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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 three times larger 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

Respuesta :

I18ntech

Gravitational force is given by, [tex] F= G\frac{mM}{R^{2}} [/tex]

Where, m and M are the masses of the objects, R is the distance between them and G gravitational constant.

Gravitational force of the star on planet 1, [tex] F_{1}= G\frac{m_{1}M}{R^{2}} [/tex]

Gravitational force of the star on planet 2, [tex] F_{2}= G\frac{3m_{1}M}{(3R)^{2}} [/tex]

Ratio, [tex] \frac{F_{1}}{F_{2}}= \frac{\frac{Gm_{1}M}{R^{2}}}{\frac{G3m_{1}M}{(3R)^{2}}} [/tex]

[tex] \frac{F_{1}}{F_{2}}= \frac{3}{1} [/tex]

Therefore, the gravitational force of the star on the planet 1 is three times that on planet 2.

johanrusli

The ratio of gravitational forces F₂ : F₁ = 1 : 3

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Further explanation

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

[tex]\large {\boxed {F = G \frac{m_1 ~ m_2}{R^2}} }[/tex]

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 !

[tex]\texttt{ }[/tex]

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 = 3R₁

Asked:

ratio of force = F₂ : F₁ = ?

Solution:

[tex]F_2 : F_1 = G \frac{ M m_2} { (R_2)^2 } : G \frac{ M m_1} { (R_1)^2 }[/tex]

[tex]F_2 : F_1 = \frac{m_2} { (R_2)^2 } : \frac{ m_1} { (R_1)^2 }[/tex]

[tex]F_2 : F_1 = \frac{3m_1} { (3R_1)^2 } : \frac{ m_1} { (R_1)^2 }[/tex]

[tex]F_2 : F_1 = \frac{3} { 9 } : 1[/tex]

[tex]F_2 : F_1 = \frac{1} { 3 } : 1[/tex]

[tex]\boxed{F_2 : F_1 = 1 : 3}[/tex]

[tex]\texttt{ }[/tex]

Learn more

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

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Answer details

Grade: High School

Subject: Physics

Chapter: Gravitational Fields

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