Question

What occurs when the velocity of Earth is doubled?

a. The orbit of Earth around the Sun becomes smaller
b. The orbit of Earth does not change
c. The Earth escapes the Sun
d. The orbit becomes more elliptical

Answer 1

a. The orbit of Earth around the Sun becomes smaller.

Step-by-step 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,

`v_o=\sqrt{(G* M_s)/(R)}.`

Where G is gravitational constant and
`M_s` 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
`v_1`.

Then,
`v_1=\sqrt{(G* M_s)/(r)}`.

Here, r is radius of orbit of earth around sun when earth velocity gets doubled.

Now,
`v_1=2* v_o`.

After all calculations we get,
`r=(R)/(4)`.

Therefore, The orbit of Earth around the Sun becomes smaller.

Hence, a. is correct.

Answer 2

When the Earth's velocity doubles, then a. orbit of earth around sun becomes smaller.

Step-by-step explanation:

The velocity of the earth is given by the formula:

`$v=\sqrt{(G m)/(r)}$`

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,

`$\Rightarrow v=2 \sqrt{(G m)/(r)}$`

If velocity is doubled, then the only thing that could possibly change is the radius of orbit.

`$\Rightarrow v \propto 2 \sqrt{(1)/(r)}$`

Radius of the earth's orbit decreases with increase in velocity of earth.

`$\Rightarrow v \propto \sqrt{(4)/(r)}$`

If the velocity is doubled, the orbit becomes four times smaller. Thus,

`\therefore r=(r)/(4)`