gravitación
Understanding the Concept of Gravitation
Introduction to Gravitation
- The concept of gravitation explains how Earth and other planets orbit around the Sun due to the gravitational force exerted by the Sun's mass.
- This gravitational force is described by a law that states it is inversely proportional to the square of the distance between two objects.
Gravitational Force Formula
- The formula for gravitational attraction between two masses (m1 and m2) separated by a distance (r) is given as:
[ F = G m_1 cdot m_2/r^2 ]
where G is the universal gravitational constant, approximately 6.67 times 10^-11 , N,m^2/kg^2 .
Example Calculation of Gravitational Force
- An example involves two masses: one of 4 kg and another of 2 kg, separated by a distance of 40 cm (0.4 m).
- Using the formula, the calculated gravitational attraction between these masses is 3.34 times 10^-9 N, indicating a very small force.
Calculating Earth's Mass
Data Required for Calculation
- To calculate Earth's mass, we use:
- Gravitational acceleration at Earth's surface: 9.8 m/s^2
- Radius of Earth: 6.38 times 10^6 m
Deriving Earth's Mass
- The weight ( W ) can be expressed as:
- W = m' g = G fracM_earth m'r^2
- Here, M_earth represents Earth's mass.
- By rearranging this equation and substituting known values, we find that Earth's mass is approximately 5.98 × 10^24 kg.