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The Moon is $3.9 \times 10^{5} \mathrm{km}$ from Earth's center and $1.5 \times 10^{8} \mathrm{km}$ from the Sun's center. If the masses of the Moon, Earth, and the Sun are $7.3 \times 10^{22} \mathrm{kg}$ $6.0 \times 10^{24} \mathrm{kg},$ and $2.0 \times 10^{30} \mathrm{kg},$ respectively, find the ratio of the gravitational forces exerted by Earth and the Sun on the Moon.

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0.47

Physics 101 Mechanics

Chapter 7

Gravitation

Section 2

Using the Law of Universal Gravitation

Dynamics of Rotational Motion

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The Moon is $3.9 \times 10…

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The moon is 3.9 x 105 km f…

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Suppose the centers of Ear…

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Calculate the force of gra…

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The masses of the Moon and…

02:48

Earth's mass $(M)=5.9…

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The Moon, whose mass is $7…

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The mass of the Earth is $…

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The Moon's mass is $7…

In this problem, we are going to calculate the ratio of gravitation force exerted on the moon by earth and sun. That is f e, divided by f s. We can write the formula for f e, as f equals to capital g m e m m divided by r m square. Let'S call it equation number 1 here this is the gravitation constant m. Is the mass of earth is the mass of the moon, and this r m is the distance between the centers of these 2 objects? Similarly, we can write the formula 4. F s: s f; s equals to capital g m s; m m divided by r s m square. We call it equation. Number 2. Now dividing equation number 2 by equation: ding equation: number 1. By equation number 2: we can write f e, divided by f s, equals to m e 2 m a r s m square, divided by m h, r e m square. We call it equation number 3. By inserting values into this question. We can write f e, divided by f s, equals to we have the value, for me, is 6.38 multiplied by 10 or a pat 24 into. We have the value for this s. M is 1.5 multiplied with 10 raise power, 11 meter whole square divided by. We have the value for this. Ms is 2.0 multiplied by 10. This power 30 keg into the resht r m, has the value of 3.9 multiplied by 10 as power 8 meter, and that is square on it. So from here we can write the value for this ratio is divided by f s equals to 0.47. So this is our required answer. Thank you.

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