Newton's Law of Universal Gravitation

[rvnt]

Homework Statement

I am doing a lab-"Kepler's Laws and Newton's Law of Universal Gravitation". There is an image representing various positions, at equal intervals, of a satelitte in an elliptical orbit around the earth. A list of planets and their radi and periods are given. I have calculated acceleration using two formulas a=GMm/r^2 and a=4pi^2r/T^2
Question states: "Calculate acceleration using the two equations and compare the results. Do your results confirm Newton's law of universal gravitation?"

Homework Equations

F=Gm1m2/r^2

The Attempt at a Solution

Ex. of results: accleration obtained for Venus using 1st equation= 5.5407*10^24 and using 2nd equation=0.0113286
I was expecting them to be the same...please help

 

[thrill3rnit3]

Homework Statement

I am doing a lab-"Kepler's Laws and Newton's Law of Universal Gravitation". There is an image representing various positions, at equal intervals, of a satelitte in an elliptical orbit around the earth. A list of planets and their radi and periods are given. I have calculated acceleration using two formulas a=GMm/r^2 and a=4pi^2r/T^2
Question states: "Calculate acceleration using the two equations and compare the results. Do your results confirm Newton's law of universal gravitation?"

Homework Equations

F=Gm1m2/r^2

The Attempt at a Solution

Ex. of results: accleration obtained for Venus using 1st equation= 5.5407*10^24 and using 2nd equation=0.0113286
I was expecting them to be the same...please help

a=GMm/r^2 is wrong

go back to the general equation

F=Gm1m2/r^2
m1=mass of Venus
m2=mass of satellite

F=m2a=Gm1m2/r^2

a=Gm1/r^2

compare to the one you originally had (a=GMm/r^2)

 

[rvnt]

But mass of the satellite isn't given..?

 

[rvnt]

Wait...so as you said to use a=Gm1/r^2...for venus I got a=(6.67*10^-11)(4.8690*10^24)/(1.08*10^11)^2= 2.784*10^-8

 

[rwisz]

I would like to first clarify that Newton's Law of Universal Gravitation states that every object in the universe attracts every other object with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between them. This law was proposed by Sir Isaac Newton in 1687 and has been widely accepted and used in physics and astronomy.

In regards to the given question, it is important to note that the two equations used to calculate acceleration, a=GMm/r^2 and a=4pi^2r/T^2, are derived from Kepler's Laws of Planetary Motion and are based on the assumption that the force of gravity between two objects is the only force acting on them. Therefore, the results obtained from these equations can be considered as a confirmation of Newton's Law of Universal Gravitation.

However, it is also important to note that the results may not be exactly the same due to factors such as measurement errors, approximations made in the calculations, and the presence of other forces. Therefore, a small difference between the two calculated accelerations for Venus is expected and does not necessarily indicate a discrepancy with Newton's Law.

In conclusion, based on the results obtained and the assumptions made in the calculations, it can be said that they do confirm Newton's Law of Universal Gravitation. However, further experiments and calculations may be needed to obtain more accurate results and confirm the law with greater precision.