Solving Satellite Speed Problem: Draw Path for Faster & Slower Orbits

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In summary, the conversation discusses the behavior of a satellite at different speeds in circular orbits of a given radius around a planet. The question asks for a drawing of the satellite's path in both cases, and different solutions are proposed by the participants. The summary concludes by mentioning the role of mechanical energy and radial speed in determining the satellite's orbit.
  • #1
impendingChaos
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Homework Statement


When a satellite is at the desired altitude over the equator or Jupiter its velocity has the correst direction but the speed is (a) slightly faster that the correct speed for a circular orbit of the radius and (b) is slighly slower than the correct speed for a circular orbit of the radius

The question then offers two spheres to represent the planet and the path if the satellite had the proper speed, one must now draw the new path of the satellite for both cases.


The Attempt at a Solution



I believe that in instance (a), the path would be greater from the accepted path of the sattellite with proper speed, for a time, but would then return to the original path of the correct sattelite speed once it has circled the planet due to gravity, forming an ellipse around the circular orbit of the correctly sped satellite.

I feel the same will happen for instance (b) except the ellipse will form inside the path for a satellite of the correct speed.

My friends believe this is incorrect and the sattelite will (a) spiral away from the planet outwards (away form the correct path) and (b) spiral inwards (inside the correct path)

Simply need some hint to help me justify which is correct.
Thx.
C.N.
 
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  • #2
Planetary (and satellite) motions are generally descibed by conic sections. Which type of orbit it follows is determined by the total mechanical energy of the satellite. The other fact to consider is that its radial speed is zero at the point in consideration. This suggests that the satellite will be at the symmetrical point of the orbit, eg. if it is an elliptical orbit it will either be at aphelion or perihelion.
 
  • #3


I would approach this problem by considering the laws of planetary motion and the principles of orbital mechanics. The correct speed for a satellite in a circular orbit is determined by the balance between the gravitational force of the planet and the centrifugal force of the satellite's motion. If the satellite is slightly faster or slower than this correct speed, it will experience a net force in the direction of the planet or away from it, respectively.

In instance (a), where the satellite is slightly faster than the correct speed, the net force will be towards the planet, causing the satellite to move closer to the planet. This will result in a smaller orbital radius and a more elliptical path. However, the satellite will still maintain its orbital motion around the planet due to the balance of forces.

In instance (b), where the satellite is slightly slower than the correct speed, the net force will be away from the planet, causing the satellite to move further away from the planet. This will result in a larger orbital radius and a more elliptical path. Again, the satellite will still maintain its orbital motion around the planet.

In both cases, the satellite will not spiral away or towards the planet, as suggested by your friends. This is because the gravitational force of the planet will always act to keep the satellite in its orbit, regardless of its speed. Therefore, your initial understanding of the satellite forming an ellipse around the correct orbit is correct.

In conclusion, to solve the satellite speed problem, it is important to consider the balance of forces and the laws of planetary motion. The satellite will maintain its orbital motion around the planet, but its path will vary depending on its speed relative to the correct speed for a circular orbit.
 

What is the purpose of solving satellite speed problems?

The purpose of solving satellite speed problems is to optimize the path of a satellite in order to achieve a faster or slower orbit, depending on the specific needs and objectives of the mission. This can help maximize efficiency and reduce costs in space exploration and communication.

What factors affect the speed of a satellite orbit?

The speed of a satellite orbit is affected by several factors such as the mass and size of the satellite, the altitude of the orbit, the gravitational pull of the Earth, and any external forces such as atmospheric drag or solar radiation. These factors must be taken into consideration when solving satellite speed problems.

What tools and techniques can be used to solve satellite speed problems?

Some common tools and techniques used to solve satellite speed problems include mathematical equations and models, computer simulations, and real-time tracking and monitoring systems. These methods can help scientists and engineers accurately predict and adjust the speed of a satellite's orbit.

How do you draw a path for a faster orbit?

To draw a path for a faster orbit, scientists can use mathematical calculations to determine the optimal trajectory, taking into account the satellite's speed, altitude, and other variables. This path may involve adjusting the satellite's altitude and angle of inclination, as well as utilizing gravitational assists from other celestial bodies.

What are the potential challenges in solving satellite speed problems?

Some potential challenges in solving satellite speed problems include unexpected external forces such as space debris or solar flares, which can disrupt the planned trajectory. Additionally, accurately predicting and adjusting the speed of a satellite's orbit requires precise calculations and monitoring, which can be challenging and complex tasks.

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