# I'm unable to understand the 2nd law of kepler please give me some information about this and send me video which show the 2nd kepler law please help I'm new

### Asked by kashmirsunil | 24th May, 2020, 09:06: PM

Expert Answer:

###
###
**Kepler's second law**:
Consider that a planet of mass 'm' revolving around the Sun of mass 'M' in a circular orbit of radius 'r'. Let 'v' be its orbital velocity. Suppose that at any isntant the planet is at point A in its orbit and after an in small time dt, it reaches point B. As such, the circular path of the planet between points A and B may be considered as straight.
If dA is small area swept by the line joining the planet to the Sun in time dt, then
dA=area of ΔABS=
or dA= .... (1)
If dθ is the angular displacement of the planet in time dt i.e., when it moves from point A to B, then AB=r dθ.
Substituting AB with rdθ and AS with 'r' in equation(1), we get,
Dividing the above equation by dt, we get,
where ω=is the angular speed of the planet in its orbit and is the areal velocity of the planet.
Multiplying and divind the R.H.S of the equation(2) by 'm' i.e., the mass of the planet, we get,

Since, m r^{2} ω = L, the angular momentum of the planet about the axis through the Sun, we have,
... (3)
As no external torque acts on the planet during its orbital motion, its angular momentum (L) must remain constant. Since both L amd m are constant, the equation(3) becomes, ... (4)
Hence, when a planet moves around the Sun, its areal velocity remains constant. It proves Kepler's second law of planetary motion.

For video based explanation click on link given below in blue: -
PS : -You will be required to fill in the details if the pop up comes up asking for the same.

###
**Kepler's second law**:
Consider that a planet of mass 'm' revolving around the Sun of mass 'M' in a circular orbit of radius 'r'. Let 'v' be its orbital velocity. Suppose that at any isntant the planet is at point A in its orbit and after an in small time dt, it reaches point B. As such, the circular path of the planet between points A and B may be considered as straight.
If dA is small area swept by the line joining the planet to the Sun in time dt, then
dA=area of ΔABS=
or dA= .... (1)
If dθ is the angular displacement of the planet in time dt i.e., when it moves from point A to B, then AB=r dθ.
Substituting AB with rdθ and AS with 'r' in equation(1), we get,
Dividing the above equation by dt, we get,
where ω=is the angular speed of the planet in its orbit and is the areal velocity of the planet.
Multiplying and divind the R.H.S of the equation(2) by 'm' i.e., the mass of the planet, we get,

Since, m r^{2} ω = L, the angular momentum of the planet about the axis through the Sun, we have,
... (3)
As no external torque acts on the planet during its orbital motion, its angular momentum (L) must remain constant. Since both L amd m are constant, the equation(3) becomes, ... (4)
Hence, when a planet moves around the Sun, its areal velocity remains constant. It proves Kepler's second law of planetary motion.

For video based explanation click on link given below in blue: - **Kepler's second law**:

^{2}ω = L, the angular momentum of the planet about the axis through the Sun, we have,

### Answered by Shiwani Sawant | 24th May, 2020, 11:02: PM

## Concept Videos

- please solve it sir
- keplers 1st law
- Q1.What is orbital velocity? Q2.What is transpoder?
- The Earth-Moon distance is about 60 times the radius of the earth. What will be the approximate angular diameter of the earth as seen from the moon?
- What are the Kepler's Laws of Planetary Motion?
- What is the angular momentum of a satellite (mass, m) with respect to the centre of orbit?
- How many years will a planet take to complete one revolution around sun when the mean distance of sun from planet is 9 times that of sun and earth?
- State the conditions in which a body can be weightless.
- Name a polar satellite. State its uses.

### Kindly Sign up for a personalised experience

- Ask Study Doubts
- Sample Papers
- Past Year Papers
- Textbook Solutions

#### Sign Up

#### Verify mobile number

Enter the OTP sent to your number

Change