# Relationship of a planet's mass, size, and acceleration due to gravity

• yoosnb
In summary: This can be proved using the principle of superposition which states that if two particles or waves are in contact and one is disturbed then the other is also disturbed. This is because the waveform of the disturbed particle is added to the waveform of the undisturbed particle. If we take a look at the waveforms for two particlesA and B that are in contact and one is disturbed then we can see that the waveform of particle A is added to the waveform of particle B. This means that if we were to take the waveforms of particle A and particle B and add them together we would get a waveform that is the sum of the two original waveforms. This is called the principle of superposition.
yoosnb
Homework Statement
Planet A and Planet B have the same mass, but planet A is twice larger than planet B. A ball dropped above the surface of planet A has an acceleration due to gravity of 10 m/s^2. which of the following is true if a ball is dropped 100 m from the surface of planet A.
Relevant Equations
A. If the ball is dropped 100 m from the surface of planet B, it will reach the ground at the same length of time it does at planet A.

B. at 1 s of its fall, the speed of the ball at planet A is less than the speed of the ball at planet B

C. the acceleration of the ball at planet A exceeds the acceleration of the ball at planet B.

D. the distance traveled by the ball at planet A is twice the distance traveled by the ball at planet B.
Choice D is obviously wrong therefore leaving us with choices A, B, and C. Can someone explain the relationship of the three variables stated above (mass, volume, and acceleration due to gravity)? Thank you.

Hello yoos, !

The whole idea of PF is that we help you with questions and hints, but you come up with the relevant equations and an attempt at solution yourself. So: what relationships have you learned so far between
• radius of a sphere and volume
• volume and mass
• mass, distance to center and gravitational acceleration
?

Hello,

Can the formula for Gravitational force between two objects be used in this scenario?

If yes, then I may have something in mind.

Gf = (G*m1*m2)/r2

Since mass is constant, we can disregard the numerator, leaving us with

Gf = 1/r2

Making the acceleration due to gravity inversely proportional to its radius or size. Therefore the answer is B.

Is this a valid solution/explanation for the problem?

yoosnb said:
Don't see the logic ...
yoosnb said:
Gf = 1/r2
Never, never, never write something like that. It's dimensionally wrong and at some point it will bite you hard.Calculations/physics arguments in reasoning are possible for the cases (you sure there is only one correct answer ?)

e.g. A: B has a higher ##g \Rightarrow ## A is wrong.

I believe you got it right that B is the correct option, however your reasoning might not be entirely correct. It seems though that you got the core idea that is that the force varies with inverse square of the distance from the center of the planet.

To prove it correctly one way is to consider the ratio ##\frac{F_A}{F_B}## that is the ratio of the force the ball experiences at planet A (at the surface of the planet or at height 100m) ,##F_A##, to the force that experiences at planet B ##F_B## which ratio of forces is equal to the ratio of accelerations ##\frac{g_A}{g_B}## at planet A and planet B.

yoosnb

## 1. How does a planet's mass affect its acceleration due to gravity?

The mass of a planet directly affects its acceleration due to gravity. The more massive a planet is, the stronger its gravitational pull will be. This means that objects on the surface of a more massive planet will experience a greater acceleration due to gravity compared to objects on a less massive planet.

## 2. Does a planet's size have an impact on its acceleration due to gravity?

Yes, a planet's size also plays a role in its acceleration due to gravity. The larger the planet's radius, the farther away objects are from its center, resulting in a weaker gravitational pull. This means that objects on the surface of a larger planet will experience a weaker acceleration due to gravity compared to objects on a smaller planet.

## 3. Is there a relationship between a planet's mass and its size?

Yes, there is a relationship between a planet's mass and its size. Generally, the larger the planet's mass, the larger its size will be. However, this relationship is not always true as other factors such as composition and density can also affect a planet's size.

## 4. How does the acceleration due to gravity differ on different planets?

The acceleration due to gravity can vary greatly on different planets depending on their mass and size. For example, the acceleration due to gravity on Earth is 9.8 m/s², while on Mars it is only 3.7 m/s². This is because Mars has a lower mass and a smaller size compared to Earth.

## 5. Can the acceleration due to gravity be manipulated on a planet?

No, the acceleration due to gravity is a natural force that cannot be manipulated on a planet. It is determined by the planet's mass and size, which are fixed properties. However, on a smaller scale, the acceleration due to gravity can be altered by changing the distance between objects or by introducing external forces such as air resistance or magnetic fields.

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