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I really don't understand how to do this someone help please.

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- Thread starter lilkrazyrae
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In summary: I'm just getting a little carried away with this stuff!In summary, the mass of the moon is 0.0123 times that of the Earth. A spaceship is traveling along a line connecting the centers of the Earth and Moon. At what distance from the Earth does the spaceship find the gravitational pull of the Earth equal in magnitude to that of the Moon? Express your answer as a percentage of the distance between the centers of the two bodies.

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I really don't understand how to do this someone help please.

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- #2

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[tex]F=\frac{Gm_1m_2}{r^2}[/tex]

G being the gravitational constant, m1 and m2 being the masses of the body making the force and the body receiving the force, and r being the distance between. Make m1 the mass of the ship. Now you require the force from the moon and the force from the Earth to be equal. Do you see what equation to set up?

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Or in other words, you can make the mass of the spaceship whatever you like. Personally I would choose mass = 1.inha said:

Why you can do this? Because the mass of the ship doesn't change. You can find out the

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Ok once again I'm lost you end up with r^2 canceling out too I cannot find anyother way to set it up

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inha's hint is very useful. You assumed that the two measures of radius are equal when in fact they are not. Well...they are at d/2 (according to inha's variables).lilkrazyrae said:Ok once again I'm lost you end up with r^2 canceling out too I cannot find anyother way to set it up

Initially we told you that

[tex]F_{gravity}=\frac{Gm_1m_2}{r^2}[/tex]

So it follows that:

[tex]F_{earth}=\frac{Gm_{ship}m_{earth}}{r^2}[/tex]

where

[tex]F_{moon}=\frac{Gm_{ship}m_{moon}}{r^2}[/tex]

but the

You want to find out when these two equations equal each other, or in other words:

[tex]F_{moon}= F_{earth}[/tex]

So begin by setting their equations equal to each other (I'm sure you've already done this, but pay attention to the variables...same letters but different subscripts):

[tex]\frac{Gm_{ship}m_{moon}}{r_{m}^2}=\frac{Gm_{ship}m_{earth}}{r_{e}^2}[/tex]

where [itex]r_{m}[/itex] is the distance between the ship and the moon, and [itex]r_{e}[/itex] is the distance between the ship and the earth. Remember that the mass of the moon is only 0.0123 the mass of the earth. That expresses the mass of the moon

[tex]\frac{Gm_{ship}0.0123m_{earth}}{r_{m}^2}=\frac{Gm_{ship}m_{earth}}{r_{e}^2}[/tex]

Notice how the variables start to drop off. G, the mass of the ship, and the mass of the Earth m cancel out now:

[tex]\frac{0.0123}{r_{m}^2}=\frac{1}{r_{e}^2}[/tex]

Getting it? I hope I haven't done too much, lol! But I'm sure your confusion was because you weren't keeping in mind that, even though the variable letters all represent similar IDEAS, you should not assume that they represent the same QUANTITIES OF THOSE IDEAS in this problem. If you have two different distances you should use two different variables. In this case we use

[tex]\frac{Gm_{ship}m_{moon}}{r_{m}^2}=\frac{Gm_{ship}m _{earth}}{r_{e}^2}[/tex]

[tex]\frac{Gab}{d^2}=\frac{Gae}{f^2}[/tex]

Where

a = mass of the ship

b = mass of the moon

d = distance between ship and moon

e = mass of the earth

f = distance between ship and earth

Notice that you don't run into the problem you had earlier, with the r^2 cancelling out here, because you can't cancel f's with d's!

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

The distance between the Earth and the Moon can be calculated using the formula d = r * θ, where d is the distance, r is the radius of the Earth, and θ is the angular diameter of the Moon as seen from Earth.

The gravitational pull between the Earth and the Moon is approximately 1.98 x 10^20 Newtons. This is the force that keeps the Moon in orbit around the Earth.

To calculate the percentage of gravitational pull between the Earth and the Moon, you would divide the gravitational pull between the two objects by the gravitational pull between the Earth and the Sun, which is approximately 3.52 x 10^22 Newtons. This will give you the percentage of the Earth's gravitational pull that is responsible for keeping the Moon in orbit.

Calculating the Earth-Moon distance percentage is important for understanding the relationship between the two objects and their gravitational forces. It also helps scientists study the effects of gravitational pull on the Moon's orbit and how it affects Earth's tides and other natural phenomena.

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