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

The planet will experience a force of
`1.72*10^(23)N`

Step-by-step 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(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))((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.