Graviational acceleration given mass and radius

In summary, the problem asks for the gravitational acceleration at the surface of a planet with five times the mass of Earth and twice the radius. Using the equation GM/r^2 and the given values for the mass and radius of Earth, the initial attempt did not yield the correct answer. However, after checking units and following the two rules for solving physics problems, the correct answer was obtained.
  • #1
gh_pluvilias
8
0

Homework Statement


If you lived on a planet with five times the mass of Earth and twice the radius, what would be the gravitational acceleration at the surface of your planet?


Homework Equations


GM/r^2
Mass of Earth = 6.00*10^24 kg
Radius of Earth = 6.38*10^3 km

The Attempt at a Solution


So, when I started out doing this, I quickly plugged in Earth's radius (in m), mass (in kg) and the gravitational constant just to make sure it came out at 9.8 because I know that's what Earth's gravitational acceleration from the surface is, but none of the answer I get are even close. I can't even get this right and I still have to do the actual problem (using 5x the mass and 2x the radius).
 
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  • #2
Two rules for doing physics problems:
1 - Check your units
2 - Never put in a hard number until you can't avoid it

You're tripping over rule 1 - which of your numbers is not in SI units?

Remember rule 2 when you're doing the question proper. The approach I suspect you are about to use will work, but there is a way to do it without needing to know either the Earth's mass or radius.
 
  • #3
Thanks, I actually went back and redid it later and got the answer I was looking for.
 

Related to Graviational acceleration given mass and radius

What is gravitational acceleration?

Gravitational acceleration is the acceleration experienced by an object due to the force of gravity. It is a measure of how quickly an object falls towards the center of a massive body, such as a planet or a star.

How is gravitational acceleration calculated?

The formula for calculating gravitational acceleration is a = GM/r^2, where G is the gravitational constant, M is the mass of the massive body, and r is the distance between the object and the center of the massive body. This formula is known as Newton's Law of Universal Gravitation.

What is the relationship between mass, radius, and gravitational acceleration?

The relationship between mass, radius, and gravitational acceleration is inverse. This means that as the mass or radius of a massive body increases, the gravitational acceleration decreases. Similarly, as the mass or radius decreases, the gravitational acceleration increases.

Can gravitational acceleration be negative?

No, gravitational acceleration cannot be negative. It is always a positive value, as it represents the acceleration towards the center of gravity of a massive body.

How does gravitational acceleration vary on different planets?

Gravitational acceleration varies on different planets depending on their mass and radius. For example, the gravitational acceleration on Earth is 9.8 m/s^2, while on the moon it is 1.6 m/s^2. This means that objects will fall towards the surface of the moon at a slower rate than they would on Earth.

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