Respuesta :
Answer
given,
Mass of satellite, m = 4500 kg
Mass of the earth, M = 6 x 10²⁴ Kg
Earth circular orbit radius, R = 9.3 x 10⁶ m
a) To find the speed of the satellite
we need to equate the gravitation force between earth and satellite with the centripetal force.
[tex]\dfrac{GMm}{R^2}=\dfrac{mV^2}{R}[/tex]
[tex]V = \sqrt{\dfrac{GM}{R}}[/tex]
[tex]V = \sqrt{\dfrac{6.67\times 10^{-11}\times 6\times 10^{24}}{9.3\times 10^6}}[/tex]
V = 6559.89 m/s
b) Minimum amount of energy of satellite
[tex]E = \dfrac{GMm}{r}-\dfrac{1}{2}mv^2[/tex]
[tex]E =\dfrac{6.67\times 10^{-11}\times 6\times 10^{24}\times 4500}{9.3\times 10^6}}-\dfrac{1}{2}\times 4500\times 6559.89^2[/tex]
E = 9.68 x 10¹⁰ J
Minimum amount of energy require to move satellite is equal to E = 9.68 x 10¹⁰ J
The minimum amount of energy that is required to move the satellite is 9.68 x 10¹⁰ J.
A) The speed of the satellite can be calculated by equating the gravitational force and centripetal force on the satellite,
[tex]\begin {aligned} \dfrac {GMm}{R^2} &= \dfrac {m V^2}R\\\dfrac {GM }R&= V^2\\V& = \sqrt {\dfrac {GM}R}\end {aligned}[/tex]
Where,
[tex]V[/tex] = speed of satellite =?
[tex]G[/tex] - gravitational constant = [tex]6.67 \times 10^{-11}[/tex]
[tex]M[/tex] - mass of earth = 6 x 10²⁴ Kg
[tex]R[/tex] - radius of the circular orbit of satellite = 9.3 x 10⁶ m
Put the value in the formula, we get:
V = 6559.89 m/s
B) Minimum amount of energy of satellite to move
[tex]E =\dfrac {GMm}{R} - \dfrac 12 mv^2[/tex]
Put the values in the formula, we get:
E = 9.68 x 10¹⁰ J
Therefore, the minimum amount of energy that is required to move the satellite is 9.68 x 10¹⁰ J.
To know more about gravitational constant,
https://brainly.com/question/858421
