**Title: Understanding Orbital Mechanics: Calculating Mass and Orbital Periods****Two Planets in Circular Orbits**Two planets, \( p_1 \) and \( p_2 \), orbit around a star \( S \) in circular orbits with speeds \( v_1 = 45.0 \, \text{km/s} \) and \( v_2 = 58.0 \, \text{km/s} \), respectively.**Problem (a): Mass of the Star**- **Objective**: Calculate the mass of the star \( S \) in kilograms.- **Given**: The orbital period of the planet \( p_1 \) is 710 years.- **Task**: Determine the mass using the information provided.\[ \text{Mass of the star} = \boxed{ \text{kg} } \]**Problem (b): Orbital Period of \( p_2 \)**- **Objective**: Determine the orbital period of planet \( p_2 \) in years.- **Given**: The speed of planet \( p_2 \) is 58.0 km/s.- **Task**: Calculate the orbital period using the available data.\[ \text{Orbital Period of } p_2 = \boxed{ \text{yr} } \]**Note**: The problems involve applying principles of gravitational dynamics, utilizing the known speeds and periods of the planets to derive the mass of the star and the unknown orbital period.

(a) Compare the gravitational force and centripetal force. FC=FGmpv2R=GmpmsR2v2=GmsR The speed due…

Two planets P, and P, orbit around a star S in circular orbits with speeds v1 = 45.0 km/s, and v2 = 58.0 km/s respectively. (a) If the period of the first planet P, is 710 years what is the mass, in kg, of the star it orbits around? kg (b) Determine the orbital period, in years, of P,. yr

Two planets P, and P, orbit around a star S in circular orbits with speeds v1 = 45.0 km/s, and v2 = 58.0 km/s respectively. (a) If the period of the first planet P, is 710 years what is the mass, in kg, of the star it orbits around? kg (b) Determine the orbital period, in years, of P,. yr

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)...

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Concept explainers

Centripetal Force

A particle, body, object or certain mass while travelling in a rotational path or semicircular path, experiences an inertia force. If that inertia force pulls the towards the inward of the imaginary circle in the rotation, it is termed as centripetal force.

Question

**Title: Understanding Orbital Mechanics: Calculating Mass and Orbital Periods**

**Two Planets in Circular Orbits**

Two planets, \( p_1 \) and \( p_2 \), orbit around a star \( S \) in circular orbits with speeds \( v_1 = 45.0 \, \text{km/s} \) and \( v_2 = 58.0 \, \text{km/s} \), respectively.

**Problem (a): Mass of the Star**

- **Objective**: Calculate the mass of the star \( S \) in kilograms.
- **Given**: The orbital period of the planet \( p_1 \) is 710 years.
- **Task**: Determine the mass using the information provided.

\[ \text{Mass of the star} = \boxed{ \text{kg} } \]

**Problem (b): Orbital Period of \( p_2 \)**

- **Objective**: Determine the orbital period of planet \( p_2 \) in years.
- **Given**: The speed of planet \( p_2 \) is 58.0 km/s.
- **Task**: Calculate the orbital period using the available data.

\[ \text{Orbital Period of } p_2 = \boxed{ \text{yr} } \]

**Note**: The problems involve applying principles of gravitational dynamics, utilizing the known speeds and periods of the planets to derive the mass of the star and the unknown orbital period.

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