In: Physics
1) Because of the mass involved in constructing and transporting a lander, the first human expedition to Mars will likely be an orbital mission. A geosynchronous orbit seems plausible, allowing astronauts in the spacecraft to have continuous line-of-sight control of rovers on the surface. What is the altitude above the surface of Mars for geosynchronous orbit? You’ll need to do some research to find the mass of Mars and its rotation period.
2) Using the expression for the escape velocity from a
planet.
a) Describe the physics that went into your derivation of the
escape velocity and list the formula again.
b) Use this formula to calculate the escape velocity of Mars and
compare it with Earth. List the sources where you obtained the
properties of each planet for your calculation.
c) What insight might you glean from the above calculation on why
Mars has a thinner atmosphere than the Earth?
3) Assuming that the outer planets (Saturn, Uranus, and Neptune) are in equilibrium with the solar radiation, calculate the effective surface temperature of these 3 planets and show all intermediate steps. You can assume albedos of 0.5, 0.6, and 0.6, for Saturn, Uranus, and Neptune, respectively. The solar luminosity is 3.83 x 1026 W. How do these temperatures compare with their observed temperatures?
ONE QUESTION A TIME PLEASE AS PER THE RULES AND GUIDELINES...
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From the web, the rotation period of mars is 24 hours 37 minutes which is equal to 88620 seconds
Mass of mars = 0.642e24 Kg
From kepler's law
T2 = (42 / GM)r3
r3 = GMT2 / 42
r3 = 6.67e-11*0.642e24* 886202 / 42
r3 = 8.5185e21
r = 2.042e7 m
r = 20420 Km
This includes radius of mars, so we need to subtract
Therefore, altitude of geosynchronous orbit above mars = 20420 Km - 3396 Km = 17024 Km
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equating kinetic energy and potential work
1/2mv2 = GMm / R
escape velocity is given as
v = sqrt (2GM / R)
where M is mass and R is radius of body.
escape velocity of mars, v = sqrt (2*6.67e-11*0.642e24 / 3396000)
v = 5.02 Km/s
The escape velocity from earth = 11.2 Km/s which is more than mars's