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A satellite has a total energy of –4.4 x 10^11 The satellite is orbiting 650 km above Earth’s surface. What is the mass of the satellite? (Choose the closest answer)



A 84096.5 kg

B 74096.5 kg

C 64096.5 kg

D 54096.5 kg

E 14096.5 kg


Sagot :

Answer:

Option E

Explanation:

As we know

[tex]m = \frac{-2RU}{GM} \\[/tex]

Where R is the radius of the orbit

G is the gravitational Constant =[tex]6.67*10^{-11}[/tex]

U is the total energy and

M is the mass of Earth [tex]= 5.98*10^{24}[/tex]

radius of earth [tex]= 6.378*10^6[/tex]

Radius of the orbit  = radius of the earth [tex]+ 650[/tex] km

Radius of the orbit (R) = [tex](6.378*10^6)+(6.5*10^5)[/tex]

Substituting the given values, we get -

[tex]m = \frac{ (2((6.378*10^6)+(6.5*10^5))(-4.4*10^{11}))}{((6.67*10^{-11})(5.98*10^{24}))}\\ = 15505.6[/tex]

Option E is the nearest answer