Question

How would the speed of earth’s orbit around the sun change if earth’s distance from the sun increased by 4 times?

a. it would increase by a factor of 2.
b. it would increase by a factor of 4.
c. it would decrease by a factor of 2.
d. the speed would not change.

Answer 1

C, it is the only logical choice, and if it were to get further away like that earth would no longer support life.

Answer 2

c. it would decrease by a factor of 2.

Step-by-step explanation:

As we know that centripetal force on Earth due to Sun is due to gravitational attraction force of Sun

Now we will have

`F_c = (GMm)/(r^2)`

`(mv^2)/(r) = (GMm)/(r^2)`

now we have

`v = \sqrt{(GM)/(r)}`

now if the orbital radius or the distance from sun is increased by factor of 4

so the orbital speed is changed by

`v' = \sqrt{(GM)/(4r)}`

so the speed would be given as

`v' = (v)/(2)`

so it is half of the initial speed