Artificial 57081

Determine the average speed and orbit of the Earth's first artificial satellite. Its distance from the Earth's surface in the perigee was 226 km, and in the apogee, 947 km.

Correct answer:

v =  13321.1513 m/s
T =  5.0575 min

Step-by-step explanation:

$$\begin{gathered} a=226\text{km} \\ b=976\text{km} \\ o=f(a,b) \\ o=4042.29\text{km} \\ O=\pi \cdot (a+b)=3.1416\cdot (226+976)\doteq 3776.1944\text{km} \\ {o}_2=o\to \text{m}=o\cdot 1000\text{m}=4042.29\cdot 1000\text{m}=4042290\text{m} \\ {b}_2=b\to \text{m}=b\cdot 1000\text{m}=976\cdot 1000\text{m}=976000\text{m} \\ \mu =3.986004418\cdot 10^{14}=3.986004418\cdot 10^{14}{\text{m}}^3{\text{/s}}^2 \\ {T}_1=2\pi \cdot \sqrt{b_2^3/\mu }=2\cdot 3.1416\cdot \sqrt{976000^3/3.986004418\cdot 10^{14}}\doteq 303.449\text{s} \\ v=o_2/T_1=4042290/303.449=13321.1513\text{m/s}=1.332\cdot 10^4\text{m/s} \end{gathered}$$

$T=T_1\to \text{min}=T_1:60\text{min}=303.449:60\text{min}=5.057\text{min}=5.0575\text{min}$

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