Question

1) Using only astronomical data, calculate the speed of the planet Venus in its essentially circular orbit around the sun.

Answer 1

Answer:

1)     v_orbit = 3.49*10^4 m/s

2)    F = 5.51*10^22 N

Explanation:

1) In order to calculate the speed of Venus in its orbit, you use the following formula:

$v_{orbit}=\sqrt{\frac{GM_s}{R}}$         (1)

v_orbit: speed of Venus = ?

G: Cavendish's constant = 6.674*10^-11.m^3kg^-1s^-2

Ms: mass of the sun = 1.98*10^30 kg

R: distance between the center of Sun and the center of Venus = 1.08*10^11m

You replace the values of the parameters in the equation (1):

$v_{orbit}=\sqrt{\frac{(6.674*10^{-11}m^3kg^{-1}s^{-2})(1.98*10^{30})}{1.08*10^{11}m}}\\\\v_{orbit}=3.49*10^4\frac{m}{s}$

The speed of Venus in its orbit around the Sun is 3.49*10^4 m/s

2) The force is given by the following formula:

$F=G\frac{M_vM_s}{R^2}$

Ms: mass of Venus = 4.87*10^24 kg

$F=(6.674*10^{-11}m^3kg^{-1}s-2})\frac{(4.87*10^{24}kg)(1.98*10^{30}kg)}{(1.08*10^{11}m)^2}\\\\F=5.51*10^{22}N$

The Sun exertes on Venus a force of 5.51*10^22 N