Question

Venus is orbiting round the sun in 225 days. Calculate the orbital radii and speed of
venus. (Mass of the sun = 2 x 1030 kg, G = 6.67 x 10-11 Nm2
/kg2)

Answer 1

Answer:

R = 1.7*10^9

V = 2.7*10^5

Explanation:

See attachments.. First r then v

Answer 2

Given that,

Venus is orbiting round the sun in 225 days.

Mass of the sun, $M=2\times 10^{30}\ kg$

To find,

The orbital radii and speed of  Venus.

Solution,

Since, 1 day = 86400 seconds

$225\ days=225\times 86400\\\\T=19440000\ s$

Using Kepler's third law to find the orbital radii. So,

$T^2=\dfrac{4\pi^2}{GM}R^3\\\\R^3=\dfrac{T^2GM}{4\pi^2}\\\\R^3=\dfrac{(19440000)^2\times 6.67\times 10^{-11}\times 2\times 10^{30}}{4\pi^2}\\\\R=\left(1.27\cdot10^{33}\right)^{\dfrac{1}{3}}\\\\R=1.08\times 10^{11}\ m$

So, orbital radii is $1.08\times 10^{11}\ m$.

Speed of Venus is given by :

$V=\dfrac{d}{t}\\\\V=\dfrac{2\pi R}{t}\\\\V=\dfrac{2\pi \times 1.08\times 10^{11}}{19440000}\\\\V=34906.58\ m/s$

Learn more,

Orbital speed

https://brainly.in/question/910050

https://brainly.com/question/1829011