Acceleration Due to Gravity of the Sun

Homework Statement

What is the acceleration due to gravity of the sun at the distance of the earth's orbit?

Homework Equations

law of gravity = Gm/r^2
Sun's Mass: 1.99x10^30 kg,
earth-sun distance: 150x10^6 km

The Attempt at a Solution

((6.67*10^(-11)) * (1.99*10^30))/ (2.25*10^12)

= 58992444.4444

Does this appear correct?

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hage567
Homework Helper
Your distance term is not correct. You need to convert it to meters before you square it.

Out of curiousity...why is r="2.25" where did that come from?
What are you adding to the mean Earth-Sun distance of 1 AU?

Casey

((6.67*10^(-11)) * (1.99*10^30))/ (2.25*10^22)

= 0.005899244 m/s^2 ~0.00

((6.67*10^(-11)) * (1.99*10^30))/ (2.25*10^22)

= 0.005899244 m/s^2 ~0.00
Looks much better. But again, what are you using for a radius?

Casey

I'm using the distance from the Earth to the Sun.
1.50 x 10^11 = r
r^2 = 2.25*10^22

Ah. I did not notice that you already squared r. Silly me. Anyway, I do not know what degree of accuracy you are looking for, but you may want to account for the fact that by Newton's Shell Theorem, r would be the distance from the center of one mass to the center of the other.

Casey

g=Gm/r^2
For sun,
g=6.67*10^-11*1.989*10^30/(695000000)^2
=274.51m/s

Isn't it right?

The earlier posts were almost correct the Sun’s acceleration on the Earth is -
2pi * Orbital Velocity in (meters/sec ) / Orbital Period (in seconds)
= 29785.513 * 6.28318531 / 31557600
= 0.00593036 m/s2

NB. The Orbital Velocity squared * Radius is a constant for all the planets.
Eg. OV^2 * R(AU) = approx 887177000

For the Earth using OV = 29785.52 and R(AU) = 1 then K = 887177201
For Saturn using OV = 9644.8848 and R(AU) = 9.5371 then K = 887177310

without an doubt, the correct answer to the question is from Saladsamurai
because distance from earth to sun is 1.50x10^8 km or 1.50x10^11m

Yes, the distance between sun and Earth is approx 1.5E+11
Since g = OV^2/R then it still comes out at 0.005914512
Orbital Velocity squared = 887176784.7
Check it yourself.

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