Answer:
The radius of orbit=[tex]2.49\times 10^7 m[/tex]
Explanation:
We are given that
Orbital speed=[tex]4.00\times 10^3[/tex]m/s
We have to find the radius of orbit of spacecraft.
We know that
Gravitational constant=[tex]6.67\times 10^{-11}m^3/kgs^2[/tex]
Mass of earth=[tex]5.972\times 10^{24} kg[/tex]
Orbital speed=[tex]\sqrt{\frac{GM}{r}}[/tex]
Where G= Gravitational constant
M=Mass of earth
r=Radius of orbit
Substitute the values in the formula
[tex]4\times 10^3=\sqrt{\frac{6.67\times 10^{-11}\times 5.972\times 10^{24}}{r}[/tex]
Squaring on both sides
[tex]16\times 10^6=\frac{6.67\times 10^{-11}\times 5.972\times 10^{24}}{r}[/tex]
[tex]r=\frac{6.67\times 10^{-11}\times 5.972\times 10^{24}}{16\times 10^6}[/tex]
[tex]r=2.49\times 10^7 m[/tex]
Hence, the radius of orbit=[tex]2.49\times 10^7 m[/tex]
