Elliptical orbit question

The conversation discusses a satellite that is orbiting a planet with a mass of 4X 10^20 kg at a distance of 10^7m with a velocity of 30 degrees. The question asks for the eccentricity of the orbit, which is found by using the equations for mechanical energy and gravitational potential energy. The attempt at a solution involves finding the vertical velocity and plugging it into the equation for gravitational potential energy, but it does not give the correct answer. To solve the problem, you may want to think about how eccentricity is related to the semi-major axis and semi-latus rectum, and how they are related to the information given in the problem. In summary, the conversation discusses finding the eccentricity of a
  • #1

Homework Statement


a satellite is set to orbit a planet of mass 4X 10^20 kg .
It is placed at a distance of separation of 10^7m with a velocity of 30 degrees to the line connecting the center of the planet and the satellite. What will be its eccentrity fo orbit? (Answer is .89)


Homework Equations


ME = KE + PE
KE = 1/2 mv^2
PE = -GMm/r

The Attempt at a Solution


I did 40m/s *sin (30) = vertical velocity.
Then, I plugged it into the equation -GMm/r = .5m(40m/s *sin (30))^2 + -GMm/r

I didn't get the answer though...
please help!
 
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  • #3
You may want to think (or read in your textbook) about how eccentricity (e) is related to the semi-major axis (a) and semi-latus rectum (p), and how those two again are related to the information you were given in the problem text.
 

1. What is an elliptical orbit?

An elliptical orbit is the path that an object follows around a larger object in space, such as a planet orbiting a star. Unlike a circular orbit, an elliptical orbit is not perfectly round and has a slightly elongated or oval shape.

2. How is an elliptical orbit different from a circular orbit?

An elliptical orbit is different from a circular orbit in that it is not perfectly round. The shape of an elliptical orbit is elongated or oval, while a circular orbit is a perfect circle. Additionally, the object in an elliptical orbit will vary in distance from the larger object it is orbiting, whereas a circular orbit has a constant distance.

3. What causes an object to have an elliptical orbit?

An object has an elliptical orbit due to the influence of gravity. The larger object that the smaller object is orbiting exerts a gravitational force, which causes the smaller object to follow a curved path around it. The shape of the orbit depends on the speed and direction of the smaller object's initial velocity.

4. Can an object have a perfectly circular orbit?

Yes, an object can have a perfectly circular orbit, but it is rare. In order for an object to have a perfectly circular orbit, it would need to have the exact velocity and direction to balance the gravitational force of the larger object it is orbiting. Any slight variation in these factors can result in an elliptical orbit.

5. What are some real-life examples of objects in elliptical orbits?

There are many real-life examples of objects in elliptical orbits. Some notable ones include planets orbiting the Sun, comets orbiting the Sun, moons orbiting planets, and artificial satellites orbiting Earth. Even the Moon's orbit around Earth is slightly elliptical.

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