How Do You Calculate Earth's Radial and Transverse Velocity Components?

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SUMMARY

The discussion focuses on calculating the radial and transverse components of Earth's velocity and acceleration using the equation r=1/A+Bcos(theta), with constants A=0.666667x10^-11 and B=0.113333x10^-12. The radial velocity is determined by dr/dt, while the transverse velocity is calculated as r*dθ/dt. Participants emphasize differentiating the given equation of motion to derive these components, providing a clear pathway for solving the problem without directly giving the answer.

PREREQUISITES
  • Understanding of calculus, specifically differentiation.
  • Familiarity with polar coordinates and their applications in physics.
  • Knowledge of gravitational physics, particularly the equation (theta dot)=(1/r^2)(sqrt(GM/A)).
  • Basic understanding of the motion of celestial bodies.
NEXT STEPS
  • Study differentiation techniques in calculus to apply them effectively in physics problems.
  • Explore polar coordinate systems and their relevance in celestial mechanics.
  • Research gravitational physics, focusing on the implications of the equation (theta dot)=(1/r^2)(sqrt(GM/A)).
  • Investigate the motion of celestial bodies, particularly the dynamics of Earth’s orbit around the Sun.
USEFUL FOR

Students studying physics, particularly those focusing on celestial mechanics, as well as educators and anyone interested in the mathematical modeling of planetary motion.

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Homework Statement


Find the radial and transverse components of the velocity and acceleration of the Earth, in terms of (theta) and (theta dot=d(theta)/dt)



Homework Equations


r=1/A+Bcos(theta)
Where A and B are constants given as A=0.666667x10^-11 and B=0.113333x10^-12
(theta dot)=(1/r^2)(sqrt(GM/A))

The Attempt at a Solution


I'm not quite sure how to start the problem, so if someone could give me a push in the right direction for working this question out that would be a big help.
I would prefer to work it out myself, so i am not asking for the answer, just where to start the question.

Thanks :)
 
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Wouldn't the radial velocity be dr/dt and the transverse velocity r*dθ/dt ?
Just differentiate your r=1/A+Bcos(theta), the equation of motion for the Earth around the sun, to find those velocities.
 

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