Earthed

How to calculate radial acceleration of the earth around the sun?

How do you calculate the radial acceleration of the earth in its orbit around the sun?



Use f=ma to find radial forcethat holds earth in orbit. Check by calculating gravitational attraction between earth and sun using newton's law of gravity.



can anyone help me answering this question please?



thanks!

Public Comments

1. The radial acceleration of the earth's orbit around the sun remains at one "G"
2. Hint! use the Givens like earth spins around the sun once every 365.25 days.
3. The point about an orbit is that there is no acceleration: the tendency of the Earth to fall into the sun is exactly balanced by its forward momentum, so that it maintains a constant radial speed and never gets any closer to the sun.
4. The orbit is close enough to a circle that we can model it as such for a simple back-of-the-envelope calculation.
   
   
   
   Centripetal acceleration = omega^2 r
   
   = (2 pi / T)^2 r
   
   
   
   So you know the period, T, is one year. Convert that to seconds.
   
   You can look up the orbital radius, r.
   
   
   
   Plugnchug.
   
   
   
   By setting that equal to the gravitational acceleration from newton's law:
   
   a = GM/r^2
   
   we determined the mass of the sun.
5. a = (omega)^2 r.
   
   Now omega = 2 pi radians/year = 1.99 x 10^-7 rad/s
   
   r = 1.49 x 10^8 m
   
   so a = 5.90 x 10^-6 m/s^2
   
   Note that you don't need to use the law of gravitation to get this result.