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- Homework Statement
- Imagine a trip from Earth to Mars in terms of gravitational potential energy.

Assuming you have a mass of 70 kg70, what is your change in gravitational potential energy in moving from the surface of the Earth to the surface of Mars in GJ? Don't forget the sun!

- Relevant Equations
- Universal gravitation

My attempt:

Let ##M_e## be the mass of the Earth and ##M_m## be the mass of the person. Let ##D_{EM}## be the distance from Earth to Mars and let ##R_e## be the radius of the earth.

Defining these constants (leaving off units for brevity):

Masses in Kilograms (G is not a mass but I'll leave it in this group)

##M_e = 5.97x10^{24}##

##G = 6.67x10^{-11}##

##M_m = 70##

Distances in meters...

##D_{EM} = 3.594x10^8##

##R_e = 6.38x10^6##

Then...

##\Delta{U} = U_{mars} - U_{earth}##

## = -\frac{GM_eM_m}{D_{EM}+R_e} - (-\frac{GM_eM_m}{R_e})##

## = -\frac{GM_eM_m}{D_{EM}+R_e} + \frac{GM_eM_m}{R_e}##

## = -\frac{(6.67x10^{-11})(5.97x10^{24})(70)}{3.594x10^{11} + 6.38x10^6} + \frac{(6.67x10^{-11})(5.97x10^{24})(70)}{6.38x10^6} ##

## = 4.37x10^9 J##

## = 4.37 GJ##

But this is incorrect. I understand that when dealing with gravitational potential energy we "move" the mass from infinity to it's "destination" and take the difference to get the potential energy.

It's obvious here I didn't include the sun. I understand that it's supposed to be a hint but I cannot imagine a reason the sun would factor into the potential energy between two other planets. Maybe my professor meant something related to the calculation of the distances? I am unsure. Any help would be greatly appreciated.

Let ##M_e## be the mass of the Earth and ##M_m## be the mass of the person. Let ##D_{EM}## be the distance from Earth to Mars and let ##R_e## be the radius of the earth.

Defining these constants (leaving off units for brevity):

Masses in Kilograms (G is not a mass but I'll leave it in this group)

##M_e = 5.97x10^{24}##

##G = 6.67x10^{-11}##

##M_m = 70##

Distances in meters...

##D_{EM} = 3.594x10^8##

##R_e = 6.38x10^6##

Then...

##\Delta{U} = U_{mars} - U_{earth}##

## = -\frac{GM_eM_m}{D_{EM}+R_e} - (-\frac{GM_eM_m}{R_e})##

## = -\frac{GM_eM_m}{D_{EM}+R_e} + \frac{GM_eM_m}{R_e}##

## = -\frac{(6.67x10^{-11})(5.97x10^{24})(70)}{3.594x10^{11} + 6.38x10^6} + \frac{(6.67x10^{-11})(5.97x10^{24})(70)}{6.38x10^6} ##

## = 4.37x10^9 J##

## = 4.37 GJ##

But this is incorrect. I understand that when dealing with gravitational potential energy we "move" the mass from infinity to it's "destination" and take the difference to get the potential energy.

It's obvious here I didn't include the sun. I understand that it's supposed to be a hint but I cannot imagine a reason the sun would factor into the potential energy between two other planets. Maybe my professor meant something related to the calculation of the distances? I am unsure. Any help would be greatly appreciated.