Question

3-4) develop a mathematical model to calculate the magnitude of the gravitational force between earth and the satellite at its orbital distance. show all work, including an equation and substitution with units. 2

1. what is the magnitude of the gravitational field strength at the satellite’s orbital altitude? 1

a) 0.22 n/kg
b) 0.45 n/kg
c) 2.2 n/kg
d) 9.8 n/kg

Explanation:

Step1: Recall Gravitational Field Strength Formula

The gravitational field strength \( g \) at a distance \( r \) from the center of a mass \( M \) is given by \( g=\frac{GM}{r^{2}} \), or alternatively, since \( F = mg \) (from Newton's second law, where \( F \) is the gravitational force on a mass \( m \) in the field), we can also use \( g=\frac{F}{m} \) (where \( F \) is the gravitational force on mass \( m \)).

Step2: Use Given Data (from Problem 3 - 4)

From problem 3 - 4, we know the gravitational force \( F_G = 1223.46\space N \) on the satellite, and the mass of the satellite \( m = 5.50\times10^{3}\space kg \) (from the formula \( F_G=\frac{Gm_1m_2}{r^{2}} \), where \( m_2 \) is the satellite's mass).

Step3: Calculate \( g \)

Using \( g=\frac{F}{m} \), substitute \( F = 1223.46\space N \) and \( m = 5.50\times10^{3}\space kg \):

$$ g=\frac{1223.46\space N}{5.50\times10^{3}\space kg}\approx0.22\space N/kg $$

Answer:

A) 0.22 N/kg