#5 please For non-solid systems, the force of gravity determines orbital motion. We know that the strength of gravity depends on mass and distance. Therefore, we can learn about the mass distribution (how much mass is located in a given area) in astronomical systems by studying rotation curves. We will start with a simple case: our solar system.**Keplerian Orbits**4) Let’s consider the planets orbiting the Sun. They actually travel in ellipses, but their orbits are nearly circular. As you did for the ants, write a formula for the speed of a planet around the Sun in terms of its distance from the Sun, \( R \). Use the period, \( P \), for the time required for one orbit. Rearrange your speed formula to solve for \( P \).\[v = \frac{2 \pi R}{P} \Rightarrow P = \frac{2 \pi R}{v}\]Recall the proportionality relation form of Kepler’s Law of planetary motion, \( P^2 \propto a^3 \). Note that \( a \) is the same as \( R \) when we’re approximating the planetary orbits as circles, so use \( R \) for the distance. 5) Use the expression you wrote down in question 4) relating speed \( v \), period \( P \), and distance from the Sun \( R \), to eliminate \( P \) from the proportionality form of Kepler’s Law \( (P^2 \propto a^3) \). You should be left with an expression only in terms of speed \( v \) and distance \( R \). Simplify your answer.6) Rearrange this proportionality to solve for speed \( v \) in terms of distance \( R \).Based on this expression, you now know how the speed of a planet varies with distance from the Sun. We will be taking a closer look at the actual rotation curve of the solar system and its relation with the solar system’s mass distribution.*Continues on next page →*

Answered: Image /qna-images/answer/bcc07a04-15e5-4760-a670-abfdbbb07bc5.jpg

5) Use the expression you wrote down in question 4) relating speed (v), period (P), and distance from the Sun (R), to eliminate P from the proportionality form of Kepler's Law (P2 x a³). You should be left with an expression only in terms of speed (v) and distance (R). Simplify your answer.

5) Use the expression you wrote down in question 4) relating speed (v), period (P), and distance from the Sun (R), to eliminate P from the proportionality form of Kepler's Law (P2 x a³). You should be left with an expression only in terms of speed (v) and distance (R). Simplify your answer.

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

See similar textbooks

Similar questions

Value of acceleration of a vehicle is:a)inversely proportional to its massb)independent from its massc)is inversely proportional to number of electric motorsd)independent from coefficient of rotating masses
21 - What is the unit of this vector? a) m B) N NS) NS D) kg TO) N/C
The momentum of a moving object will change if O the velocity remains the same O the object is not in equilibrium O The net force acting on the object is zero None of these
Calculate the Net Force.
What do you do when you are driving and see that a police officer has another car pulled to the side of the road?
If the water falls from a dam into a turbine wheel 19.6m below, then the velocity of water at the turbine is? (g=9.8m/s) a) 9.8m/s b) 19.6m/s c) 39.2m/s d) 98m/s
Question 4
What is the minimum horizontal force F needed to make the box start moving in (Figure 1)? The coefficients of kinetic and static friction between the box and the floor are 0.23 and 0.41, respectively. Express your answer in newtons to two significant figures. 15| ΑΣΦ wwwww ? N
A property of an object to resist a change of state is known as inertia weight mass friction
3 - What is the velocity of a 2 kg object dropped from a height of 20 m when it hits the ground, in m/s? a) 25.7 B) 15.6 NS) 19.8 D) 6.8 TO) 12.54
List all agents of external force
[carpet-18] PLCNA A rope attached to a load of 175 kg bricks lifts the bricks with a steady acceleration of 0.12 m/s² straight up. What is the tension in the rope? * 8. A. 2028_N D. 1976 N 1736_N B. 1645_N E. C. 1894 N F. 1792_N 1--1 PWQLV F₁ Pigshow.jpeg m1 Pig show.jpeg m₂