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---------------------- 2276 - MARS - Forth Rock from the Sun
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- On August 27, 2003, Mars was the closest to the third rock, Earth, as it has been in the last 60,000 years. Mars will be only 34,649,589 miles away. The last time it was that close homo sapiens, sapiens subspecies were the only surviving humanoid on Earth, just before these humans crossed the ice bridge over the Bering Straits into North America.
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- Mar’s closeness on this orbit is caused by the slightly elliptical orbit Mar’s has due to the gravity of Jupiter. The average separation is 140 million miles, so 35 million miles brings our neighbor unusually close.
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- Mars is only one tenth the mass of the Earth while having a diameter about half as large as that of Earth. Therefore the density of Mars is much less than Earth’s, 3,900 kilograms / meter^3 compared to 5,500 kilograms / meter^3. Since ordinary rock is typically 3,500 kilograms / meter^3 we can conclude that Mars does not have an iron core like the Earth has.
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- Each terrestrial planet has a core which is mostly iron and nickel, a mantle, which is denser rock, and a crust, which is lighter rock. The upper mantel and crust is called the lithosphere. The internal temperature of the planet plays a major role in determining the thickness of the lithosphere, or crust. Hot planets have thin crust, like the Earth. Cooler planets have thick crusts, like Mars. If the crust is very thick, volcanoes will never occur.
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- Mars is much smaller than the Earth and cooled much more rapidly, decreasing both the temperature and the pressure in the core. It no longer has a molten core, and therefore has no internal heat to keep the internal pressure high and to drive volcanic activity. Mar’s global magnetic field vanished and its tectonic plate activity ceased 4 billion years ago
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- How do we know the mass of Mars? How do we know its density is so much less than Earth’s? How can we conclude it has no iron core?
- Well, we measure the orbits of the moons and we do the math:
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- We use the moons of Mars to determine its mass. There are two moons orbiting Mars, Phobos and Deimos, discovered in 1877. Phobos means “fear” and Deimos means “panic“. Both are very small and potato shaped indicating that they were not formed like our Moon but are likely captured asteroids. We can use their orbits to determine the mass of Mars using Johan Kepler’s math formula.
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- Johan Kepler came up with the formula in 1609 describing the relationship between a planets period, its mass, and its distance from the Sun.
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Kepler’s 3rd law = the ratio of the square of the period and the cube of the semi-major axis of the orbit is the same for all planets. If the period is measured in years and the semi-major axis in astronomical units then the law is simply:
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----------------------------------------- Period^2 = Axis^3.
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---------------------------------------- (Years)^2 = (Au)^3
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- Converting this to meters and seconds makes the formula more complicated and adds the Gravitational Constant of proportionality.
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-------------------------- Period^2 = 4* pi^2 * axis^3 / G * ( m + M )
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--------------------------------------- M = mass of Mars
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--------------------------- Mass, m , for Deimos is negligible in this calculation
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--------------------- Gravitational Constant = G = 6.669 * 10^-11 meters^3/ kg * sec^2
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-------------------------- We need to measure the radius of Deimos’ orbit.
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- We make our measurement when Mars is opposite the Earth from the Sun. The angular distance of Deimos from Mars is measured to be 61 arcseconds.
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- To convert this angular distance into a linear distance we need to know the distance from Earth to Mars. ( The long side of the right triangle having the angle of 61 arcseconds.) That is why we made our measurements when Mars is opposite Earth from the Sun, because the distance of the Earth-Sun subtracted from Mars-Sun equals the Earth-Mars distance.
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------------------------- How do we measure the Mars-Sun distance?
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------------------------- We observe the orbit period for Mars to be 687 days.
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------------------------- Using the same Kepler formula:
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-------------------------- Period ^2 = 4 * pi^2 * radius^3 / G ( m + M )
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(To make equations easier to read all numbers are rounded off to 2 significant digits)
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------------ G is the Gravitational Constant = 6.7 * 10^-11 meters^3/ kg * sec^2
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- “M” is the mass of the Sun and “m” is the mass of Mars. Let’s first calculate the mass of the Sun, “M”
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- The mass of the Sun can be calculated knowing the orbit period of Earth:
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- The orbit period is one year and the orbit radius is one astronomical unit.
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------------------------- Period ^2 = 4 * pi * radius ^3 / G * ( m + M )
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------------------------- ( m + M ) = 4 * pi * 1 AU^3 / G * ( 1 year )^2
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- The mass of the Earth is 5.97*10^24 Kilograms, but will be negligible in our calculation.
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- ( m + M ) = 39.48 * ( 1.5 * 10^11 m)^3 / 6.669*10^-11 * ( 3.16810^7 sec )^2
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------------------------ M = 2 * 10^30 kilograms
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- The mass of Mars, “m“, can be considered negligible in this calculation. The mass of the Sun is 2 * 10^30 kilograms.
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----------------------- Period ^2 = 4 * pi * radius ^3 / G * ( m + M )
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---------------------- (690 days )^2 = 39 * radius^3 / 6.7*10^-11 * 2*10^30
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---------------------- (690 * 8.7*10^4 sec )^2 = 39 * radius^3 / 13 * 10^19
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----------------------- 3.5 * 10^15 = 3 * radius^3 / 10^19
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--------------------- radius^3 = 12 * 10^33
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----------------- Radius of the orbit of Mars = 2.3 * 10^11 meters = 229 * 10^9 meters
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----------------- The orbit for Earth can be calculated the same way = 150 * 10^9 meters.
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----------------- Subtracting we get the Earth-Mars distance = 79*10^9 meters
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- Using the small angle formula to determine the linear distance for the orbit of Deimos:
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------------------- Angle in arcseconds = 206,265 * orbit of Deimos / Earth-Mars distance
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----------------- 61 arcseconds = 206,265 * orbit of Deimos / 79 * 10^9 meters
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------------------Radius of the orbit of Deimos = 24* 10^6 meters.
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- The period of Deimos orbit is 30 hours. Now back to Kepler’s formula and we can calculate the mass of Mars.
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-------------------------- ( 30 hours )^2 = 4 * pi^2 radius^3 / G ( m + M )
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------------------------- ( 30 * 3600 sec)^2 = 39 * ( 2.4*10^7)^3 / 6.7*10^-11 * M
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- Again we are assuming the mass of Deimos is negligible compared to the mass of Mars.
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---------------------------- 120* 10^8 = 39 * 13*10^21 / 6.7*10^-11 * M
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---------------------------- 790 * 10^-3* M = 512*10^21
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--------------------------- M = .65 * 10^24 kilograms
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------------------------- The mass of Mars = 0.65 * 10^24 kilograms
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------------------------- The mass of Earth = 6.0 * 10^24 kilograms
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-------------------------- The Earth is 9 times more massive than Mars.
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------------------------ Mar’s diameter is about one half that of Earth’s = 53%
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--------------------- - Diameter of Mars = 6,794 kilometers = 53%
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--------------------- - Diameter of Earth = 12,756 kilometers
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--------------------- - Volume of Mars = 4/3 * pi * (3.393 * 10^6 meters)^3
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--------------------- - Volume of Earth = 4/3 * pi * (6.378 * 10^6 meters)^3
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--------------------- - Volume of Mars = 164 * 10^18 m^3 = 15% the volume of Earth
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--------------------- - Volume of Earth = 1087 * 10^18 m^3
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-------------------------------- Density = mass / volume
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--------------------- - Density of Mars = 3970 kg / meter^3 = 72% the density of Earth
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---------------------- Density of Earth = 5,500 kg / meter^3
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- We have learned that the density of Mars is about the same as normal rock. We can conclude that Mars has no iron core like the Earth’s. And, as a consequence, Mars has no magnetic field like the Earth’s. But, Mars once had a watery surface and volcanic activity long before the water evaporated into its thin atmosphere and the planet cooled down.
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- On the Tharsis Plateau there are several volcanoes with the largest, Olympus Mons, towering three times higher than our Mount Everest. ( 27,000 meters). The base of Olympus Mons is 600 kilometers, about the size of the state of Utah.
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- Because Mars has on iron core, or molten mantle, it has no plate tectonic activity. On Earth the hot spot under the volcano continued to move, such as that forming the Hawaiian Islands. Olympus Mons stayed stationary for millions of years and grew taller and taller.
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- Valles Marineris is a giant rift 4,000 kilometers long, 190 kilometers wide and 8 kilometers deep. This is like a giant Grand Canyon, but it was not formed by water like the Colorado River, or by plate tectonics. It was formed like a giant river bed of iron-rich clay that dried up. Cooling and shrinking crust split the planet open at the equator.
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- The atmosphere on Mars is 95% carbon dioxide, very similar proportions to the atmosphere on Venus, but much thinner. The atmospheric pressure is only 1/100 the pressure on the surface of Earth.(0.6%)
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- There is no greenhouse effect to heat the planet in such a thin atmosphere and the temperature ranges from –220 degrees to + 70 degrees Fahrenheit. Even at these temperatures liquid water would furiously boil and rapidly evaporate because the atmosphere is so thin.
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- The gravitational attraction is so low any evaporated water vapor would eventually escape into space. Only the polar ice caps, at –170 degrees Fahrenheit, contain frozen water and frozen carbon dioxide ( dry ice). However, there is a chance that liquid water could still exists deep underground on Mars.
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- If there is water there, maybe some evidence of life on Mars exists as well. What are the similarities and differences between such life and life on Earth? Significant similarities might suggest a common origin.
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- There is much more to learn about Mars. Our probes to the planet have discovered much of what we know today. Mariner 9 in 1971 was the first soft-landing on another planet. Viking Orbiter 1 in 1976, was the first craft to search for life on another planet. Mars Global Surveyor in 1997. Surveyor has mapped the planet’s surface to 330 meter resolution, and to 1 meter in elevation.
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- February 16, 2019 384 24
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-------------------------- Saturday, February 16, 2019 --------------------------
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