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Assume that you stay on the earth's surface. what is the ratio of the sun's gravitational force on you to the earth's gravitational force on you?

Respuesta :

meerkat18
First, let's determine the gravitational force of the Earth exerted on you. Suppose your weight is about 60 kg. 

F = Gm₁m₂/d²
where
m₁ = 5.972×10²⁴ kg (mass of earth)
m₂ = 60 kg
d = 6,371,000 m (radius of Earth)
G = 6.67408 × 10⁻¹¹ m³ kg⁻¹ s⁻²

F = ( 6.67408 × 10⁻¹¹ m³ kg⁻¹ s⁻²)(60 kg)(5.972×10²⁴ kg)/(6,371,000 m )²
F = 589.18 N

Next, we find the gravitational force exerted by the Sun by replacing,
m₁ = 1.989 × 10³⁰ kg
Distance between centers of sun and earth = 149.6×10⁹ m
Thus,
d = 149.6×10⁹ m - 6,371,000 m = 1.496×10¹¹ m

Thus,
F = ( 6.67408 × 10⁻¹¹ m³ kg⁻¹ s⁻²)(60 kg)(1.989 × 10³⁰ kg)/(1.496×10¹¹ m)²
F = 0.356  N

Ratio = 0.356  N/589.18 N
Ratio = 6.04
johanrusli

The ratio of gravitational force of the sun to the earth's gravitational force is about 1 : 1580

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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:

radius of Earth = Re = 6.4 × 10⁶ m

mass of the Earth = Me = 6.0 × 10²⁴ kg

distance from Sun to Earth = Rs = 147 × 10⁹ m

mass of the Sun = Ms = 2.0 × 10³⁰ kg

Asked:

ratio of gravitational force of the sun and the earth = ?

Solution:

[tex]F_s : F_e = G \frac{ m M_s }{R_s^2} : G \frac{ m M_e }{R_e^2}[/tex]

[tex]F_s : F_e = \frac{ M_s }{R_s^2} : \frac{ M_e }{R_e^2}[/tex]

[tex]F_s : F_e = \frac{ 2 \times 10^{30} }{(147 \times 10^9)^2} : \frac{ 6.0 \times 10^{24} }{ (6.4 \times 10^6)^2}[/tex]

[tex]F_s : F_e \approx 1 : 1580[/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

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