Calculate the weight of the sun

What you need:

• Pencil and paper
• Possibly. Formula collection
• Calculating with powers of ten (wiss. Notation)
• calculator

Orbit around the sun - you should know these forces

• The weight, physically more precise: the mass of the sun, as with all celestial bodies, cannot of course be determined with a scale. But you can calculate this mass from an equilibrium of forces that applies to the earth's orbit around the sun: centrifugal force of the earth = gravitational force between the sun and the earth.
• Explanation: The earth is kept on its orbit exactly when centrifugal force and attraction by the sun are in balance. You are familiar with this observation, for example, from a chain carousel.
• The formula for centrifugal force (or physically more precise centripetal force) of a circular motion can be found in your collection of formulas. It reads F = 4 π²r
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  _* m_E./ T² with the force F (in Newtons), m_E. = Mass of the earth (in kg) as well as r = distance between the earth and the sun (in meters) and T = orbit time of the earth around the sun (in seconds!).
• The formula for the gravitational force can also be found in your formula collection. It reads F = G _* m_{S *} m_E. / r². Here again F means the force, G is the general gravitational constant (6.672 _* 10^-11 m³ / (kg _* s²); you don't have to remember this complicated unit now), m_S. and m_E. are the masses of the sun or Earth (in kilograms) and r is again the distance (see above).

The "weight" of the sun - this is how you calculate m_S.

It looks complicated at first, but on closer inspection it is not. Do not let large exponents and powers of ten in the calculation be put off.

1. You must first equate the two forces: 4 π²r _* m_E./ T² = G _* m_S. * m_E. / r²
2. The balance of forces is independent of the earth's mass m_E., which is also physically clear, because the earth plays the test body in the sun-earth system and the circular motion. You might as well send a ball there.
3. Now solve the equation for the solar mass and get: m_S. = 4 π²r³ / (T² * G).
4. Now insert the known values: r = 1.5 _* 10¹¹ m (mean distance from the earth to the sun), T = 365 days = 365 x 24 x 3600 s = 3.15 _* 10⁷ s as well as the gravitational constant G (see above).
5. You then get m for the mass (weight) of the sun_S. = 2 _* 10³⁰ kg, a very good estimate, the exact value you can find in your formulary is 1.991 _* 10³⁰ kg.