Respuesta :
Answer:
The Force of Gravity is less on the moon
Explanation:
The universal gravitational law allows to find the results for the outside exerted by the sun and the moon on a body located at two points on Earth and several related questions are:
Moon force
- nearest point F₁ = 3,443 10⁻⁵ N
- farthest point F₂ = 3,210 10⁻⁵ N
Sun force
- closest point F₃ = 5.9302 10⁻³ N
- farthest point F₄ = 5.9286 10⁻³ N
- The force exerted by the sun is about 180 times greater than the force exerted by the moon on the body.
- The variation of the force is greater for the force exerted by the moon
The gravitation universal law is proportional to the mass of the bodies and inversely proportional to the distance squared, this force is also called the force of gravity
F = [tex]G \frac{Mm}{r^2 }[/tex]
Where F is the force, M and m the mass of the two bodies and r the distance between them.
Let's calculate this force for an object of m = 1 kg located on the surface of the Earth by the Moon
We use the tabulated data:
- Moon mass M= 7.349 10²² kg
- Distance from Earth to Moon [tex]R_{em}[/tex]= 3.84 10⁸ m
- Radius of the Earth [tex]R_e[/tex] = 6.371 10⁶ m
let's substitute
F = [tex]6.67 \ 10^{11} \ 7.349 10^{22} \ \frac{1}{r^2}[/tex]
F = [tex]\frac{4.902 \ 10^{12}}{r^2}[/tex]
Let's find the distance from the mass to the Moon, they ask that the object be in two points:
- The most closed point
The distance between the moon and the earth is measured from its center therefore the distance of the object is the distance from the earth to the luma minus the radius of the earth
[tex]r_1 = Rem - Re[/tex]r
r₁ = 3.844 10⁸ - 6.371 10⁶
r₁ = 3.780 10⁸ m
Let's calculate
F₁ = [tex]\frac{4.902 \ 10^{12}}{(3.780 \ 10^8)^2}[/tex]
F₁ = 3,443 10⁻⁵ N
- The farthest point
in this case the body is on the opposite side of the earth
r₂ = Rem + Re
r₂ = 3.844 10⁸ + 6.3771 10⁶
r₂ = 3.908 10⁸ m
we calculate
F₂ = 4.902 1012 / (3.908 10⁸) ²
F₂ = 3,210 10⁻⁵ N
It is requested to calculate the same forces for the sun
we substitute
F = [tex]G \frac{M_s m}{r^2}[/tex]
F = 6.67 10⁻¹¹ 1.989 10³⁰ [tex]\frac{1}{r^2}[/tex]
F = 1.327 10²⁰ [tex]\frac{1}{r^2}[/tex]
look for the strength for two points of the body
- The closest is the distance from the sun to the earth minus the radius of the earth
r₃ = Rse -Re
r₃ = 1.496 10¹¹ - 6.371 10⁶
r₃ = 1.4959 10¹¹ m
we calculate
F₃ = 1.327 10²⁰ / (1.4959 1011) ²
F₃ = 5.9302 10⁻³ N
- farthest point
r₄ = [tex]R_{se} + R_e[/tex]
r₄ = 1.496 10¹¹ + 6.371 10⁶
r₄ = 11.4961 10¹¹ m
F₄ = 1.327 10²⁰ / (1.4961 1011) ²
F₄ = 5.9286 10⁻³ N
To answer which force is greater, let's look for the relationship between the two forces
[tex]\frac{F_{sum}}{F_{moon}} = \frac{F_4}{F_2} = \frac{5.93 \ 10^{-3}}{3.2 \ 10_{-5} }[/tex]
[tex]\frac{F_{sum}}{F_{moon}}[/tex] = 1.85 10²
Consequently, the force of the sun is 10² times greater than the force of the Moon.
We look for the difference between the strength at the two points
Moon
ΔF_m = F₁-F₂
ΔF_m = (3,443 - 3,210) 10⁻⁵
ΔF_m = 0.233 10⁻⁵ N
Sun
Δf_s = F₃ - F₄
Δf_s = (5.9302 -9.9286) 10⁻³
Δf_s = 0.002 10-3 N
We observe that there is a greater difference in the force of the moon for the body located in two opposite points of the Earth.
In Conclusion using the universal gravitational law we can find the results for the outside exerted by the sun and the moon on a body located at two points on Earth and several related questions are:
Moon force
- nearest point F₁ = 3,443 10⁻⁵ N
- farthest point F₂ = 3,210 10⁻⁵ N
Sun force
- closest point F₃ = 5.9302 10⁻³ N
- farthest point F₄ = 5.9286 10⁻³ N
- The force exerted by the sun is about 180 times greater than the force exerted by the moon on the body.
- The variation of the force is greater for the force exerted by the moon
Learn more here: brainly.com/question/858421
