How Do You Calculate the Mass of the Sun from Mars' Orbital Motion?

In summary, to calculate the orbital speed of Mars relative to the sun, use the formula v= 2(pi)(r)/ T, where r is the radius of the orbit and T is the orbital period. Using this formula, the orbital speed of Mars is approximately 24145.7 m/s. To calculate the mass of the sun, use the formula F = Gm1m2/r^2, where G is the gravitational constant, m1 is the mass of the sun, m2 is the mass of Mars, and r is the distance between them. Equating this formula with the formula for force, mv^2/r, you can solve for m1, which is the mass of the sun.
  • #1
quickslant
90
0
Mars travels around the sun in 1.88 (earth) years, in an approximately circular orbit with radius 2.28 x 10^8 kilometers determine

a)orbital speed of Mars relative to sun
b)mass of the sun..

for part a) i did

v= 2(pi)(r)/ T

which i got 2(3.14)(2.28x10^11 meters)/ 5.93 x10^7 seconds

v= 24145.7 m/s

if that's correct, how do i calculate the mass of the sun
 
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  • #2
Have you done gravitational force?

So you know that the force between them is

F = Gm1m2/r^2

And force also = mv^2/r where m is the mass of mars.

If you equate them, I think you can solve for m1, the mass of the sun.
 
  • #3
?

To calculate the mass of the sun, you can use the formula for centripetal force:

F = (mv^2)/r

Where F is the centripetal force, m is the mass of the planet (in this case, Mars), v is the orbital speed of the planet, and r is the distance from the planet to the sun.

Rearranging the formula to solve for the mass of the sun, we get:

m (mass of sun) = (F x r)/v^2

To find the centripetal force, we can use the formula for gravitational force:

F = G (m1 x m2)/r^2

Where G is the gravitational constant, m1 is the mass of the sun, m2 is the mass of Mars, and r is the distance between them.

Plugging in the values for G, m2 (mass of Mars), and r, we can solve for the mass of the sun:

m (mass of sun) = (6.67 x 10^-11)(6.39 x 10^23 kg)(2.28 x 10^11 m)/ (24145.7 m/s)^2

m (mass of sun) = 1.99 x 10^30 kg

Therefore, the mass of the sun is approximately 1.99 x 10^30 kg.
 

Related to How Do You Calculate the Mass of the Sun from Mars' Orbital Motion?

1. What is the "Kind of Weird Orbital Problem"?

The "Kind of Weird Orbital Problem" refers to a phenomenon in celestial mechanics where the orbit of a planet or satellite does not follow the expected elliptical path predicted by Newton's laws of motion.

2. What causes the "Kind of Weird Orbital Problem"?

The "Kind of Weird Orbital Problem" can be caused by a number of factors, including the gravitational influence of other bodies, non-uniform mass distribution, and relativistic effects.

3. How is the "Kind of Weird Orbital Problem" studied?

Scientists study the "Kind of Weird Orbital Problem" through mathematical models and simulations, as well as observations of planetary and satellite orbits using telescopes and spacecraft.

4. Why is the "Kind of Weird Orbital Problem" important?

The "Kind of Weird Orbital Problem" is important because it challenges our understanding of gravity and the laws of motion, and can have implications for space missions and satellite operations.

5. Can the "Kind of Weird Orbital Problem" be solved?

While the "Kind of Weird Orbital Problem" cannot be solved completely, scientists continue to make progress in understanding and predicting orbital behavior through advancements in technology and theoretical models.

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