Question

Suppose NASA wants a satellite to revolve around Earth 5 times a day. What should be the radius of its orbit if we neglect the presence of the Moon? (G=6.67*10^ -11 N*m^2/kg^2, Mearth=5.97*10^24 kg). Answer is 1.44*10^7 m

Answer 1

Answer:

r = 1.44 × $10^{7}$ m

Explanation:

given data

satellite to revolve = 5 time a day

G = 6.67 × $10^{-11}$ Nm²/kg²

Mass earth = 5.97 × $10^{24}$  kg

to find out

radius of its orbit

solution

first we get here Time taken for one complete revolution that is

time taken = $\frac{24}{5}$

time taken = 4.8 hours

time taken = 4.8 hours × 3600 sec

time taken = 17280 sec

and

time is express as

T = 2π × $\sqrt{\frac{r^3}{GM} }$    .............1

put hre value we get

17280 = 2π × $\sqrt{\frac{r^3}{6.67*10^{-11}*5.97*10^{24}} }$

solve it we get

r = 1.44 × $10^{7}$ m