Question

How much energy would be required to move the earth into a circular orbit with a radius 2.0 kmkm larger than its current radius

Answer 1

`3.52* 10^(25)\ \text{J}`

Step-by-step explanation:

G = Gravitational constant =
`6.674* 10^(-11)\ \text{Nm}^2/\text{kg}^2`

M = Mass of Sun =
`1.989* 10^(30)\ \text{kg}`

m = Mass of Earth =
`5.972* 10^(24)\ \text{kg}`

`r_i` = Initial radius of orbit =
`1.5* 10^(11)\ \text{m}`

`r_f` = Final radius of orbit =
`((1.5* 10^(11))+2* 10^3)\ \text{m}`

Energy required is given by

`E=(1)/(2)\Delta U\\\Rightarrow E=(GMm)/(2)((1)/(r_i)-(1)/(r_f))\\\Rightarrow E=(6.674* 10^(-11)* 1.989* 10^(30)* 5.972* 10^(24))/(2)((1)/(1.5* 10^(11))-(1)/((1.5* 10^(11))+2* 10^3))\\\Rightarrow E=3.52* 10^(25)\ \text{J}`

The energy required would be
`3.52* 10^(25)\ \text{J}`.