Two objects have masses of #42 MG# and #25 MG#. How much does the gravitational potential energy between the objects change if the distance between them changes from #48 m# to #15 m#?

Question

Two objects have masses of #42   MG# and #25    MG#. How much does the gravitational potential energy between the objects change if the distance between them changes from #48  m# to #15   m#?

Layla Ahmed · Accepted Answer

The change in gravitational potential energy is #=321*10^-5J#

The potential energy per kilogram at a point in a field is known as the gravitational potential.

So the units are #J, "Joules"#

#Phi=-G(M_1M_2)/R#

The universal constant of gravitation is

G is 6.67 * 10^-11 Nm^2 kg^-2.

The masses causing the field is #=M_1 kg# and #=M_2 kg#

The mass is #M_1=42MG=42*10^6g=42*10^3kg#

The mass is #M_2=25MG=25*10^6g=25*10^3kg#

The distance between the centers is #=Rm#

The distance #R_1=48m#

The distance #R_2=15m#

Consequently,

#Phi_1=(-G*(42*10^3*25*10^3)/48)#

#Phi_2=(-G*(42*10^3*25*10^3)/15)#

Thus,

#Phi_1-Phi_2=(-G*(42*10^3*25*10^3)/48)-(-G*(42*10^3*25*10^3)/15)#

#=42*25*10^6*6.67*10^-11(1/15-1/48)#

#=321*10^-5J#

Nora Arzate · Answer

undefined $$ \Delta U = G \cdot \frac{{m_1 \cdot m_2}}{{r_1}} - G \cdot \frac{{m_1 \cdot m_2}}{{r_2}} $$
$$ \Delta U = (6.674 \times 10^{-11} \, \text{N} \cdot \text{m}^2/\text{kg}^2) \cdot \left(\frac{{42 \times 10^6 \, \text{kg} \cdot 25 \times 10^6 \, \text{kg}}}{{48 \, \text{m}}} - \frac{{42 \times 10^6 \, \text{kg} \cdot 25 \times 10^6 \, \text{kg}}}{{15 \, \text{m}}}\right) $$