High School

A satellite has a total energy of \(-4.4 \times 10^{11}\) J. The satellite is orbiting 650 km above Earth's surface. What is the mass of the satellite? (Choose the closest answer)

A. 84,096.5 kg

B. 74,096.5 kg

C. 64,096.5 kg

D. 54,096.5 kg

E. 14,096.5 kg

Answer :

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