Acceleration of Planet/Sun System

In summary, we are asked to calculate the acceleration of gravity produced by a planet with 5 times the mass of Earth orbiting a star with 1.5 times the mass of the sun at a distance of 3 astronomical units (AU). Using the formula for acceleration of gravity between two bodies, we find that the acceleration of the planet due to the star's gravity is 9.84e-9 m/s^2. This is much smaller than the acceleration we experience on the surface of Earth (9.8 m/s^2), as expected due to the larger distance and smaller mass of the star.
  • #1
aurora7790

Consider a planet with a mass 5x that of the Earth a distance of 3AU away from a star with a mass 1.5x that of the sun.

-What is the acceleration of the planet due to gravity from the planet on the star?
-How does this answer compare with the acceleration we feel on the surface of the Earth g=9.8m/s^2? How many times larger or smaller is it?

*Remember that acceleration of a body with mass M2 toward a body with mass M1 is a=(GM1)/r^2

I assumed that I was looking for how the star's gravity affects the acceleration of the planets orbit but the second part, that asked how it differs from the Earth's acceleration, makes me wonder if I'm finding the force of gravity on the planet, but wouldn't that require the planets radius?

Anyway this is what I calculated using what I was given (Mp= mass of planet)
a=(GMp)/r^2=(6.67e-11)(5*5.977e24kg)/(3*1.5e11)^2= 9.84e-9 m/s^2
 
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  • #2
Hello and wecome to PF!

aurora7790 said:
-What is the acceleration of the planet due to gravity from the planet on the star?
The wording of this question is very odd. Are you sure you typed it exactly word for word?
 
  • #3
TSny said:
Hello and wecome to PF!

The wording of this question is very odd. Are you sure you typed it exactly word for word?
Yes I know the wording is what is throwing me off, it is typed exactly how it is on my worksheet
 
  • #4
aurora7790 said:
Yes I know the wording is what is throwing me off, it is typed exactly how it is on my worksheet
That's too bad. The gravity "from the planet on the star" will not produce "acceleration of the planet".

The answer to the first question will relate nicely to the second question if you interpret the first question as:

"Calculate the acceleration of gravity produced by the star at the location of the planet."
or, equivalently
"What is the acceleration of the planet due to gravity from the planet on the star?
 
Last edited:

1. What is the acceleration of the planet/sun system?

The acceleration of the planet/sun system is determined by the gravitational force between the sun and the planet. This acceleration is known as the centripetal acceleration and is given by the formula a = v²/r, where v is the velocity of the planet and r is the distance between the planet and the sun.

2. How does the acceleration of the planet/sun system affect the orbit of the planet?

The acceleration of the planet/sun system determines the shape and size of the orbit of the planet. If the acceleration increases, the orbit becomes more elliptical, while a decrease in acceleration results in a more circular orbit.

3. Can the acceleration of the planet/sun system change over time?

Yes, the acceleration of the planet/sun system can change over time due to various factors such as the changing positions of the planets, the effects of other celestial bodies, and the gradual decrease of the sun's gravitational pull as it loses mass.

4. How is the acceleration of the planet/sun system calculated?

The acceleration of the planet/sun system can be calculated using the laws of motion and gravity, specifically Newton's second law (F = ma) and the universal law of gravitation (F = GmM/r²). By combining these equations, we can determine the acceleration of the planet/sun system.

5. What is the significance of understanding the acceleration of the planet/sun system?

Understanding the acceleration of the planet/sun system is crucial for predicting the movements and behaviors of celestial bodies. It also helps us understand the formation and evolution of our solar system and other planetary systems in the universe.

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