Gravitational Force: Mass & Distance Impact

In summary, when the masses of two planets are doubled but the distance between them remains the same, the gravitational force between them is quadrupled. This can be shown mathematically using the equation F_{g} = \frac{Gm_{1}m_{2}}{r^{2}} and algebraically by doubling the masses and showing that the second force is 4 times greater than the original force or that the original force is 1/4 the second force.
  • #1
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1. Show that the gravitational force between two planets is quadrupled if the masses of both planets are doubled but the distance between them stays the same.



2. F = G m1m2/d2 ??



3. confused...
 
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  • #2


Okay let's say that we have the following:

G (Gravitational constant) = 6.67E-11
mass of planet 1 = 200,000 kg
mass of planet 2 = 40,000 kg
lets say that the distance r = 10,000 m
all are numbers I just randomly made up

Using the equation: [tex]F_{g} = [/tex] [tex]\frac{Gm_{1}m_{2}}{r^{2}}[/tex]

we just plug in and find that the Force of gravity is:

[tex]\frac{(6.67E-11)(200000)(40000)}{(10000)^{2}}[/tex] which gives 5.336E-9

If we double the masses but keep the distance between them the same:

[tex]\frac{(6.67E-11)(400000)(80000)}{(10000)^{2}}[/tex] gives the value 2.1344E-8


If we divide the force with the doubled masses by the original force:

[tex]\frac{2.1344E-8}{5.336E-9}[/tex] = 4

Thus the gravitational force has been increased by a factor of 4, and quadrupled. HOWEVER THIS IS ONLY AN EXAMPLE, AND PROBABLY NOT WHAT THE QUESTION IS ASKING.


Most likely, the question is asking for some algebra actually showing that doubling the masses results in quadrupled force.


Start with

[tex]F_{g}[/tex] = [tex]\frac{Gm_{1}m_{2}}{r^{2}}[/tex]

the question asks you to show that if the masses are doubled, then the force of gravity
quadruples

so just double the masses and do some algebra to show that either:
a)the second force is 4 times greater than the original force or
b)the original force is 1/4 the second force

Here I'll even get you started:

[tex]F_{g2}[/tex] = [tex]\frac{G(2m_{1})(2m_{2})}{r^{2}}[/tex] = ?
 
Last edited:
  • #3


thx so much!
 

Related to Gravitational Force: Mass & Distance Impact

1. What is gravitational force?

Gravitational force is an attractive force that exists between any two objects with mass. It is one of the four fundamental forces of nature and is responsible for holding objects together and keeping planets in orbit around the sun.

2. How does mass impact gravitational force?

The greater the mass of an object, the stronger its gravitational force. This means that larger objects have a greater gravitational pull than smaller objects. For example, the sun has a much larger mass than the Earth, and therefore has a stronger gravitational force that keeps the Earth in orbit.

3. How does distance impact gravitational force?

The farther apart two objects are, the weaker their gravitational force. This is known as the inverse square law. As distance increases, the gravitational force decreases exponentially. This is why the moon, which is farther away from the Earth than other objects, has a weaker gravitational force on us.

4. What is the formula for calculating gravitational force?

The formula for calculating gravitational force is F = G * (m1 * m2)/d^2, where F is the force, G is the gravitational constant, m1 and m2 are the masses of the two objects, and d is the distance between them.

5. How does the value of the gravitational constant impact gravitational force?

The gravitational constant, denoted by G, is a universal constant that determines the strength of the gravitational force. A higher value of G would mean a stronger gravitational force, while a lower value would result in a weaker force. The exact value of G is still being researched and is subject to slight variations.

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