Comparing gravitational acc at surface of 2 diff planets

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SUMMARY

The discussion focuses on calculating the gravitational acceleration at the surface of Planet X, which has five times the diameter and seven times the mass of Earth. The correct formula to determine the ratio of gravitational acceleration is gX : ge = (7GM_E) / (25R_E^2) * (R_E^2 / GM_E). The initial miscalculation arose from incorrect variable substitution, leading to an erroneous result of 175 instead of the correct ratio. The clarification provided by participants highlights the importance of proper variable management in gravitational equations.

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Homework Statement


Planet X has five times the diameter and
seven times the mass of the earth.
What is the ratio gX : ge of gravitational
acceleration at the surface of planet X to the
gravitational acceleration at the surface of the
Earth?Well, I used the equation:
[tex]\frac{Fplanetx}{FplanetE}[/tex]= [tex]\frac{Mx}{Me}[/tex] * ([tex]\frac{Rx})({Re}[/tex])2
i decided to use variables:
Mx= 7Me
Rx= ((2Re)*5)/2= 5
plugging in:
7Me/Me(25Re)
i got 175...but none of the answers have that big of a number
I would really appreciate it if someone could help me figure out what I did wrong.
 
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You should get
[tex]\frac{g_x}{g_E}= \frac{7GM_E}{25R_E^2} \times \frac{R_E^2}{GM_E}[/tex]
 
ohh i see what i did wrong.. Thanks for your help! :)
 

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