# Do planets in elliptical orbits exhibit constant magnitudes of acceleration in their orbits?

I'm trying to reason through a problem. Consider Jupiter, which orbits the sun in an elliptical path. Is the magnitude of its acceleration constant throughout its orbit?

My reasoning leads me to think no. The net force on Jupiter in the centripetal direction is due to its gravitational interaction with the sun. Assume that other planetary interactions do not apply here. Hence, the simple net force on Jupiter is $$F_{g}=G\frac{M_{Jupiter}M_{Sun}}{r^2}$$. Since net force depends on the radius of Jupiter's orbit, which is non circular, it varies with Jupiter's orbital position, indicating a non constant acceleration.

The motion of the planets around the sun involves a constant acceleration. Here, however, acceleration means “changing direction” instead of “changing speed;” both are valid under the Second Law.

This leads me to think that my above reasoning is faulty. Could someone explain to me where I went wrong? Everything else I found on Google was unrelated, instead focusing on the non constant velocity of planet's in their orbits.

Thanks.

• The website you quoted is probably assuming a circular orbit. – psitae May 30 at 3:41
• Not only the centripetal acceleration is due to gravitational interaction with the Sun. The total (net) acceleration is due to this interaction, assuming gravity is the only force and neglecting interactions with other bodies. For elliptical orbits the acceleration includes a centripetal and a tangential acceleration. – nasu May 30 at 16:20