# Math Help - Equilibrium physics help!

1. ## Equilibrium physics help!

The Cassini probe, mass 5,712 kg, is in a circular orbit with a radius of 1.2×108 m around the planet Saturn. How much work must its engine do to change it to a circular orbit with a radius of 1.1×109 m?
[Mass of Saturn = 5.68×1026 kg]

[Specify units of 'J', 'kJ' or 'MJ' in your answer.]

2. Originally Posted by jddery
The Cassini probe, mass 5,712 kg, is in a circular orbit with a radius of 1.2×108 m around the planet Saturn. How much work must its engine do to change it to a circular orbit with a radius of 1.1×109 m?
[Mass of Saturn = 5.68×1026 kg]

[Specify units of 'J', 'kJ' or 'MJ' in your answer.]
HI

According to the energy principles ,

Word done = the change in total energy of the satellite , U

$\triangle U=U_f-U_i$

$=-\frac{GMm}{2r'}-(-\frac{GMm}{2r})$

$=\frac{GMm}{2}[\frac{1}{r}-\frac{1}{r'}]$

$
=\frac{6.67\times 10^{-11}\times 5.68\times 1026\times 5712}{2}[\frac{1}{1.2\times 108}-\frac{1}{1.1\times 109}]
$

$
=-9.26\times 10^{-6}J
$

3. ## how are you getting G?

how are you getting G
for your equation

(GMm)/2* (1/r-1/r2)

4. Originally Posted by jddery
how are you getting G
for your equation

(GMm)/2* (1/r-1/r2)
G is the gravitational constant . Its not given in the question but it should be in your notes .