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The mass of the moon is 7.36×1022kg and its distance to the Earth is 3.84×108m. What is the gravitational force of the moon on the earth? The moon's force is what percent of the sun's force?

Answer 1

Elena Antonova

#F=1.989*10^20 kgm/s^2#
#3.7*10^-6%#

Using Newton's gravitational force equation

#F=(Gm_1m_2)/(r^2)#

and assuming that the mass of the Earth is

#m_1=5.972*10^24kg#

and #m_2# is the given mass of the moon with #G# being

#6.674*10^-11Nm^2/(kg)^2#

gives #1.989*10^20 kgm/s^2# for #F# of the moon.

Repeating this with #m_2# as the mass of the sun gives

#F=5.375*10^27kgm/s^2#

This gives the moon's gravitational force as #3.7*10^-6%# of the Sun's gravitational force.

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Answer 2

Luca de

To calculate the gravitational force between the Moon and the Earth, you can use Newton's law of universal gravitation:

( F = G \frac{{m_1 m_2}}{{r^2}} )

Where:

( F ) is the gravitational force,
( G ) is the gravitational constant ((6.674 \times 10^{-11} , \text{N m}^2/\text{kg}^2)),
( m_1 ) and ( m_2 ) are the masses of the Moon and the Earth respectively, and
( r ) is the distance between their centers ((3.84 \times 10^8 , \text{m})).

Substitute the values and calculate ( F ).

To find what percent the Moon's force is of the Sun's force, use the same formula for the gravitational force between the Sun and the Earth, substituting the relevant values. Then, calculate the percentage.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.