# Kepler's Third Law and Newton's Law of Universal Gravitation for Planet P

• 3dsmax
In summary, the mass and radius of Planet "P" are 2.89 and 1.89 times that of Earth, respectively, and it is located 7.8 times further from the Sun. To find the amount of force applied by the Sun on Planet "P", the formula Fg=6.67 e-11 (m1m2)/r^2 can be used. To calculate the orbital velocity, the formula v=√(GM/r) is recommended. For the period velocity, the formula T^2=r^3 can be used. In regards to the question about the minimum velocity for a person to feel weightless while driving a car over a hill with a radius of 84 meters,

## Homework Statement

a. Planet "P" has a mass that is 2.89 times that of the Earth, an equatorial radius that is 1.89 times that of the Earth and is located 7.8 times further from the Sun than the Earth is. What is the amount of force applied to the planet by the Sun?

b.what is the orbital velocity of planet "p". What formula do i use for that?

c.What is the period velocity of Planet "P"?

## Homework Equations

a. Fg=6.67 e-11 (m1m2)/r^2

c. T^2=r^3

## The Attempt at a Solution

NOTE THE EDIT: Fg= 6.67 e-11 [(1.99e30 x (2.89)(5.28e24)] / [(7.8)(1.5 e11)]^2

Fg= 1.48 e21
(but i know the answer is 1.68 e 21)
What did i do wrongFIXED THIS ONEc. t^2 = 7.8^3
t= 21.8 years

Last edited by a moderator:
5.28e24 is not the mass of the earth.
5.98324 first of all is not the radius of the earth, and second is not nearly the right magnitude. But anyway, what you want for this is the mean radius of Earth's orbit, since it says the planet is 7.8 times further from the sun than the Earth is.
I think you just need to get your numbers straight, then try it again.

okay well i fixed my numbers but and still getting the wrong answer

Never mind, I see your edit.

According to my sources, the mass of the Earth is 5.98x10^24 kg, not 5.28x10^24 kg. That is where the difference is.

well i figure it all out the only other problem that i am having now is on this:

1. A 55.0 kg person drives a 2300 kg car and cruises over the top of a hill with an 84.0 meter radius. With what minimum velocity can the car move so that the drive will feel weightless?

I used the formula mu = v^2/r/g
i figure since there has to be no normal to feel weightless so i figured there has to be no friction too. So set it equal to like 0. So then i did like v^2/84m/9.81. Can i do that or is there another way?

I don't understand the "mu". For the driver to feel weightless, the force of gravity must equal the centripetal force. So you can set them equal and solve for v.

## 1. How do Kepler's Third Law and Newton's Law of Universal Gravitation relate to each other?

Kepler's Third Law and Newton's Law of Universal Gravitation are both fundamental laws of physics that describe the motion and behavior of objects in space. While Kepler's Third Law focuses on the relationship between a planet's orbital period and its distance from the sun, Newton's Law of Universal Gravitation explains the force of gravity between two objects. These two laws work together to help us understand how planets move and interact in our solar system.

## 2. What is Kepler's Third Law and how is it calculated?

Kepler's Third Law, also known as the "harmonic law," states that the square of a planet's orbital period is directly proportional to the cube of its semi-major axis (the distance between the planet and the sun). This means that the farther a planet is from the sun, the longer its orbital period will be. The equation for calculating Kepler's Third Law is T^2 = (4π^2/GM)a^3, where T is the orbital period, G is the gravitational constant, M is the mass of the sun, and a is the semi-major axis.

## 3. How does Newton's Law of Universal Gravitation explain the motion of planets?

Newton's Law of Universal Gravitation states that any two objects in the universe attract each other 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 explains the force of gravity between planets and the sun, as well as the gravitational pull between planets and other celestial bodies. It also helps us understand the elliptical paths that planets follow around the sun.

## 4. Can Kepler's Third Law and Newton's Law of Universal Gravitation be applied to other objects in the universe?

Yes, both laws can be applied to any objects in the universe that have mass and are affected by gravity. For example, they can be used to calculate the orbital period and distance of moons around a planet, or the motion of comets and asteroids in our solar system. These laws have also been used to study the movements of stars and galaxies in the universe.

## 5. How have Kepler's Third Law and Newton's Law of Universal Gravitation contributed to our understanding of the universe?

Kepler's Third Law and Newton's Law of Universal Gravitation have both played crucial roles in helping us understand the motion and behavior of objects in the universe. They have allowed us to accurately predict the paths of planets, moons, and other celestial bodies, as well as study the formation and evolution of our solar system. These laws have also provided the foundation for further advancements in astronomy and space exploration.