Cherishdisahidn
Answered

Discover new knowledge and insights with IDNLearn.com's extensive Q&A database. Join our community to access reliable and comprehensive responses to your questions from experienced professionals.

A satellite orbits at 30000km above the earth and has a velocity of 2.5km/s. Calculate its period in orbit. [radius of the earth = 6400km], leaving your answer in hours.​

Sagot :

Dashataranidn

Answer:

[tex]\large\text{$25.412$hrs}[/tex]

Explanation:

[tex]\large\text{We will use the formula to calculate the time period of the }[/tex]

[tex]\large\text{satellite:$}[/tex]

         [tex]\large\text{$T=\dfrac{2\pi r}{v}$}[/tex]

[tex]\large\text{where,$}[/tex]

        [tex]\large\text{$r = $ orbital radius (distance from center of earth to the satellite)}[/tex]

       [tex]\large\text{$v=$ velocity of satellite}[/tex]

[tex]\large\text{First let's calculate the value of $r.$}[/tex]

        [tex]\large\text{$r=$ Radius of earth + height of satellite}[/tex]

            [tex]\large\text{$=6400$km + 30000km}[/tex]

            [tex]\large\text{$=$ 36400km}[/tex]    

            [tex]\large\text{$= $ 36400000m}[/tex]

            [tex]\large\text{$=3.64\times10^7$m}[/tex]

[tex]\large\text{Convert velocity into m/s:$}[/tex]

         [tex]\large\text{$v= $ 2.5km/s = $2.5\times10^3$m/s}[/tex]

[tex]\large\text{Calculate the time period:$}[/tex]

        [tex]\large\text{$T=\dfrac{2\pi(3.64\times10^7)}{2.5\times10^3}$}[/tex]

             [tex]\large\text{$=91.48\times10^3$s}[/tex]

             [tex]\large\text{$=\dfrac{91.48\times10^3}{3600}$hrs}[/tex]

             [tex]\large\text{$\approx 25.412$hrs}[/tex]

We are delighted to have you as part of our community. Keep asking, answering, and sharing your insights. Together, we can create a valuable knowledge resource. IDNLearn.com provides the answers you need. Thank you for visiting, and see you next time for more valuable insights.