Question

An earth's satellite makes a circle around the earth in 90 minutes. Calculate the height of the satellite above the surface of the earth. Given that radius of the earth = 6400 km

Answer 1

Height of the satellite 268 km

Explanation:

given ,

T = 90 mins = 5400 s,

R = 6400 km = $6.4\times 10^{6}$  m

We know that,

T = $2\Pi\sqrt\frac{(R + H)^3}{g\times R^2}$

$R + h = (\frac{g\times r^2\times t^2}{4\times \pi^2})^{\frac{1}{3}$

r + h = $\left ( = \frac{9.8\times{(6.4\times 10^6)^2\times 5400^2}}{4\times 9.87} \right )^\frac{1}{3}$

R + h = 6668 m

h = 6668 - 6400

h = 268 km

Height of the satellite 268 km

Answer 2

The height of the satellite above the surface of the earth is 368.1 km.

Explanation:

Given that,

Time = 90 min = 5400 sec

Radius of earth = 6400 km

We need to calculate the height of the satellite above the surface of the earth

Using formula of time

$T=2\pi\sqrt{\dfrac{(R+h)^3}{gR^2}}$

$R+h=(\dfrac{gR^2T^2}{4\pi^2})^{\frac{1}{3}}$

Put the value into the formula

$R+h=(\dfrac{9.8\times(6.4\times10^{6})^2\times(5400)^2}{4\pi^2})^{\frac{1}{3}}$

$R+h=6668.1\ km$

$h=6668.1-6400$

$h=268.1\ km$

Hence,  The height of the satellite above the surface of the earth is 368.1 km.

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https://brainly.in/question/1629716