Planetary Orbits & Orbital Velocity

[Jimmy87]

Hi pf, please could someone explain why the orbital velocity increases as you get closer to the sun. I treated the situation like circular motion and did a load of calculations. I calculated the orbital velocity of all 8 planets and then the force between each of the eight planets and the sun. I thought the force would drop off as you for further away which would explain the slower orbital velocity but that isn't the case. For instance, Jupiter is 5 times further away than Earth, has a much slower orbital velocity but has a stronger gravitational pull from the Sun.

The only thing I can think of is dividing out the mass of the planet. So although Jupiter has a greater gravitational force (despite orbiting slower) it is much more massive so will require a bigger force even to orbit at this slower speed. Or to put it another way if all 8 planets had the same mass as each other then the force would decrease for all planets with increasing distance. Is that right?

 

[Matterwave]

The only thing I can think of is dividing out the mass of the planet. So although Jupiter has a greater gravitational force (despite orbiting slower) it is much more massive so will require a bigger force even to orbit at this slower speed. Or to put it another way if all 8 planets had the same mass as each other then the force would decrease for all planets with increasing distance. Is that right?

Yes, you have it basically right. Jupiter is more massive and so feels a stronger force between it and the Sun; however, because it is more massive, it requires a stronger centripetal force to give it the right centripetal acceleration for its orbit. You can "divide out" the mass of the Jupiter as long as you are not considering the reaction force on the Sun. The effect of Jupiter's large mass on the Sun means that both Jupiter and the Sun orbit the barycenter of the Jupiter-Sun system. The Barycenter is located within the Sun, but is not at the center of the Sun, so the Sun actually wobbles as Jupiter orbits around it.

 

[Jimmy87]

Yes, you have it basically right. Jupiter is more massive and so feels a stronger force between it and the Sun; however, because it is more massive, it requires a stronger centripetal force to give it the right centripetal acceleration for its orbit. You can "divide out" the mass of the Jupiter as long as you are not considering the reaction force on the Sun. The effect of Jupiter's large mass on the Sun means that both Jupiter and the Sun orbit the barycenter of the Jupiter-Sun system. The Barycenter is located within the Sun, but is not at the center of the Sun, so the Sun actually wobbles as Jupiter orbits around it.

Thanks for the answer. So is it correct to still say that planets orbit faster closer to the Sun because the pull from the Sun is greater so they need to move quicker to remain in orbit.

 

[Matterwave]

Thanks for the answer. So is it correct to still say that planets orbit faster closer to the Sun because the pull from the Sun is greater so they need to move quicker to remain in orbit.

Not the "pull is greater", but the "gravitational field is greater" so they must have a higher velocity to remain in orbit.

 

[dean barry]

Treating all the planet masses as negligible (which they are compared to the sun), and dealing with gravitational accelerations only, you can simplify the velocity calculation of any orbiting planet to :
v = sqrt ( ( G * M ) / r )
Where :
G = 6.674 E-11 (a constant)
M = suns mass in kg
r = planet orbital radius in meters