Video Transcript
The diagram below shows a planet,
in blue, orbiting a star, in orange. Do the arrows in the diagram
correctly show the direction of the gravitational force on the planet, 𝐅, and the
velocity of the planet, 𝑣?
The question is asking us to look
at the arrows in this diagram that represent the gravitational force on the planet
and the velocity of the planet and to determine if these arrows are drawn pointing
in the correct direction. Let’s draw the same diagram but
without the arrows. We will then use our knowledge of
planets orbiting around a star to determine the direction of the gravitational force
acting on and the velocity of the planet.
The first thing to remember is that
any pair of objects will experience a gravitational force between them. So this confirms that the planet
will experience a gravitational force due to the star. We also note that gravity is a
force that always attracts and that it acts from the center of mass of the
object. Therefore, if we assume that the
center of mass of the planet is in the center of the planet and that the center of
mass of the star is in the center of the star, we can determine the direction of the
gravitational force on the planet.
The direction of the gravitational
force acting on the planet due to the star will be acting along the line connecting
the centers of masses of both the planet and the star. And as we know that gravity is an
attractive force, we know that the force will also be directed towards the star. Therefore, the direction we were
given for the gravitational force on the planet is correct.
Now, to determine whether the
direction of the arrow representing the velocity of the planet is correct, let’s
take a look at the shape of the orbit. The orbit is in the shape of a
perfect circle. Therefore, we can assume that the
planet is in a circular orbit around the star. When an object is in a circular
orbit around another object, there’s a very handy relationship between the
gravitational force acting on the orbiting object and its velocity that we can use
to determine the direction of the velocity.
This relationship states that for a
circular orbit, an object’s velocity is always perpendicular to the gravitational
force acting on it. Remember that “perpendicular” just
means at a right angle, or an angle of 90 degrees. This means that the direction of
the arrow for the velocity of the planet should be drawn at an angle of 90 degrees
to the direction of the arrow for the gravitational force acting on the planet. This direction is exactly the same
as what is being shown in the diagram that we have been given. So, the direction we were given for
the velocity is also correct.
Therefore, the answer to the
question is yes. The arrows in the diagram do
correctly show the direction of the gravitational force on the planet and the
velocity of the planet.
