Draw a free body diagram for a satellite in an elliptical orbit showing why its speed increases as it approaches its parent body and decreases as it moves away.
show gravity vector toward Earth, always toward Earth. Show present velocity. Note that as it aproaches, the force of gravity is partly in the direction of velocity, causing it to speed up. https://www.physicsclassroom.com/Class/circles/u6l4b7.gif
Oh, boy! I've never been so excited to draw a diagram in my life! Here you go:
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Alright, let me explain the comedy behind this masterpiece! 🎭
As the satellite orbits the parent body, let's call it the "star of the show," it goes through an elliptical path. When the satellite moves closer to the star, it experiences a gravitational attraction, like a human to a pizza delivery guy. We all want our pizza hot, after all!
This attraction causes the satellite's speed to increase since the gravitational force "pulls" the satellite inwards. Think of it like a roller coaster going downhill – the closer the satellite gets, the faster it goes. Weeee!
Now, when the satellite moves away from the star, it starts to lose that gravitational pull, just like a balloon floating away from a disappointed clown. 😢 Imagine waving goodbye to your dreams of delicious pizza! Consequently, the satellite's speed decreases as it moves further away from the star.
And that, my friend, is the dramatic comedy behind the speed changes of a satellite in an elliptical orbit. I hope my artistic skills made this explanation a bit more entertaining for you! 🤡
To draw a free body diagram for a satellite in an elliptical orbit, we need to consider the forces acting on the satellite.
1. Centripetal Force (Fc): The centripetal force acts towards the center of the orbital path and is responsible for keeping the satellite in its orbit. It is provided by the gravitational force between the satellite and its parent body (usually a planet or a star).
2. Gravitational Force (Fg): The gravitational force acts between the satellite and its parent body. It always pulls the satellite towards the parent body.
3. Tangential Velocity (V): The satellite also has a velocity tangent to its orbital path, which is either increasing or decreasing depending on its position in the elliptical orbit.
Now, let's consider the two extreme positions of the satellite in the elliptical orbit:
1. When the satellite is closest to the parent body (perigee):
- The centripetal force (Fc) acts towards the center of the orbit.
- The gravitational force (Fg) acts towards the parent body.
- The velocity vector (V) is perpendicular to both Fc and Fg.
2. When the satellite is farthest from the parent body (apogee):
- The centripetal force (Fc) still acts towards the center of the orbit.
- The gravitational force (Fg) still acts towards the parent body.
- The velocity vector (V) is again perpendicular to both Fc and Fg.
In both cases, the centripetal force is constant as it depends on the mass of the satellite and the radius of its orbit. However, the gravitational force is stronger when the satellite is closer to the parent body and weaker when it is farther away.
Since the gravitational force changes, the speed of the satellite changes accordingly. As the satellite approaches its parent body, the gravitational force increases, resulting in a higher centripetal force requirement. To satisfy this increased force, the velocity of the satellite also increases.
Conversely, as the satellite moves away from the parent body, the gravitational force decreases, leading to a lower centripetal force requirement. The velocity of the satellite decreases to match this reduced force.
Remember, this diagram only focuses on the forces acting on the satellite in an elliptical orbit and does not consider other factors such as atmospheric drag or additional forces from external bodies.
To draw a free body diagram for a satellite in an elliptical orbit, we need to consider the forces acting on it.
A satellite in orbit experiences two primary forces: gravitational force and centripetal force. Gravitational force pulls the satellite towards its parent body, while centripetal force acts towards the center of the orbit, keeping the satellite in its orbit.
As the satellite approaches its parent body, the gravitational force increases because the distance between them decreases. The free body diagram would show two vectors: one representing the gravitational force pointing towards the parent body, and another representing the centripetal force, pointing towards the center of the orbit.
When the satellite moves away from the parent body, the gravitational force decreases because the distance between them increases. The free body diagram would still have two vectors, but the gravitational force vector would be shorter than before, while the centripetal force vector remains the same.
In both cases, the magnitude of the centripetal force remains constant, as long as the satellite maintains a consistent speed. However, because the gravitational force changes, the elliptical orbit causes the satellite's speed to vary.
So, to summarize, the free body diagram for a satellite in an elliptical orbit would include a gravitational force vector pointing towards the parent body and a centripetal force vector pointing towards the center of the orbit. The changing distance between the satellite and its parent body causes the gravitational force to vary, resulting in the satellite's speed increasing as it approaches the parent body and decreasing as it moves away.