Question

The gravitational force of a star on an orbiting planet 1 is f1. planet 2, which is three times as massive as planet 1 and orbits at twice the distance from the star, experiences gravitational force f2. part a what is the ratio f2f1? you can ignore the gravitational force between the two planets.

Answer 1

The ratio F₂ : F₁ = 3 : 4

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Further explanation

Newton's gravitational law states that the force of attraction between two objects can be formulated as follows:

$\large {\boxed {F = G \frac{m_1 ~ m_2}{R^2}} }$

F = Gravitational Force ( Newton )

G = Gravitational Constant ( 6.67 × 10⁻¹¹ Nm² / kg² )

m = Object's Mass ( kg )

R = Distance Between Objects ( m )

Let us now tackle the problem !

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Given:

Gravitational force on planet 1 = F₁

Gravitational force on planet 2 = F₂

mass of planet 1 = m₁

mass of planet 2 = m₂ = 3m₁

distance between planet 1 and star = R₁

distance between planet 2 and star = R₂ = 2R₁

Asked:

ratio of force = F₂ : F₁ = ?

Solution:

$F_2 : F_1 = G \frac{ M m_2} { (R_2)^2 } : G \frac{ M m_1} { (R_1)^2 }$

$F_2 : F_1 = \frac{m_2} { (R_2)^2 } : \frac{ m_1} { (R_1)^2 }$

$F_2 : F_1 = \frac{3m_1} { (2R_1)^2 } : \frac{ m_1} { (R_1)^2 }$

$F_2 : F_1 = \frac{3} { 4 } : 1$

$\boxed{F_2 : F_1 = 3 : 4}$

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Learn more

• Impacts of Gravity : brainly.com/question/5330244
• Effect of Earth’s Gravity on Objects : brainly.com/question/8844454
• The Acceleration Due To Gravity : brainly.com/question/4189441

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Answer details

Grade: High School

Subject: Physics

Chapter: Gravitational Fields

Answer 2

Let  us consider two bodies having masses m and m' respectively.

Let they are  separated by a distance of r from each other.

As per the Newtons law of gravitation ,the gravitational force between two bodies is given as -  $F = G\frac{mm'}{r^{2} }$   where G is the gravitational force constant.

From the above we see that F ∝ mm' and $F\alpha \frac{1}{r^{2} }$

Let the orbital radius of planet  A is $r_{1}$  = r and mass of planet is $m_{1}$.

Let the mass of central star is m .

Hence the gravitational force for planet A  is $f_{1} =G \frac{m_{1}*m }{r^{2} }$

For planet B the orbital radius  $r_{2} =2r_{1}$ and mass $m_{2} = 3 m_{1}$

Hence the gravitational force $f_{2} =G\frac{m m_{2} }{r^{2} }$

                                                 $f_{2} =G\frac{m*3m_{1} }{[2r_{1}] ^{2} }$

                                                 $= \frac{3}{4} G\frac{mm_{1} }{r_{1} ^{2} }$

Hence the ratio is  $\frac{f_{2} }{f_{1} } = \frac{\frac{3}{4}G mm_{1/r_{1} ^2} }{Gmm_{1}/r_{1} ^2 }$

                                      $=\frac{3}{4}$     [ ans]