Answer to Question #165641 in Physics for Vic

Question

You are to obtain some of the values in the table using Newton’s law of universal

gravitation. In all calculations involving the mass of Sun, use M = 1.989 × 1030 kg. Assume

that all orbits are circular.

1. Calculate the acceleration of each planet due to the gravity of Sun.

2. Recall that an object in uniform circular motion experiences acceleration

directed towards the midpoint of the circle according to the equation

a = v^2/r^,

where a is the acceleration of the object, v is the velocity of the object, and r is

the radius of the circular path. Calculate the mean orbital velocity of each planet

using the above equation. Express your answers in units of km/s.

Answer 1

$$\begin{pmatrix} \bold{Planet} & \bold{a (10^{-3}\frac{m}{s^2}) } & \bold{v (\frac{km}{s})}\\ Mercury & 39.6 & 47.9\\ Venus & 11.3 & 35.0\\Earth & 5.9 & 29.8\\Mars & 2.6 & 24.1\\Jupiter & 0.22 & 13.1\\Saturn & 0.065 & 9.64\\Uranus & 0.016 & 6.80\\Neptun & 0.0066 & 5.43\\ \end{pmatrix}$$