Comparing gravitational acc at surface of 2 diff planets

AI Thread Summary
The discussion centers on calculating the gravitational acceleration ratio between Planet X and Earth, given that Planet X has five times the diameter and seven times the mass of Earth. The initial calculation used incorrect values, leading to an erroneous result of 175. The correct formula for the ratio of gravitational accelerations is derived as gX/ge = (7GM_E)/(25R_E^2) × (R_E^2/GM_E). This highlights the importance of accurately applying the gravitational formula and understanding the relationship between mass and radius in gravitational calculations. The user acknowledges their mistake and expresses gratitude for the clarification.
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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:
\frac{Fplanetx}{FplanetE}= \frac{Mx}{Me} * (\frac{Rx})({Re})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
\frac{g_x}{g_E}= \frac{7GM_E}{25R_E^2} \times \frac{R_E^2}{GM_E}
 
ohh i see what i did wrong.. Thanks for your help! :)
 
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