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 on the diagram and determine if they’ve been drawn in the correct
directions. To begin, let’s draw the same
diagram, but without the arrows. We can then use our knowledge of
planetary orbit 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 due to their mass. We also note that gravity is a
force that always attracts and that it acts from the centers of mass of the
objects. 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 will be acting along the line connecting the centers of
mass of both the planet and the star. And as we know that gravity is an
attractive force, we know that the force on the planet will be directed towards the
star. Therefore, we know that the
direction of the gravitational force on the planet is drawn correctly in the given
diagram.
Now, we need to determine whether
the direction of the arrow representing the velocity of the planet is correct. Notice that the orbit is in the
shape of a perfect circle. And therefore we can assume that
the planet is in a circular orbit around the star. Let’s recall that in the special
case of 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 at 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. The velocity arrow should then
point vertically either upwards or downwards.
But this is not what’s being shown
in the given diagram. Here, the angle between the arrows
is less than 90 degrees, so the arrows are not perpendicular. This diagram is therefore
incorrect. So the answer to this question is
no. The arrows in the diagram do not
correctly show the direction of the gravitational force on the planet and the
velocity of the planet.
