The force of gravity between Earth and the Sun is ________ the force of gravity between Earth and the Moon.For reference,the average distance between Earth and the Moon is 0.003 AU,the mass of the Moon is 7 × 10²² kg,and the mass of the Sun is 2 × 10³⁰ kg.
A) 86,000 times larger than
B) 260 times larger than
C) 140 times smaller than
D) 6,400 times smaller than

Question

Quizplus · Accepted Answer

The force of gravity between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between them. Using this formula, we can calculate the gravitational force between Earth and the Moon:

Fmoon = G × (mEarth × mMoon) / d²
where G is the gravitational constant, mEarth is the mass of Earth, mMoon is the mass of the Moon, and d is the distance between Earth and the Moon.

Plugging in the values given, we get:
Fmoon = (6.67 × 10^-11 N m²/kg²) × (5.97 × 10²⁴ kg) × (7 × 10²² kg) / (0.003 AU)²
Fmoon = 1.99 × 10²⁰ N

Now, let's calculate the gravitational force between Earth and the Sun:

Fsun = G × (mEarth × mSun) / d²
where mSun is the mass of the Sun and d is the distance between Earth and the Sun. The average distance between Earth and the Sun is 1 AU, which is about 333,000 times larger than the distance between Earth and the Moon.

Using the same formula as before, we get:
Fsun = (6.67 × 10^-11 N m²/kg²) × (5.97 × 10²⁴ kg) × (2 × 10³⁰ kg) / (1 AU)²
Fsun = 3.52 × 10²² N

To compare the two forces, we can divide the force of gravity between the Sun and the Moon by the force of gravity between Earth and the Sun:

Fmoon / Fsun = (1.99 × 10²⁰ N) / (3.52 × 10²² N) = 0.0566

Therefore, the force of gravity between Earth and the Sun is about 18 times smaller than the force of gravity between Earth and the Moon. The closest answer is B, which states that it is 260 times larger than the force between Earth and the Moon, so that is the best choice.

The Force of Gravity Between Earth and the Sun Is