenberg · 1979 · Mencionado por 742 — Printed in U.S.A. VIKING RELATIVITY EXPERIMENT: VERIFICATION OF SIGNAL RETARDATION BY SOLAR GRAVITY R. D. REASENBERG, I. I. SHAPIRO, P. E. MACNEIL, AND ...
21 nov 2024 — Measurements of the round-trip time of flight of radio signals transmitted from the earth to the Viking spacecraft are being analyzed to test ...
por RD Reasenberg · 1982 · Mencionado por 4 — New results from the Viking relativity experiment The predicted general relativistic effect of solar gravity on the round-trip times of electromagnetic ...
por II Shapiro · 1977 · Mencionado por 117 — Abstract. Measurements of the round-trip time of flight of radio signals transmitted from the earth to the Viking spacecraft are being analyzed ...
25 nov 1976 — The theory included gravitational time dilation, where time passes differently in regions of different gravitational potential. NASA has ...
Analysis of 14 months of data obtained from radio ranging to the Viking spacecraft verified, to an estimated accuracy of 0.1%, the prediction of the general theory of relativity that the round-trip times of light signals traveling between the earth and Mars are increased by the direct effect of solar gravity. The corresponding value for the metric parameter gamma is 1.000 plus or minus 0.002, where the quoted uncertainty, twice the formal standard deviation, allows for possible systematic errors.
Describe how Einsteinian gravity slows clocks and can decrease a light wave’s frequency of oscillation
Recognize that the gravitational decrease in a light wave’s frequency is compensated by an increase in the light wave’s wavelength—the so-called gravitational redshift—so that the light continues to travel at constant speed
General relativity theory makes various predictions about the behavior of space and time. One of these predictions, put in everyday terms, is that the stronger the gravity, the slower the pace of time. Such a statement goes very much counter to our intuitive sense of time as a flow that we all share. Time has always seemed the most democratic of concepts: all of us, regardless of wealth or status, appear to move together from the cradle to the grave in the great current of time.
But Einstein argued that it only seems this way to us because all humans so far have lived and died in the gravitational environment of Earth. We have had no chance to test the idea that the pace of time might depend on the strength of gravity, because we have not experienced radically different gravities. Moreover, the differences in the flow of time are extremely small until truly large masses are involved. Nevertheless, Einstein’s prediction has now been tested, both on Earth and in space.
The Tests of Time
An ingenious experiment in 1959 used the most accurate atomic clock known to compare time measurements on the ground floor and the top floor of the physics building at Harvard University. For a clock, the experimenters used the frequency (the number of cycles per second) of gamma rays emitted by radioactive cobalt. Einstein’s theory predicts that such a cobalt clock on the ground floor, being a bit closer to Earth’s center of gravity, should run very slightly slower than the same clock on the top floor. This is precisely what the experiments observed. Later, atomic clocks were taken up in high-flying aircraft and even on one of the Gemini space flights. In each case, the clocks farther from Earth ran a bit faster. While in 1959 it didn’t matter much if the clock at the top of the building ran faster than the clock in the basement, today that effect is highly relevant. Every smartphone or device that synchronizes with a GPS must correct for this (as we will see in the next section) since the clocks on satellites will run faster than clocks on Earth.
The effect is more pronounced if the gravity involved is the Sun’s and not Earth’s. If stronger gravity slows the pace of time, then it will take longer for a light or radio wave that passes very near the edge of the Sun to reach Earth than we would expect on the basis of Newton’s law of gravity. (It takes longer because spacetime is curved in the vicinity of the Sun.) The smaller the distance between the ray of light and the edge of the Sun at closest approach, the longer will be the delay in the arrival time.
In November 1976, when the two Viking spacecraft were operating on the surface of Mars, the planet went behind the Sun as seen from Earth as shown in Figure 1. Scientists had preprogrammed Viking to send a radio wave toward Earth that would go extremely close to the outer regions of the Sun. According to general relativity, there would be a delay because the radio wave would be passing through a region where time ran more slowly. The experiment was able to confirm Einstein’s theory to within 0.1%.
Time Delays for Radio Waves near the Sun.
Figure 1. Radio signals from the Viking lander on Mars were delayed when they passed near the Sun, where spacetime is curved relatively strongly. In this picture, spacetime is pictured as a two-dimensional rubber sheet.
Gravitational Redshift
What does it mean to say that time runs more slowly? When light emerges from a region of strong gravity where time slows down, the light experiences a change in its frequency and wavelength. To understand what happens, let’s recall that a wave of light is a repeating phenomenon—crest follows crest with great regularity. In this sense, each light wave is a little clock, keeping time with its wave cycle. If stronger gravity slows down the pace of time (relative to an outside observer), then the rate at which crest follows crest must be correspondingly slower—that is, the waves become less frequent.
To maintain constant light speed (the key postulate in Einstein’s theories of special and general relativity), the lower frequency must be compensated by a longer wavelength. This kind of increase in wavelength (when caused by the motion of the source) is what we called a redshift in Radiation and Spectra. Here, because it is gravity and not motion that produces the longer wavelengths, we call the effect a gravitational redshift.
The advent of space-age technology made it possible to measure gravitational redshift with very high accuracy. In the mid-1970s, a hydrogen maser, a device akin to a laser that produces a microwave radio signal at a particular wavelength, was carried by a rocket to an altitude of 10,000 kilometers. Instruments on the ground were used to compare the frequency of the signal emitted by the rocket-borne maser with that from a similar maser on Earth. The experiment showed that the stronger gravitational field at Earth’s surface really did slow the flow of time relative to that measured by the maser in the rocket. The observed effect matched the predictions of general relativity to within a few parts in 100,000.
These are only a few examples of tests that have confirmed the predictions of general relativity. Today, general relativity is accepted as our best description of gravity and is used by astronomers and physicists to understand the behavior of the centers of galaxies, the beginning of the universe, and the subject with which we began this chapter—the death of truly massive stars.
Relativity: A Practical Application
By now you may be asking: why should I be bothered with relativity? Can’t I live my life perfectly well without it? The answer is you can’t. Every time a pilot lands an airplane or you use a GPS to determine where you are on a drive or hike in the back country, you (or at least your GPS-enabled device) must take the effects of both general and special relativity into account.
GPS relies on an array of 24 satellites orbiting the Earth, and at least 4 of them are visible from any spot on Earth. Each satellite carries a precise atomic clock. Your GPS receiver detects the signals from those satellites that are overhead and calculates your position based on the time that it has taken those signals to reach you. Suppose you want to know where you are within 50 feet (GPS devices can actually do much better than this). Since it takes only 50 billionths of a second for light to travel 50 feet, the clocks on the satellites must be synchronized to at least this accuracy—and relativistic effects must therefore be taken into account.
The clocks on the satellites are orbiting Earth at a speed of 14,000 kilometers per hour and are moving much faster than clocks on the surface of Earth. According to Einstein’s theory of relativity, the clocks on the satellites are ticking more slowly than Earth-based clocks by about 7 millionths of a second per day. (We have not discussed the special theory of relativity, which deals with changes when objects move very fast, so you’ll have to take our word for this part.)
The orbits of the satellites are 20,000 kilometers above Earth, where gravity is about four times weaker than at Earth’s surface. General relativity says that the orbiting clocks should tick about 45 millionths of a second faster than they would on Earth. The net effect is that the time on a satellite clock advances by about 38 microseconds per day. If these relativistic effects were not taken into account, navigational errors would start to add up and positions would be off by about 7 miles in only a single day.
Key Concepts and Summary
General relativity predicts that the stronger the gravity, the more slowly time must run. Experiments on Earth and with spacecraft have confirmed this prediction with remarkable accuracy. When light or other radiation emerges from a compact smaller remnant, such as a white dwarf or neutron star, it shows a gravitational redshift due to the slowing of time.
Glossary
gravitational redshift
an increase in wavelength of an electromagnetic wave (light) when propagating from or near a massive object
La sonda Viking llegó a Marte en el verano de 1976 y atravesó una conjunción superior el 25 de noviembre, cuando Marte pasó directamente detrás del Sol visto desde la Tierra. Esto brindó a los investigadores la oportunidad de utilizar la sonda en un experimento para probar la relatividad general.
Esta imagen muestra la superficie de Marte vista desde el módulo de aterrizaje Viking 2. (Fuente: NASA)
Después de completar las misiones principales, los objetivos de la misión de continuación de Viking incluyeron un experimento de radiociencia de relatividad de conjunción solar. Los científicos comenzaron un experimento que utilizó los módulos de aterrizaje y los orbitadores como transpondedores, enviando señales de radio al módulo de aterrizaje en Marte y dando instrucciones al módulo de aterrizaje para que respondiera las señales. Se midieron los tiempos de viaje de ida y vuelta de las señales de radio que iban desde la Tierra hasta los módulos de aterrizaje y los orbitadores Viking.
El uso de medición de distancia unidireccional de banda dual permitió estimar la contribución del plasma de la corona solar a los retrasos del eco obtenidos a partir de la medición de distancia a la nave espacial.
Los datos confirmaron el efecto de retardo temporal de Shapiro, que establece que las señales de radar que pasan cerca de un objeto masivo tardan ligeramente más en viajar hasta un objetivo y más tiempo en regresar que si la masa del objeto no estuviera presente.
Publicada por Albert Einstein en 1916, la teoría general de la relatividad predijo que los retrasos de ida y vuelta o ecos de las señales de luz que viajan entre la Tierra y Marte se verían incrementados por el efecto directo de la gravedad solar. La teoría incluía la dilatación del tiempo gravitacional, según la cual el tiempo transcurre de manera diferente en regiones con diferente potencial gravitacional.
La NASA ha seguido poniendo a prueba la relatividad general, más recientemente con la sonda espacial Cassini (ver una representación artística de la NASA de sus pruebas a la derecha ) y con Gravity Probe B, que también confirmó la teoría.
Para conocer más momentos de la historia de la tecnología, consulte este blog . EDN se esfuerza por ser históricamente preciso en estas publicaciones. Si ve algún error, notifíquenoslo .
Nota del editor : este artículo se publicó originalmente el 25 de noviembre de 2013 y se editó el 25 de noviembre de 2019.
Recreación artística del efecto de la gravedad del Sol en la señales procedentes de la sonda Cassini.
El efecto Shapiro, llamado así en honor del físico Irwin Shapiro (no confundir con el físico Stuart Louis Shapiro), es un efecto resultante de la relatividad general según el cual el tiempo de llegada de una señal que se propaga en el espacio se ve afectado por la presencia de materia en su cercanía. Este efecto es la doble combinación del hecho de que la señal observada ya no se propaga en línea recta —y, por lo tanto, recorre un camino más largo de lo que sería en ausencia de masa en su proximidad— y de que el transcurso del tiempo se ve afectado por la presencia de masa.
El efecto Shapiro es un efecto elemental de la relatividad general, pero al contrario que otros efectos de este tipo —refracción de la luz, precesión del periastro, corrimiento al rojo gravitacional— no se predijo en el momento del descubrimiento de la relatividad general, alrededor de 1915, sino cerca de cincuenta años más tarde, por Irwin Shapiro en 1964.1
El efecto Shapiro —dilatación gravitacional de desfases temporales— consiste en un retraso en los tiempos de llegada de los fotones que pasan cerca del Sol. Por tanto, no solo la trayectoria de la luz es desviada por el campo gravitatorio solar, sino que los fotones también son frenados.
Este efecto, nada despreciable, fue calculado y observado por primera vez por Shapiro en 1964. Su experiencia consistió en medir el tiempo de ida y vuelta de la Tierra a Mercurio de fotones de radio emitidos en nuestro planeta cuando su recorrido era próximo a la superficie solar. El menor o mayor tiempo para atravesar dicho campo está relacionado con las distancias relativas de la Tierra y Mercurio respecto al Sol.
El efecto Shapiro se puede medir en el sistema solar, especialmente mediante el estudio de los tiempos de llegada de las señales emitidas por una sonda posada en otro planeta. La primera constatación precisa de la medida del efecto Shapiro fue hecha por las sondas Viking que aterrizaron en Marte.2 Anteriormente, el efecto Shapiro se había detectado mediante el estudio del eco radar emitido desde la Tierra y reflejado en otro planeta.3 Este primer método era relativamente impreciso porque el eco recibido era extremadamente débil (10-21W para una señal emitida de 300 kW) y por el hecho de que la superficie del planeta sobre el que se reflejaba la señal era relativamente grande. A la inversa, las señales emitidas desde una sonda en un planeta eran mucho más precisas, pero con un coste considerablemente mayor, ya que requerían el envío de dicha nave espacial a un planeta.4
También se puede detectar en un púlsar binario, donde la emisión pulsátil extremadamente regular del púlsar es modulada por el efecto Shapiro como consecuencia del desplazamiento del púlsar alrededor de su compañera. En este caso, al ser el efecto directamente proporcional a la masa de la compañera del púlsar, permite determinar la masa de este bajo determinadas condiciones. Este efecto relativista, que permite determinar la masa de una o de ambas estrellas componentes conociendo los detalles de la órbita de un sistema binario, forma parte de los parámetros post keplerianos. El efecto Shapiro en un púlsar binario fue detectado por primera vez en PSR B1913+16, en 1984,5 y unos años más tarde en PSR B1534+12 de manera mucho más convincente.
*Does not include Crossword-only or Cooking-only subscribers.
About the Archive
This is a digitized version of an article from The Times’s print archive, before the start of online publication in 1996. To preserve these articles as they originally appeared, The Times does not alter, edit or update them.
Occasionally the digitization process introduces transcription errors or other problems; we are continuing to work to improve these archived versions.
The most accurate long‐distance measurements ever made, by means of radio signals between the Viking spacecraft on Mars and antennas on Earth, have produced new confirmation of Einstein's theory of relativity, a Viking project scientist reported yesterday.
The measurement was so incredibly precise, according to Dr. Irwin I. Shapiro of the Massachusetts Institute of Technology, that the “uncertainty” over span of 200 million miles was less than five feet—that is, an accuracy of five parts in 10 million millionths.
Dr. Shapiro and his colleagues on the Viking radio science team went to such pains to see if, as Einstein predicted, the sun's gravitational force bends and delays radio signals (or any form of radiation) as they travel particularly close to such a massive body.
Estimated Delay of Waves
And it did. Dr. Shapiro believes that, after further. analysis, the Viking experiment will show that the delay in the travel time of the radio waves caused by the sun's gravity was close to calculations (a delay of 200 millionths of a second) based on Einstein's theory.
Results of the experiment were reported at a news conference held at the Jet Propulsion Laboratory in Pasadena, Calif. The Viking 1 and 2 spacecraft are being controlled there.
The experiment was conducted last Nov. 25, Thanksgiving Day, at the time of solar conjunction. At that time, Mars moved behind the sun in relation to Earth, causing a total blackout of communications between the Vikings and Earth.
But just before and after the blackout, radio signals were transmitted from antennaes at Goldstone, Calif., and Canberra, Australia, to both of the Viking orbiters and landers and then from the spacecraft back to Earth. The round‐trip travel times of the signals were carefully clocked. The transmissions were repeated frequently to check for accuracy.
The results, Dr. Shapiro said, were “in very good agreement with the theory of general relativity.”
Not that he expected to prove Einstein wrong. Previous tests using spacecraft communications systems tended to confirm the theory, but the Viking test is considered twice as accurate, or more, than the previous ones.
In a telephone interview after the conference, Dr. Shapiro said:
“I would have been very surprised Einstein was wrong. But one just can't take theories for granted. Physics is an experimental approach to nature. Einstein came along to explain deviations in Newton's theory of gravity. And at some level of probing we may find Einstein's theory will break down and no longer be a totally adequate theory of the way nature behaves.”
Knowledge of gravitation is essential to the understanding of elementary particles, quasars and neutron stars and the very destiny of the universe—whether will go on expanding or eventually collapse on itself.
Possible Seismic Event on Mars
Other scientists reported at the news conference on a possible Martian seismic event recorded by the Viking 2 lander, the distinct day‐night differences of wind conditions at the Viking 2 site and heavy build‐up of clouds over the polar regions in recent weeks.
Dr. Donald L. Anderson of the California Institute of Technology, leader of the Viking seismology team, said that the Viking 2 lender's seismometer detected “an unusual event” in mid‐November. If it was a seismic tremor, it would be the first marsquake recorded by manmade instruments and, according to Dr. Anderson, must have occurred about 4,000 miles away from the landing site and been of a magnitude of six or more on the Richter scale, which is a major tremor on Earth.
Whatever it was, Dr. Anderson said, it occurred in the evening when the Martian winds that sometimes shake the spacecraft had died down and when vibration‐producing activity on board the spacecraft was at a minimum.
Tema anterior
A report, “Viking relativity experiment: verification of signal retardation by solar gravity” published in 1979 by researchers at MIT and the Jet Propulsion Laboratory, analyzed 14 months of data obtained from radio ranging to Viking to verify the prediction of the general theory of relativity.
How to calculate your weight on other planets.
Running on Mars. Credit: adme.media
Mars colony, concept Credit: Getty Images/e71lena
![Time Delays for Radio Waves near the Sun. The curvature of spacetime near the Sun is shown in this diagram with the Sun at the bottom of a sag (similar to that illustrated in Figure 24_03_Spacetime]). The Viking spacecraft is at upper right, the Earth is at lower left and the Sun is between the two. The radio signal from Viking is drawn as a red arrow that goes down into the “sag”, and back out on its way to Earth, thus travelling a greater distance than if the Sun were not there.](https://pressbooks.bccampus.ca/astronomy1105/wp-content/uploads/sites/235/2017/08/OSC_Astro_24_05_Waves-1.jpg)
Figure 1. Radio signals from the Viking lander on Mars were delayed when they passed near the Sun, where spacetime is curved relatively strongly. In this picture, spacetime is pictured as a two-dimensional rubber sheet. 
