Answer to Question #304325 in Astronomy | Astrophysics for Anuj S Sharma

Question

The James Webb Space Telescope is positioned around 1.5 million kilometres from the Earth on

the side facing away from the Sun. The telescope remains at this distance and orbits around the

Sun with the Earth’s orbital velocity.

(a) Why is it important to position the JWST behind the Earth?

(b) Determine the angular velocity ω of the telescope as it orbits around the Sun.

The centrifugalFω and gravitational forceFG are acting on objects orbiting the Sun: F = Fω−FG

(c) Based on this, how much should the telescope accelerate towards or away from the Sun?

(d) Why is the orbit of the telescope stable nonetheless? What otherforces need to be considered?

Answer 1

$T=a^{\frac 32}=(R+h)^\frac 32,$

$\omega=\frac{2\pi}T=\frac{2\pi}{(R+h)^\frac 32}=1.96\cdot 10^{-7}~\frac{rad}s.$