Answer:
[tex]W_{star}=1.29x10^{14}N[/tex]
Explanation:
In order to solve this problem, we must start by finding our mass, which can be found by using the following formula:
[tex]F_{g}=mg[/tex]
when solving for the mass we get that:
[tex]m=\frac{F_{g}}{g}[/tex]
which yields:
[tex]m=\frac{690N}{9.81m/s^{2}}=70.34kg[/tex]
Now, generally when using the force of gravity equation on a planet, we take the r to be the distance between the center of the planet to its surface. This is the radius of the planet, since the problem provides us with the diameter, we can use it to find the radius:
[tex]r=\frac{d}{2}[/tex]
so we get that:
[tex]r_{star}=\frac{17.0km}{2}=8.5km[/tex]
we can convert this to meters so all our dimensionals are the same, so we get:
[tex]8.5km*\frac{1000m}{1km}=8500m[/tex]
We can now find our weight at the star by using the force of gravity formula:
[tex]F_{g}=G\frac{m_{1}m_{2}}{r^{2}}[/tex]
when plugging all the provided data in, we get:
[tex]F_{g}=(6.67x10^{-11}N\frac{m^{2}}{kg^{2}})\frac{(70.34kg)(1.99x10^{30}kg)}{(8 500m)^{2}}[/tex]
which yields:
[tex]W=1.29x10^{14}N[/tex]
