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

[quickslant]

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

 

[rsk]

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.

 

[kyle8921]

?

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.