Question

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

Venus = 4.87x10^24
2) Using only astronomical data, calculate the gravitational force that the sun must be exerting on Venus.

Answer 1

1) v_orbit = 3.49*10^4 m/s

2) F = 5.51*10^22 N

Step-by-step explanation:

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

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

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

`F=(6.674*10^(-11)m^3kg^(-1)s-2})((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