Respuesta :
Explanation:
Given that,
Altitude [tex]h= 2.803\times10^{6}\ m[/tex]
We need to calculate the radius
[tex]r=R+h[/tex]
Where, R = radius of the earth
h = radius of altitude
Put the value into the formula
[tex]r=(6.38\times10^{6}+2.803\times10^{6})[/tex]
[tex]r=9.18\times10^{6}\ m[/tex]
(a). We need to calculate the period of the orbit,
Using formula of period
[tex]T^2=\dfrac{4\pi^2}{GM}r^3[/tex]
[tex]T^2=\dfrac{4\pi^2}{6.67\times10^{-11}\times5.98\times10^{24}}\times(9.18\times10^{6})^3[/tex]
[tex]T^2=76570372.9509\ sec[/tex]
[tex]T=8750.45\ sec[/tex]
(b). We need to calculate the speed of the satellite
Using formula of speed
[tex]v^2=\dfrac{GM}{r}[/tex]
Put the value into the formula
[tex]v^2=\dfrac{6.67\times10^{-11}\times5.98\times10^{24}}{9.18\times10^{6}}[/tex]
[tex]v^2=43449455.3377\ m/s[/tex]
[tex]v=6.59\times10^{3}\ m/s[/tex]
(c). We need to calculate the acceleration of the satellite
Using formula of acceleration
[tex]a_{c}=\dfrac{v^2}{r}[/tex]
Put the value into the formula
[tex]a_{c}=\dfrac{(6.59\times10^{3})^2}{9.18\times10^{6}}[/tex]
[tex]a_{c}=4.73\ m/s^2[/tex]
Hence, This is the required solution.
