Answer:
r = 1.44 × [tex]10^{7}[/tex] m
Explanation:
given data
satellite to revolve = 5 time a day
G = 6.67 × [tex]10^{-11}[/tex] Nm²/kg²
Mass earth = 5.97 × [tex]10^{24}[/tex] kg
to find out
radius of its orbit
solution
first we get here Time taken for one complete revolution that is
time taken = [tex]\frac{24}{5}[/tex]
time taken = 4.8 hours
time taken = 4.8 hours × 3600 sec
time taken = 17280 sec
and
time is express as
T = 2π × [tex]\sqrt{\frac{r^3}{GM} }[/tex] .............1
put hre value we get
17280 = 2π × [tex]\sqrt{\frac{r^3}{6.67*10^{-11}*5.97*10^{24}} }[/tex]
solve it we get
r = 1.44 × [tex]10^{7}[/tex] m
The radius of its orbit will be "1.44 × 10⁷ m".
According to the question,
Satellite resolve a day = 5 times
Mass of earth, [tex]m_{earth}[/tex] = 5.97 × 10²⁴ kg
G = 6.67 × 10⁻¹¹ Nm²/kg²
Now,
The time taken will be:
T = [tex]\frac{24}{5}[/tex]
= 4.8 hours
By converting it into seconds, we get
= 4.8 × 3600
= 17280 sec
We know the formula,
→ T = 2π × [tex]\sqrt{\frac{r^3}{GM} }[/tex]
By substituting the above values, we get
17280 = 2π × [tex]\sqrt{\frac{r^3}{6.67\times 10^{-11}\times 5.97\times 10^{24}} }[/tex]
r = 1.44 × 10⁷ m
Thus the above approach is correct.
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