# Newton's law of universal gravitation

• chocolatelover
In summary, Newton's law of universal gravitation is represented by the following equation where F is the magnitude of the gravitational force exerted by one small object on another, M and m are the masses of the objects, and r is a distance. Force has the SI units kg·m/s2. What are the SI units of the proportionality constant G?
chocolatelover
Hi everyone,

## Homework Statement

Newton's law of universal gravitation is represented by the following equation where F is the magnitude of the gravitational force exerted by one small object on another, M and m are the masses of the objects, and r is a distance.
F = GMm/r2
Force has the SI units kg·m/s2. What are the SI units of the proportionality constant G?

## The Attempt at a Solution

Would it be m/kg s^2?

Thank you very much

Well, use dimensional analysis: in classical mechanics, primary units are Mass, Time, and Space.
You know the dimensions of F, M,m,and r, so, that means you have only 1 var with 1 equation: linear determinate.

Well, in your attempt you say m/kg?!, SI units of m are Kg, so, m/kg is meaningless(and it's not correct), try google something about dimensional analysis, to see how it works. dimensional analysis is SUPER helpful in a lot of situations..:P

Littlepig

unit on LHS must equal the unit on the RHS for the equation to make sense. So altogether GMm/r^2 must has unit of Force: Kg. m/s^2... and you can now work out unit G must be

Thank you very much

I still don't really understand it. I tried doing cross multiplication and I got G=(kgm)(r^2)/Mms^2 or Kgr^2/Ms^2. Is that anywhere close?

$$G=\frac{Fr^2}{Mm}$$

Unit of Force(F) is ___? (and now in SI units)
Unit of distance(r) is ___?
Unit of Mass(M,m) is ___?

When you get those 3 replace them into the equation and simplify.

Thank you very much

Unit of Force(F) is ___? (and now in SI units)
Unit of distance(r) is ___?
Unit of Mass(M,m) is ___?

When you get those 3 replace them into the equation and simplify.

This is what I did:

I new that the distance had to be in m, so r^2=m^2. I also knew that the mass was kg/m^3 and the force was kgm/s^2. Do I then just need to simplify this?

G=(kgm/s^2)(m^2)/(kg/m^3)(kg/m^3)

Does that look right?

thank you very much

chocolatelover said:
This is what I did:

I new that the distance had to be in m, so r^2=m^2. I also knew that the mass was kg/m^3 and the force was kgm/s^2. Do I then just need to simplify this?

Why did you put mass as kg/m^3? Isn't mass just kg?

The force is correct and r is correct. but what you put as mass is off

Thank you very much

Since I have M and m, would it be (kg)(kg)?

So, G=(kg/m^3)(m^2)/(kg)(kg)
G=1/mkg

Does that look right?

Thank you very much

chocolatelover said:
Thank you very much

Since I have M and m, would it be (kg)(kg)?

So, G=(kg/m^3)(m^2)/(kg)(kg)
G=1/mkg

Does that look right?

Thank you very much

Yes M and m would be (kg)(kg)

G=(kgms^-2)(m^2)/(kg)(kg)

now simplify that

Is it m^3/kgs^2? I don't understand how you got s^-2 or 1/s^2? Could you please explain that to me?

Thank you very much

chocolatelover said:
Is it m^3/kgs^2? I don't understand how you got s^-2 or 1/s^2? Could you please explain that to me?

Thank you very much

This is a constant. Always start with the unit you want in your answer. Then make all the other units cancel by either adding factors in the numerator or denominator. Normal practice is to never simplify constants, but you should check with your instructor to see if he actually wants that.

Thank you very much

Regards

## What is Newton's law of universal gravitation?

Newton's law of universal gravitation is a physical law that describes the gravitational force between two objects with mass. It states that every object in the universe attracts every other object with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.

## Who discovered Newton's law of universal gravitation?

Sir Isaac Newton discovered the law of universal gravitation in 1687.

## How does Newton's law of universal gravitation differ from Einstein's theory of general relativity?

While Newton's law of universal gravitation describes the force of gravity as a fundamental force acting between masses, Einstein's theory of general relativity explains gravity as the curvature of space and time caused by the presence of mass and energy.

## What are the units of measurement for the gravitational constant in Newton's law of universal gravitation?

The gravitational constant, denoted by G, has units of cubic meters per kilogram per second squared (m^3/kg/s^2).

## Is Newton's law of universal gravitation still considered valid?

Yes, Newton's law of universal gravitation is still considered valid and is used in many practical applications, such as calculating the trajectories of planets and satellites. However, it is not a complete explanation of gravity and has been superseded by Einstein's theory of general relativity in certain situations, such as near massive objects or at high speeds.

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