A planet with mass m, and radius r .

In summary, the acceleration due to gravity on the surface of a planet with mass m and radius r can be calculated using the formula a = Gm/r^2. However, this formula only applies for objects in Earth's gravitational field and not for objects on different planets. To find the acceleration on a different planet, you would need to use the formula g = G(M/R^2) where g is the free fall acceleration, M is the mass of the planet, and R is the radius of the planet.
  • #1
J_o_S
18
0
A planet with mass m, and radius r...

what is the acceleration due to gravity on the surface of the planet?

a = Gm/r^2

correct?

I'm pretty sure I'm right, but I will sleep better if someone can confirm this :smile:

thanks
 
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  • #2
Thats fine, just make sure m is the mass of the earth, not the object.
 
  • #3
good thing i asked :)

so the mass of the planet (not earth) doesn't matter at all?
 
  • #4
You were asking about the acceleration of an object in Earth's gravitational field, which is only dependant on the mass of the Earth and the object's distance from the earth.

What is this other planet you mention? There are no planets near the surface of the earth.. atleast that i know of
 
  • #5
whozum said:
You were asking about the acceleration of an object in Earth's gravitational field, which is only dependant on the mass of the Earth and the object's distance from the earth.

What is this other planet you mention? There are no planets near the surface of the earth.. atleast that i know of


sorry, just want to make sure we're clear here. I think there might be a misunderstanding.

Lets call the planet: "Planet X"

I am given the mass and radius of Planet X. I want to find out the acceleration due to gravity on the surface of Planet X.


Now I thought I was supposed to use the mass of planet X, not earth, since Earth doesn't have anything to do with the question
 
  • #6
Sorry, my misunderstanding. You are completely correct.
 
  • #7
Put in a nutshell:

[tex]g = G\frac{M}{R^2}[/tex],

where g is the free fall acceleration at the surface of the planet,
M is the mass of the planet,
and R is the radius of the planet.
 

Related to A planet with mass m, and radius r .

1. What is the mass of the planet?

The mass of the planet is a measure of the amount of matter it contains. It is denoted by the variable m and is typically measured in kilograms (kg).

2. How is the radius of a planet determined?

The radius of a planet is typically determined using remote sensing techniques such as radar or by measuring the planet's gravitational pull on other objects. It is denoted by the variable r and is typically measured in meters (m).

3. What is the relationship between mass and radius for a planet?

The mass and radius of a planet are directly related, as the mass of a planet increases, so does its radius. This is due to the gravitational force pulling matter towards the center of the planet, causing it to expand and increase in size. This relationship is described by the equation r∝m^(1/3), where ∝ represents proportionality.

4. Can the mass and radius of a planet change over time?

Yes, the mass and radius of a planet can change over time due to various factors such as collisions with other objects, volcanic activity, or erosion. However, these changes are typically very slow and may not be noticeable in a human lifetime.

5. How does the mass and radius of a planet affect its gravity?

The mass and radius of a planet directly affect its gravity. A planet with a larger mass and radius will have a stronger gravitational pull, meaning objects on its surface will weigh more. This is described by the equation g=G(m/r^2), where g represents the strength of gravity, G is the gravitational constant, and r is the radius of the planet.

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