A planet has mass m₁ and is at a distance r, from the sun. A second planet has mass m₂ = 10m₁ and at a distance of r₂ = 2r₁ from the sun. Determine the ratio of the gravitational force experienced by the planets.

Monica08

4 months ago

B is the answer

jejuis

2 years ago

To determine the ratio of the gravitational forces experienced by the planets, we can use Newton's law of universal gravitation, which states:

\[ F = \frac{{G \cdot m_1 \cdot m_2}}{{r^2}} \]

where:
- \( F \) is the gravitational force,
- \( G \) is the gravitational constant (a constant value),
- \( m_1 \) and \( m_2 \) are the masses of the two objects (in this case, the planets),
- \( r \) is the distance between the centers of the two objects.

Let's denote the gravitational force experienced by the first planet as \( F_1 \) and the gravitational force experienced by the second planet as \( F_2 \).

For the first planet:
\[ F_1 = \frac{{G \cdot m_1 \cdot m_{\text{sun}}}}{{r_1^2}} \]

For the second planet:
\[ F_2 = \frac{{G \cdot m_2 \cdot m_{\text{sun}}}}{{r_2^2}} \]

We want to find the ratio \( \frac{{F_1}}{{F_2}} \):

\[ \frac{{F_1}}{{F_2}} = \frac{{\frac{{G \cdot m_1 \cdot m_{\text{sun}}}}{{r_1^2}}}}{{\frac{{G \cdot m_2 \cdot m_{\text{sun}}}}{{r_2^2}}}} \]

\[ \frac{{F_1}}{{F_2}} = \frac{{m_1}}{{m_2}} \cdot \frac{{r_2^2}}{{r_1^2}} \]

Substitute the given values:
\[ \frac{{F_1}}{{F_2}} = \frac{{m_1}}{{10m_1}} \cdot \frac{{(2r)^2}}{{r^2}} = \frac{{1}}{{10}} \cdot 4 = \frac{{4}}{{10}} = \frac{{2}}{{5}} \]

So, the ratio of the gravitational force experienced by the planets is \( 2 : 5 \).

Therefore, the correct answer is:

B. \( 2 : 5 \)

agadido

3 years ago

you have no use in this web

samlaz

2 years ago

Answer

Dave333

4 years ago

Only Jesus is my glory🤷