A planet has a mass of 7.93 × 1023 kg and a radius of 2.58 × 106 m. (a) What is the acceleration due to gravity on this planet? (b) How much would a 67.0-kg person weigh on this planet?
g= GM/r^2
weight= mg
Is little g = gravity. So I would have
9.8 = G(7.93 × 10^23)/(2.58 × 10^6)
Than I would solve for g?
2012..dangg
To find the acceleration due to gravity on the planet, we can use the formula:
\( g = \frac{G \cdot M}{r^2} \)
where
g = acceleration due to gravity
G = gravitational constant (approximately 6.674 × 10^-11 Nm^2/kg^2)
M = mass of the planet
r = radius of the planet
Let's calculate it step by step:
(a) Acceleration due to gravity:
\( g = \frac{G \cdot M}{r^2} \)
\( g = \frac{6.674 \times 10^{-11} \times 7.93 \times 10^{23}}{(2.58 \times 10^6)^2} \)
Calculating this expression will give us the answer for part (a).
(b) Weight of a person on this planet:
The weight of a person can be found using the formula:
\( W = m \cdot g \)
where
W = weight of the person
m = mass of the person
g = acceleration due to gravity (which we calculated in part (a))
Let's calculate it using the given information:
\( W = 67.0 \times g \)
Calculating this expression will give us the answer for part (b).