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Astronomy/Force of Attraction

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Expert: - 3/29/2009


Question
What is the force of attraction between the Sun and the Earth? I have the formula but I feel like I'm leaving something out and my number does not seem to be coming out like I feel like it should.

Answer
Hello,

If the result isn't coming out as you think it should, it may be that your units are inconsistent.  Using the SI system you should have:

M (mass of Sun) = 2 x 10^30  kg

m(mass of Earth) = 6 x 10^24 kg

G (Newtonian gravitational constant) = 6.7 x 10^ -11 N m^2/ kg^2

r (distance from Earth to Sun) = 1.5 x 10^11 m


Using the above, and the Newtonian equation:


F = G Mm/ r^2

where 'F' denotes the force of attraction,

you should get:

F =   (6.7 x 10^-11 Nm^2/kg^2)(2 x 10^30 kg)(6 x 10^24 kg)/ (1.5 x 10^11 m)^2

or F = 3.5 x 10^22 N  (Newtons)


Of course, understand that the r used here is the *mean distance*. In fact, the force F will vary since Earth's distance will vary (the orbit being elliptical) with the maximum force of attraction occurring at perihelion (closest point) and the minimum occurring at aphelion.  

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Philip Stahl

Expertise

I have forty years of experience in Astronomy, specifically solar and space physics. My specialties include the physics of solar flares, sunspots, including their effects on Earth and statistics as applied to astronomical investigations.

Experience

Astronomy: more than forty years experience starting with construction of my own simple telescopes. Worked at university observatory in college, doing astrographic measurements. M.Phil. degree in Physics/Solar Physics and more than ten years as researcher.

Organizations
American Astronomical Society (Solar Physics and Dynamical Astronomy divisions), American Mathematical Society, American Geophysical Union

Publications
Solar Physics (journal), The Journal of the Royal Astronomical Society of Canada, The Proceedings of the Meudon Solar Flare Workshop (1986), The Proceedings of the Caribbean Physics Conference (1985). Books: 'Selected Analyses in Solar Flare Plasma Dynamics', 'Physics Notes for Advanced Level'.

Education/Credentials
B.A. Astronomy, M. Phil. Physics

Awards and Honors
American Astronomical Society Studentship Award (1984), Barbados Government Award for Solar Research

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