By definition the **intensity of the gravitational field** generated by mass M is

`Gamma= G*(M)/R^2`

and the **gravitational potential** associated with mas M at distance R is

`U = Gamma*R = G*M/R`

Knowing the gravitational potential U we can write the potential energy of mass m as:

`E_p = m*U = G*(m*M)/R`

Now for the values

`G = 6.67*10^-11 m^3/(kg*s^2)`

`m = 5 kg` and `M =5.97*10^24 kg`

`R_(Earth) = 6370 km =6370*10^3 m`

`R = 36000 km =36000*10^3 m `

we have a difference in potential energy of

`E_p(R_(Earth)) - E_p(R_(Earth)+R) =G*m*M*(1/R_(Earth) -1/(R_(Earth) + R))=`

`= 6.67*10^-11*5*5.97*10^24 *(1/(6370*10^3) -1/((6370+36000)*10^3)) =`

`=2.656*10^8 J`

This energy is used to heat up the comet of mass m.

`Delta(E_p) =m*c*(Delta(T)) `

taking `Delta(T) = 2500 -(-50) =2550 C degree = 2550 K degree`

we obtain

`c = 2.656*10^8/(2550*5) =2.08*10^4 J/(kg*K)`

To compare with substances in nature the specific heat of granite, SiO2 and Al2O3 (Earth crust) is about `10^3 J/(kg*K)` .

**Further Reading**

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