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

Answer:

c. it would decrease by a factor of 2.

Explanation:

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

Now we will have

$F_c = \frac{GMm}{r^2}$

$\frac{mv^2}{r} = \frac{GMm}{r^2}$

now we have

$v = \sqrt{\frac{GM}{r}}$

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

so the orbital speed is changed by

$v' = \sqrt{\frac{GM}{4r}}$

so the speed would be given as

$v' = \frac{v}{2}$

so it is half of the initial speed