# Relating Gravitational Field Strength and Mass

• B
• taetae
In summary, tae2 is confused about how to calculate the orbital period of an asteroid that has the average radius of orbit as 2.77 AU. It says to use the value of Kepler's constant "expressed in the units of yr2/AU3" and the formula T2=Cr3. So, if my understanding is correct, to find the value of Kepler's constant you would do:C=T2/r3C=12/13 = 1yr2/AU3And then to calculate the orbital period:T=√Cr3T=√(1yr2/AU3)(2.77)3
taetae
I know the formula for calculating field strength is g= GM/r2 , however if I'm trying to show the proportionality relationship between just g and m, would g ∝ m be correct, since a larger mass equals a stronger force of gravity and vice versa?

Hello tae2,

What about the dependence of ##r## on m (c.q. vice versa) ? Think two planets of the same composition ...

PS do use consistent notation: don't change capital M for lower case m if it is not the intention to designate another variable

BvU said:
Hello tae2,

What about the dependence of ##r## on m (c.q. vice versa) ? Think two planets of the same composition ...

PS do use consistent notation: don't change capital M for lower case m if it is not the intention to designate another variable

Yup, that's where I got confused haha. The mass of the object needs to be divided by the square of it's radius. The question I'm stuck on asks for me to write a proportionality relationship for g relating to m, would g∝ m/r2 be more accurate then? Or should the constant of proportionality, G, be included as well, making it g∝ Gm/r2?

(Taking a class online is so frustrating when you don't quite understand something, I feel like I'm teaching myself!)

Last edited:
I'm also confused by what your teacher is asking. The relation between mass and gravity is the gravitational constant. It's just a constant proportion. It came about by experimentation. Newton understood the concept that two objects pulled each other and that that force was relative to the distance. He had a problem with that he needed a force of certain units and his equations had a completely different unit, so he added the G and gave it a unit. Later on once we had more precise measurements of mass and force, we were able to discover the value of this constant.

Of course then Einstein came along.

Exercise means gravitational acceleration at the surface, I would venture.

With ##m\propto r^3## and ##g \propto m/r^2## I would say: 8 times heavier, then twice the gravitational acceleration... but I agree that an online answer is a gamble

taetae said:
I feel like I'm teaching myself)
isn't so bad at all !

Thank you for the help! I hope it's ok to sneak one other question into here (I went through and did all the rest of the questions but this is the only other one I'm confused with). I just want to check whether or not I did it correctly.
It's about determining the orbital period of an asteroid (in Earth years) that has the average radius of orbit as 2.77 AU. It says to use the value of Kepler's constant "expressed in the units of yr2/AU3" and the formula T2=Cr3. So, if my understanding is correct, to find the value of Kepler's constant you would do:
C=T2/r3
C=12/13 = 1yr2/AU3

And then to calculate the orbital period:
T=√Cr3
T=√(1yr2/AU3)(2.77)3

I feel like this doesn't look right...I'm pretty sure I didn't input the correct value for C but I'm unsure how to otherwise get it..

## 1. How does mass affect gravitational field strength?

Mass is directly proportional to gravitational field strength. This means that as the mass of an object increases, its gravitational field strength also increases. This is because a greater mass has a greater pull on nearby objects due to its larger gravitational force.

## 2. What is the equation for calculating gravitational field strength?

The equation for calculating gravitational field strength is F = G(m1m2)/r^2, where F is the force of gravity, G is the gravitational constant, m1 and m2 are the masses of the objects, and r is the distance between them. This equation shows that gravitational field strength is dependent on the masses of the objects and the distance between them.

## 3. How does distance affect gravitational field strength?

The strength of the gravitational field decreases as the distance between two objects increases. This is because the further apart the objects are, the weaker the gravitational force between them becomes. This relationship is described by the inverse square law, which states that the force of gravity is inversely proportional to the square of the distance between the objects.

## 4. Can gravitational field strength be negative?

No, gravitational field strength cannot be negative. Since it is a measure of the force of gravity, it is always a positive value. However, the direction of the force of gravity can be negative if it is pulling in the opposite direction of a chosen reference point. This is often the case when dealing with objects in orbit.

## 5. How is gravitational field strength related to weight?

Gravitational field strength and weight are related, but they are not the same thing. Weight is a measure of the force of gravity on an object, while gravitational field strength is a measure of the strength of the gravitational field at a specific point in space. Weight is dependent on both mass and gravitational field strength, as weight is calculated by multiplying an object's mass by the gravitational field strength at that location.

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