How would the speed of earth's orbit around the sun change if earth's distance from the sun
increased by 4 times?
1. it would increase by a factor of 2.

2. it would increase by a factor of 4.

3. it would decrease by a factor of 2.

4. the speed would not change.

If Earth’s distance from the sun increased by 4 times then the speed of Earth’s orbit around the sun would decrease by a factor of 2.

Option 3

Explanation:

From Newton’s second law of motion, it is known that any kind of external force acting on an object will be equal to object’s mass and acceleration exerted on the object. So in this case, the gravitational force between Earth and Sun will be equal to the mass (M) and acceleration exerted on Earth.

It is known that,

Thus, substituting this, we get,

Also, we know,

Then, comparing both the equation, we get the orbital velocity as,

So, here G is gravitational constant, M is the mass of Sun and r is the distance of separation of Earth from Sun.

If the distance of Earth from Sun increases by 4 times so r’ will be 4r. Thus the new orbital velocity v’ will be

So,  

Thus, the orbital speed will be decreased by a factor of 2 when the distance of Earth from the Sun increased by 4 times.

the entire statement is true and correct.  

there's no diagram, nothing is illustrated, and no question is asked.