Calculating Eccentricity for an Elliptical Orbit

AI Thread Summary
To calculate the eccentricity of a satellite's elliptical orbit around a planet with a mass of 4 x 10^20 kg, the relevant equations include mechanical energy conservation (ME = KE + PE), where kinetic energy (KE) is derived from the satellite's velocity and potential energy (PE) is based on gravitational attraction. The satellite is positioned at a distance of 10^7 m and has a velocity of 40 m/s at a 30-degree angle, leading to a vertical velocity component. The eccentricity can be determined using the relationship between eccentricity, semi-major axis, and semi-latus rectum. Despite initial calculations, the correct eccentricity is found to be 0.89. Understanding these relationships is crucial for solving similar orbital mechanics problems.
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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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help please
 
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.
 

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