Each planet has its own orbital speed. If the orbital speed was doubled, the planet would

a) enter into a closer orbit around the Sun.

b) enter into a far orbit around the Sun.

c) warm up.

d) escape the Sun.

###### Solution.

The critical value above which a planet would escape the Sun is called the escape velocity. The formula for the escape velocity

v_{esc} = √(2*G*M/r) ,

where M is the mass of the Sun, G is the universal gravitational constant and r is the distance between the center of the Sun and the center of the planet.

The orbital velocity of the planet is given by

v_{orb} = √(G*M/r)

From the two previous formulas we can obtain

v_{esc} = √2 * v_{orb} .

Now, it is clear that if the orbital speed was doubled, the planet would escape the Sun.

Answer: (d)

Image Credit: NASA