Acceleration Due to Gravity of the Sun

[ideefixem]

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?

 

[hage567]

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

 

[Saladsamurai]

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

 

[ideefixem]

How about this...

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

= 0.005899244 m/s^2 ~0.00

 

[Saladsamurai]

How about this...

((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

 

[ideefixem]

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

 

[Saladsamurai]

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

 

[shwetali]

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

Isn't it right?

 

[Mangone]

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

 

[Mangone]

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

 

[Lizwi]

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

 

[Mangone]

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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