(1) What is the linear speed of the earth in its orbit about the sun? Give your answer in meters per second. (Consider the earth's orbit to be a circle of radius 1.50×1011 m.)
(2) What is the linear speed of Jupiter in its orbit about the sun? Give your answer in meters per second. (Consider the orbit of Jupiter to be a circle of radius 7.78×1011 m and that it takes 11.90 yr for one orbit around the sun.)
To calculate the linear speed of an object in orbit, we can use the formula:
Linear speed = 2π * radius / time period.
Let's calculate the linear speed of the Earth first:
(1) Given:
Radius of Earth's orbit (r) = 1.50 × 10^11 m.
The time period for one orbit around the sun is approximately one year, which is equal to 365 days or 365 * 24 * 3600 seconds.
Time period (T) = 365 * 24 * 3600 seconds = 3.15576 × 10^7 seconds.
Using the formula, the linear speed of the Earth is:
Linear speed = 2π * r / T
Linear speed = 2π * 1.50 × 10^11 m / 3.15576 × 10^7 s
Linear speed ≈ 29,459 m/s
Therefore, the linear speed of the Earth in its orbit around the Sun is approximately 29,459 m/s.
Now, let's calculate the linear speed of Jupiter:
(2) Given:
Radius of Jupiter's orbit (r) = 7.78 × 10^11 m
Time period of one orbit (T) = 11.90 years = 11.90 * 365 * 24 * 3600 seconds
T = 3.76494 × 10^8 seconds
Using the formula, the linear speed of Jupiter is:
Linear speed = 2π * r / T
Linear speed = 2π * 7.78 × 10^11 m / 3.76494 × 10^8 s
Linear speed ≈ 13,065 m/s
Therefore, the linear speed of Jupiter in its orbit around the Sun is approximately 13,065 m/s.
To calculate the linear speed of an object in its orbit, you need to use the formula:
Linear Speed = 2π * radius / time period
For the first question:
(1) The radius of the Earth's orbit is given as 1.50×10^11 m.
The time period for one orbit around the sun is approximately 1 year, which is equal to 365 days or 31,536,000 seconds.
Using the formula, we can calculate the linear speed of the Earth:
Linear Speed = 2π * 1.50×10^11 m / 31,536,000 s
Linear Speed ≈ 29,648 m/s
Therefore, the linear speed of the Earth in its orbit around the sun is approximately 29,648 meters per second.
For the second question:
(2) The radius of Jupiter's orbit is given as 7.78×10^11 m.
The time period for one orbit around the sun is given as 11.90 years.
First, we need to convert the time period to seconds:
11.90 years * 365 days/year * 24 hours/day * 60 minutes/hour * 60 seconds/minute ≈ 375,936,000 seconds
Using the formula, we can calculate the linear speed of Jupiter:
Linear Speed = 2π * 7.78×10^11 m / 375,936,000 s
Linear Speed ≈ 13,067 m/s
Therefore, the linear speed of Jupiter in its orbit around the sun is approximately 13,067 meters per second.
C = 2pi * r meters
length of a year is t = 3.16*10^7 seconds
just divide C/t
Speed = 2*pi*r/t
= 2*3.142*1.50E11/3.16E7
= 29,829m/s