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zepelin
1 month 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?

Physics
2 answers:
kicyunya [3.2K]1 month ago
5 0
To find the gravitational force exerted on you by the Earth, we start with your weight estimated at around 60 kg.

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

Thus, 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 calculate the gravitational force due to the Sun by substituting,
m₁ = 1.989 × 10³⁰ kg and the distance between the centers of the Sun and Earth as 149.6 × 10⁹ m.
This gives us,
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

The ratio is then calculated as 0.356 N / 589.18 N, yielding Ratio = 6.04.
inna [3.1K]1 month ago
3 0

The gravitational force ratio between the sun and the earth stands at approximately 1: 1580

\texttt{ }

Further explanation

According to Newton's law of gravitation, the force attracting two bodies can be represented mathematically as follows:

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

F = Gravitational Force ( Newtons )

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

m = Mass of the Object ( kg )

R = Separation Distance ( m )

Let’s solve this now!

\texttt{ }

Given:

Earth's radius = Re = 6.4 × 10⁶ m

Earth's mass = Me = 6.0 × 10²⁴ kg

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

Sun's mass = Ms = 2.0 × 10³⁰ kg

Requested:

what is the ratio of the gravitational forces of the sun to the earth?

Solution:

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{ }

Learn more

  • Consequences of Gravity:
  • Gravity's Effect on Objects:
  • Gravity Acceleration:

\texttt{ }

Answer details

Level: High School

Field: Physics

Chapter: Gravitational Fields

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