Question

Determine the minimum amount of energy needed to move a satellite from its orbit around the Earth to an infinite distance from the Earth. The mass of the satellite is 7.45 X 10^3 kg and its orbital radius is 7.50 X 10^6 m. Take the mass of the Earth to be 5.97 X 10^24 kg.

Answer 1

Answer:
`19.80* 10^(10) J`

Step-by-step explanation:

Given

mass of satellite
`m=7.45 * 10^3 kg`

orbital radius
`R=7.50* 10^6 m`

mass of Earth
`M=5.97* 10^(24) kg`

Minimum amount of Energy to move Satellite from its orbit to an infinite distance is sum of Potential Energy + Kinetic Energy of Satellite

`W=U+K.E.`

`U=-G(Mm)/(R)`

`U=-6.67* 10^(-11)* (5.97* 10^(24)* 7.45 * 10^3)/(7.50* 10^6)`

`U=-(296.658* 10^(16))/(7.5* 10^6)`

`U=-39.55* 10^(10) J`

`K.E.=(1)/(2)* mv^2`

Where
`v=orbital\ velocity`

`v=\sqrt{(GM)/(r)}=\sqrt{(6.67* 10^(-11)* 5.97* 10^(24))/(7.50* 10^6)}`

`v^2=5.30* 10^7 m/s`

`K.E.=(1)/(2)* mv^2`

`K.E.=(1)/(2)* 7.45* 10^3* (5.30* 10^7)=19.74* 10^(10) J`

`W=-39.55* 10^(10)+19.74* 10^(10)`

`W=-19.80* 10^(10) J`

i.e.
`19.80* 10^(10) J` Energy is required to provide to move Satellite out of its orbit