Respuesta :
Answer:
Explanation:
Given
Radius of orbit [tex]r=1.5\times 10^8\ km[/tex]
As earth moves around sun it experiences a centripetal force on it which is given by
[tex]a_c=\frac{v^2}{r}[/tex]
where v=velocity of earth
Time period of Revolution
[tex]T=\frac{2\pi \cdot r}{v}[/tex]
time period is 365 days i.e. [tex]3.153\times 10^7\ s[/tex]
[tex]v=\frac{2\pi \times 1.5\times 10^{11}}{3.153\times 10^7}[/tex]
[tex]v=2.98\times 10^4\ m/s[/tex]
[tex]a_c=\frac{v^2}{r}[/tex]
[tex]a_c=\frac{9\times 10^8}{1.5\times 10^{11}}[/tex]
[tex]a_c=0.006\ m/s^2[/tex]
acceleration due to gravity is [tex]9.8\ m/s^2[/tex]
[tex]a_c[/tex] is less than gravity
The definition of centripetal acceleration allows to find the result for the acceleration of the earth around the sun is:
a = 5.95 10⁻³ m / s²
Centripetal acceleration is the acceleration of a body where all the energy is used to change the direction of the velocity keeping the value of its modulus constant.
[tex]a = \frac{v^2}{r}[/tex]
They indicate that the radius of the circular orbit is r = 1.5 10⁸ km = 1.5 10¹¹m.
In a circular motion the speed is constant, therefore we can use the uniform motion relation to find the speed.
[tex]v= \frac{L}{t}[/tex]
The length of the orbital circle is:
L = 2π r
The time for a complete orbit is called the period.
v = [tex]\frac{2\pi r}{T}[/tex]
The period of the Earth's orbit is one year.
T = 1 year (365 days / 1 year) (24 h / 1 day) (3600 s = 1 h)
T = 3.154 10⁷ s
Let's calculate the velocity.
v = [tex]\frac{2 \pi \ 1.5 \ 10^{11}}{6.154 \ 10^7}[/tex]2 pi 1.5 1011 / 3.154 10⁷
v = 2.988 10⁴ m / s
Now we can calculate the acceleration.
[tex]a = \frac{(2.988 \ 10^4)^2 }{1.5 \ 10^{11}}[/tex]
a = 5.95 10⁻³ m / s²
In conclusion using the definition of centripetal acceleration we can find the result for the acceleration of the earth around the sun is:
a = 5.95 10⁻³ m / s²
Learn more here: brainly.com/question/6082363
