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
vesc = √(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
vorb = √(G*M/r)
From the two previous formulas we can obtain
vesc = √2 * vorb .
Now, it is clear that if the orbital speed was doubled, the planet would escape the Sun.
Answer: (d)
Image Credit: NASA
