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Homework Statement
A shuttle orbiting the Earth at 400km deploys a satellite of mass 800kg into orbit a further 200km from earth. Calculate the work that must be done by the shuttle to deploy the sattelite.
Homework Equations
[tex]E_{k} = \frac{GMm}{2r}[/tex], [tex]U = -\frac{GMm}{r}[/tex]
The Attempt at a Solution
I tried using [tex]W = \Delta E_{k}[/tex] to solve the problem:
[tex]800GM\left(\frac{1}{2 \times 600000} - \frac{1}{2 \times 400000}\right)=-1.334 \times 10^{11} J[/tex]
But the solutions gives [tex]1.4 \times 10^9 J[/tex]
Moreover, using the following method gives a different answer:
[tex]\int_{400000}^{600000} \frac{GM(800)}{r^2}dr=2.658 \times 10^{11} J[/tex]
But I thought [tex]E_{tot} = E_{k} + U[/tex], so [tex]\Delta E_{k} = -\Delta U[/tex] ??
Could someone tell me why my methods do not work and what the correct method is for dealing with this? Thankyou