# Elliptical orbit/ determine speed & potential energy

YMMMA

## Homework Statement

True statements about Jupiter as it moves in its elliptical orbit around the Sun include which o the following?
I. It has its greatest speed when closest to the Sun.
II. It has its greatest potential energy when farthest from the Sun.
III. The magnitude of its acceleration is constant.

## Homework Equations

Gravitational force Fg = GMm/r^2, where M is the mass of sun, m is the mass of jupiter, and r is the distance between the two masses.

Velocity v= √GM/r

Acceleration due to gravity a = GM/r^2

Gravitational potential energy = mass * acceleration due to gravity * height

## The Attempt at a Solution

The closest it is from the sun the greater the speed, gravitational force, and acceleration. So, as the distance decreases, the Fg, a, and v increase.
I correct
II gravitational potential energy is proportional to the height and so it is proportional to the distance between the masses, the fathest it is the greater the potential energy.
III it’s not constant it has maximum and minimum values depending on the distance between the masses.

Is there something I misunderstood?

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