Question

12 formula 1 point the gravitational field strength on a planets surface is equal to 14.3 n/kg. the planet has a radius of r. an astronaut form this planet travels out to a distance of 2r from the center of the planet. what is the gravitational field strength from the planet at this location? answer

Explanation:

Step1: Recall the formula for gravitational field strength

The gravitational field strength \(g=\frac{GM}{r^{2}}\), where \(G\) is the gravitational constant, \(M\) is the mass of the planet, and \(r\) is the distance from the center of the planet.
On the planet's surface (\(r = R\)), \(g_{1}=\frac{GM}{R^{2}}=14.3\ N/kg\).

Step2: Calculate the gravitational field strength at \(r = 2R\)

At \(r = 2R\), \(g_{2}=\frac{GM}{(2R)^{2}}\).
Since \(g_{2}=\frac{GM}{4R^{2}}\) and \(g_{1}=\frac{GM}{R^{2}}\), we can express \(g_{2}\) in terms of \(g_{1}\).
We know that \(g_{2}=\frac{g_{1}}{4}\).
Substitute \(g_{1} = 14.3\ N/kg\) into the formula: \(g_{2}=\frac{14.3}{4}\).

Answer:

\(3.575\ N/kg\)