How to calculate mass of the sun? Please tell in a simple methamatical way.

Question

Emma Arguello · Accepted Answer

You can calculate the mass of the Sun from Newton's form of Kepler's 3rd law.

The orbit of a planet around the Sun is described by Newton's version of Kepler's third law, which uses the following equation to connect the orbit's semi major axis distance to its period: #p^2 alpha color(white)(')a^3# Thus, it implies: #p^2=(4pi^2)/(GM)a^3# Where a is the orbit semi major axis distance, M is the Sun's mass, p is the orbital period, and G is the gravitational constant. After rearranging the equation, we get: #M=(4pi^2a^3)/(Gp^2)# Now for planet Earth: #a=1.496*10^11m# #p=3.154*10^7s# and #G=6.67408*10^(-11)m^3Kg^(-1)s^(-2)# Putting the values into the equation gives the mass of the Sun: #M=1.99*10^30Kg#

Emma Arguello · Answer

undefined The mass of the Sun can be calculated using the gravitational force equation:

$$ F = \frac{{G \cdot m_1 \cdot m_2}}{{r^2}} $$

Where:
- $ F $ is the gravitational force between two objects,
- $ G $ is the gravitational constant ($6.674 \times 10^{-11}$ m³/kg/s²),
- $ m_1 $ and $ m_2 $ are the masses of the two objects (in this case, the mass of the Sun and the mass of another object, for example, a planet),
- $ r $ is the distance between the centers of the two objects.

Rearranging the equation to solve for the mass of the Sun ($ m_1 $):

$$ m_1 = \frac{{F \cdot r^2}}{{G \cdot m_2}} $$

By measuring the gravitational force ($ F $) experienced by an object (such as a planet) orbiting the Sun at a known distance ($ r $), and knowing the mass of the object ($ m_2 $), we