Question Video: Identifying Forces and Velocities of a Planet Orbiting a Star Physics • 9th Grade

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?

02:42

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.

Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.