Question

1. As telescopes improve, astronomers are able to detect planets orbiting other stars. One such planet orbits its star at a distance of 2.897 x 109 km. (This is far enough from the star that radius of the star can be ignored.) The star has 1.9 times the mass of our sun (msun = 2 x 1030 kg). If the planet has a mass of 5.4 x 1027 kg, what is the force of gravity it experiences

Answer 1

Answer:

The planet will experience a force of $1.72*10^{23}N$

Explanation:

The force of gravity $F$ experienced by the planet is of mass $m$ at a distance $R$ from a star of mass $M$ is given by

$F = G\dfrac{mM}{R^2},$

where $G= 6.7*10^{-11}Nm^2 /kg^2$ is the gravitational constant.

The mass of the star is two times that of the sun:

$M = 2*M_{sun} = 2*(2* 10^{30}kg) = 4*10^{30}kg$,

the mass $m$ of the planet is

$m = 5.4*10^{27}kg$,

the distance $R$ of the planet form the star is

$R =2.897*10^9km = 2.897*10^{12} m$;

therefore, the force of gravity on the planet will be

$F = (6.7*10^{-11})\dfrac{(5.4*10^{27}kg)(4*10^{30}kg)}{(2.897*10^{12}m)^2}$

$\boxed{F = 1.72*10^{23}N }$

which is the force that the planet will experience.