Respuesta :
Answer:
When the Earth's velocity doubles, then a. orbit of earth around sun becomes smaller.
Explanation:
The velocity of the earth is given by the formula:
[tex]$v=\sqrt{\frac{G m}{r}}$[/tex]
Where,
G is Gravitational constant
m is Mass of Earth
r is Radius of Earth around the sun
Velocity is a term which is used to define a fast moving object's speed in a particular direction.
When the velocity is doubled,
[tex]$\Rightarrow v=2 \sqrt{\frac{G m}{r}}$[/tex]
If velocity is doubled, then the only thing that could possibly change is the radius of orbit.
[tex]$\Rightarrow v \propto 2 \sqrt{\frac{1}{r}}$[/tex]
Radius of the earth's orbit decreases with increase in velocity of earth.
[tex]$\Rightarrow v \propto \sqrt{\frac{4}{r}}$[/tex]
If the velocity is doubled, the orbit becomes four times smaller. Thus,
[tex]\therefore r=\frac{r}{4}[/tex]
Answer:
a. The orbit of Earth around the Sun becomes smaller.
Explanation:
Now, it in the given question it is stated that what will happen when earth's velocity gets doubled. Therefore, their will be no change in quantities like mass of sun and earth.
Now, we know that orbital velocity of earth around sun is given by,
[tex]v_o=\sqrt{\dfrac{G\times M_s}{R}}.[/tex]
Where G is gravitational constant and [tex]M_s[/tex] is the mass of sun and
R is radius of orbit of earth around sun.
Now, let the velocity get doubled and let it be [tex]v_1[/tex].
Then, [tex]v_1=\sqrt{\dfrac{G\times M_s}{r}}[/tex].
Here, r is radius of orbit of earth around sun when earth velocity gets doubled.
Now, [tex]v_1=2\times v_o[/tex].
After all calculations we get, [tex]r=\dfrac{R}{4}[/tex].
Therefore, The orbit of Earth around the Sun becomes smaller.
Hence, a. is correct.
