Physics, 24.12.2019 17:31 Jenniferojeda2002

The mean diameters of mars and earth are 6.9 ✕ 103 km and 1.3 ✕ 104 km, respectively. the mass of mars is 0.11 times earth's mass.

(a) what is the ratio of the mean density of mars to that of earth?
(b) what is the value of g on mars? m/s2
(c) what is the escape speed on mars? m/s2

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Answer from: 12huskiesmidnight

(a) Ratio of mean density is 0.735

(b) Value of g on mars 0.920 m,/sec^2

Explanation:

We have given radius of mars $R_{mars}=6.9\times 10^3km=6.9\times 10^6m$ and radius of earth $R_{E}=1.3\times 10^4km=1.3\times 10^7m$

Mass of earth $M_E=5.972\times 10^{24}kg$

So mass of mars $M_m=5.972\times\times 0.11 \times 10^{24}=0.657\times 10^{24}kg$

Volume of mars $V=\frac{4}{3}\pi R^3=\frac{4}{3}\times 3.14\times (6.9\times 10^6)^3=1375.357\times 10^{18}m^3$

So density of mars $d_{mars}=\frac{mass}{volume}=\frac{0.657\times 10^{24}}{1375.357\times 10^{18}}=477.69kg/m^3$

Volume of earth $V=\frac{4}{3}\pi R^3=\frac{4}{3}\times 3.14\times (1.3\times 10^7)^3=9.198\times 10^{21}m^3$

So density of earth $d_{E}=\frac{mass}{volume}=\frac{5.972\times 10^{24}}{9.198\times 10^{21}}=649.271kg/m^3$

(A) So the ratio of mean density $\frac{d_{mars}}{d_E}=\frac{477.69}{649.27}=0.735$

(B) Value of g on mars

g is given by $g=\frac{GM}{R^2}=\frac{6.67\times 10^{-11}\times0.657\times 10^{24}}{(6.9\times 10^6)^2}=0.920m/sec^2$

$v=\sqrt{\frac{2GM}{R}}=\sqrt{\frac{2\times 6.67\times 10^{-11}\times 0.657\times 10^{24}}{6.9\times 10^6}}=3.563\times 10^4m/sec$

Answer from: penelope0

(a) 0.72

(b) 3.83 m/s^2

Explanation:

diameter of Mars = 6.9 x 10^3 km

Radius of Mars, Rm = 3.45 x 10^3 km = 3.45 x 10^6 m

diameter of earth = 1.3 x 10^4 km

radius of earth, Re = 6.5 x 10^3 km = 6.5 x 10^6 m

Let Me be the mass of earth.

Mass of Mars, Mm = 0.11 Me

(a) Volume of Mars, Vm = 4/3 x 3.14 x (3.45 x 10^6)³ = 1.72 x 10^20 m³

Volume of earth, Ve = 4/3 x 3.14 x (6.5 x 10^6)³ = 1.15 x 10^21 m³

density is the ratio of mass to the volume of the object.

$\frac{d_{m}}{d_{e}}=\frac{M_{m}}{M_{e}}\times \frac{V_{e}}{V_{m}}$

$\frac{d_{m}}{d_{e}}=\frac{0.11M_{e}}{M_{e}}\times \frac{1.15\times10^{21}}{1.72\times10^{20}}$

density of mars : density of earth = 0.72

(b) The value of acceleration due to gravity

$g=\frac{GM}{R^{2}}$

Let gm be the acceleration due to gravity on Mars

$\frac{g_{m}}{g_{e}}=\frac{M_{m}}{M_{e}}\times \frac{R_{e}^{2}}{R_{m}^{2}}$

$\frac{g_{m}}{g_{e}}=\frac{0.11M_{e}}{M_{e}}\times \frac{6.5\times6.5}{3.45\times3.45}$

gm = 3.83 m/s^2

$v=\sqrt{2gR}$

$\frac{v_{m}}{v_{e}}=\sqrt{\frac{g_{m}\times R_{m}}{g_{e}\times R_{e}}}$

$\frac{v_{m}}{v_{e}}=\sqrt{\frac{3.83\times 3.45}{9.8\times 6.5}}$

escape velocity for mars = 5.1 Km/s

Answer from: Quest

Neptune is the eighth planet from the sun. it was the first planet to get its existence predicted by mathematical calculations before it was actually seen through a telescope on sept. 23, 1846. irregularities in the orbit of uranus led french astronomer alexis bouvard to suggest that the gravitational pull from another celestial body might be responsible. german astronomer johann galle then relied on subsequent calculations to spot neptune via telescope. previously, astronomer galileo galilei sketched the planet, but he mistook it for a star due to its slow motion. in accordance with all the other planets seen in the sky, this new world was given a name from greek and roman mythology — neptune, the roman god of the sea.

Answer from: Quest

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The mean diameters of mars and earth are 6.9 ✕ 103 km and 1.3 ✕ 104 km, respectively. the mass of ma...

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