Respuesta :
So you can compute the force of gravity on the planet GMm/r^2
or (6.674 X 10^−11)(1.99 X 10^30)m / d^2(1.5 X 10^11)^2
Where d is the average distance of the planet form the sun and m is the mass of the planet (I will keep these as symbols so doing Saturn and Venus will be simple substitution into one formula in the end).
Now realize that if they are in stable circular orbit, then this force must provide the necessary centripetal force mv^2/r or mv^2 / d(1.5 X 10^11)
So we get:
(6.674 X 10^−11)(1.99 X 10^30)m / d^2(1.5 X 10^11)^2 = mv^2 / d(1.5 X 10^11)
The m's cancel out as does one 1/d(1.5 X 10^11)
(6.674 X 10^−11)(1.99 X 10^30) / d(1.5 X 10^11) = v^2
Evaluating and square rooting yeilds:
v = sqrt((8.854 X 10^8)/d)
Now plug in 0.72 for venus and 9.54 for saturn
Venus = 35067.39 m/s
Saturn = 9633.75 m/s
Some precision was lost rounding to 8.854 X 10^8, so if more presion is required just type the whole thing from before into a calculator. Anyways the process is sound
or (6.674 X 10^−11)(1.99 X 10^30)m / d^2(1.5 X 10^11)^2
Where d is the average distance of the planet form the sun and m is the mass of the planet (I will keep these as symbols so doing Saturn and Venus will be simple substitution into one formula in the end).
Now realize that if they are in stable circular orbit, then this force must provide the necessary centripetal force mv^2/r or mv^2 / d(1.5 X 10^11)
So we get:
(6.674 X 10^−11)(1.99 X 10^30)m / d^2(1.5 X 10^11)^2 = mv^2 / d(1.5 X 10^11)
The m's cancel out as does one 1/d(1.5 X 10^11)
(6.674 X 10^−11)(1.99 X 10^30) / d(1.5 X 10^11) = v^2
Evaluating and square rooting yeilds:
v = sqrt((8.854 X 10^8)/d)
Now plug in 0.72 for venus and 9.54 for saturn
Venus = 35067.39 m/s
Saturn = 9633.75 m/s
Some precision was lost rounding to 8.854 X 10^8, so if more presion is required just type the whole thing from before into a calculator. Anyways the process is sound
The orbital velocity of Venus and Saturn around the sun is 8.854 x [tex]10^8[/tex].
What is orbital velocity?
Orbital velocity is the speed required to achieve orbit around a celestial body, such as a planet or a star.
So you can compute the force of gravity on the planet
[tex]GMm/r^2[/tex]
or
[tex](6.674 \times 10^{-11})(1.99 \times 10^{30})m / d^2(1.5 \times 10^{11})^2[/tex]
Where d is the average distance of the planet from the sun and m is the mass of the planet (I will keep these as symbols so doing Saturn and Venus will be simple substitutions into one formula in the end).
Now realize that if they are in a stable circular orbit, then this force must provide the necessary centripetal force [tex]mv^2/r[/tex] or [tex]mv^2 / d(1.5 \times 10^{11})[/tex]
So we get:
[tex](6.674 \times 10^{-11})(1.99 \times 10^{30})m / d^2(1.5 \times 10^{11})^2 = mv^2 / d(1.5 \times 10^{11})[/tex]
The m's cancel out as does one
[tex]1/d(1.5 \times 10^{11})(6.674 \times 10^{-11})(1.99 \times 10^{30}) / d(1.5 \times 10^{11}) = v^2[/tex]
Evaluating and square rooting yeilds:
[tex]v = \sqrt{((8.854 \times 10^8)/d)}[/tex]
Now plug in 0.72 for venus and 9.54 for saturn
Venus = 35067.39 m/s
Saturn = 9633.75 m/s
Some precision was lost rounding to 8.854 x 10⁸, so if more precision is required type the whole thing from before into a calculator. Anyways the process is sound.
Learn more about orbital velocity here:
https://brainly.com/question/24152628
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