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3 years ago

15

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 gravitatio

nal force on you?

2 answers:

Pachacha [2.7K]3 years ago

5 0

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<span> kg
Distance between centers of sun and earth = 149.6</span>×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
<em>Ratio = 6.04</em>

skelet666 [1.2K]3 years ago

3 0

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

$\texttt{ }$

<h3>Further explanation</h3>

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

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

<em>F = Gravitational Force ( Newton )</em>

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

<em>m = Object's Mass ( kg )</em>

<em>R = Distance Between Objects ( m )</em>

Let us now tackle the problem !

$\texttt{ }$

<u>Given:</u>

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

<u>Asked:</u>

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

<u>Solution:</u>

$F_s : F_e = G \frac{ m M_s }{R_s^2} : G \frac{ m M_e }{R_e^2}$

$F_s : F_e = \frac{ M_s }{R_s^2} : \frac{ M_e }{R_e^2}$

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

$F_s : F_e \approx 1 : 1580$

$\texttt{ }$

<h3>Learn more</h3>

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

$\texttt{ }$

<h3>Answer details</h3>

Grade: High School

Subject: Physics

Chapter: Gravitational Fields

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