The new force of gravitational interaction F₂ is ¹/₄ F₀
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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 !
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Given:
initial altitude of the satellite = h₁ = R
initial force of gravitational interaction = F₀
final altitude of the satellite = h₂ = 3R
radius of the planet = R
Asked:
final force of gravitational interaction = F₂
Solution:
[tex]F_o : F_2 = G \frac{ M m} { (R + h_1)^2 } : G \frac{ M m} { (R + h_2)^2 }[/tex]
[tex]F_o : F_2 = \frac{ 1 } { (R + h_1)^2 } : \frac{ 1 } { (R + h_2)^2 }[/tex]
[tex]F_o : F_2 = (R + h_2)^2 : (R + h_1)^2[/tex]
[tex]F_o : F_2 = (R + 3R)^2 : (R + R)^2[/tex]
[tex]F_o : F_2 = (4R)^2 : (2R)^2[/tex]
[tex]F_o : F_2 = 4^2 : 2^2[/tex]
[tex]F_o : F_2 = 16 : 4[/tex]
[tex]F_o : F_2 = 4 : 1[/tex]
[tex]\boxed {F_2 = \frac{1}{4} F_o}[/tex]
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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
