Comparing gravitational acc at surface of 2 diff planets

In summary, the ratio of gravitational acceleration at the surface of planet X to the gravitational acceleration at the surface of Earth can be calculated using the equation: g_x/g_E = (7GM_E)/(25R_E^2) * (R_E^2)/(GM_E). After correcting a mistake in the calculation, the answer should be 7/25.
  • #1
Maiia
79
0

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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  • #2
You should get
[tex]\frac{g_x}{g_E}= \frac{7GM_E}{25R_E^2} \times \frac{R_E^2}{GM_E}[/tex]
 
  • #3
ohh i see what i did wrong.. Thanks for your help! :)
 

FAQ: Comparing gravitational acc at surface of 2 diff planets

What is gravitational acceleration and how does it differ between planets?

Gravitational acceleration is the measure of the force of gravity on an object. It is dependent on the mass and distance of the object from the center of the planet. The gravitational acceleration on different planets varies due to their varying masses and sizes.

Which planet has the highest gravitational acceleration at its surface?

The planet with the highest gravitational acceleration at its surface is Jupiter, with a value of 24.79 m/s². This is due to its massive size and high density.

How does the gravitational acceleration on Earth compare to other planets?

The gravitational acceleration on Earth is 9.8 m/s², which is relatively low compared to other planets. For example, Mercury has a gravitational acceleration of 3.7 m/s², while Saturn has a value of 10.4 m/s².

What factors can affect the gravitational acceleration on a planet?

The main factor that affects the gravitational acceleration on a planet is its mass. The greater the mass, the stronger the gravitational pull. The distance from the center of the planet also plays a role, as the farther away an object is, the weaker the gravitational acceleration.

How does the gravitational acceleration on a planet affect objects on its surface?

The gravitational acceleration on a planet determines the weight of objects on its surface. The higher the gravitational acceleration, the heavier an object will feel. This is why objects feel lighter on planets with lower gravitational accelerations compared to Earth.

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