i need help wit this answer?

Question

An astronaut exploring a distant solar system lands on an unnamed planet with a radius of 2550 km. When the astronaut jumps upward with an initial speed of 3.51 m/s, she rises to a height of 0.72 m. What is the mass of the planet?
kg

Answer 1

This question requires you to know two laws:

1. Conservation of Energy
2. Newton's Law of Gravitation

From the law of conservation of energy, the kinetic energy which the astronaut has at the start of her jump will equal her potential energy at the maximum height:

(1/2)mv² = mgh

Cancel the mass terms and divide both sides by h:

(1/2)v² = gh

v²/(2h) = g

The variable "g" is the acceleration on the astronaut caused by the force of gravity. Her weight on the surface of the planet is related to Newton's Law of gravitation as:

mg = GMm/r²

where:

m = Astronaut's weight
M = Planet's mass
G = Gravitational Constant = 6.6742x10^-11
g = Gravitational Acceleration
r = distance between astronaut's center of mass and the planet's center of mass

Divide both sides of this equation by m to isolate g:

mg = GMm/r²

g = GM/r²

Now set this equation equal to the one developed from the conservation of energy equation:

g = GM/r² = v²/(2h)

Manipulate the terms to solve for M:

GM/r² = v²/(2h)

GM = (vr)²/(2h)

M = (vr)²/(2Gh)

Finally, assume that the planet's center of mass resides at its core. Thus:

r = planet's radius = 2550 km = 2,550,000 m

The planet's mass can now be calculated as:

M = (3.51 * 2550000)²/(2* 6.6742x10^-11 * .72)

M = 8.34x10^23 kg

This planet's mass is about 14% that of the Earth.

Answer 2

First, compute the acceleration of the gravity on the astronaut using conservation of energy:

m*(3.51)^2=m*a*.72
a=(3.52)^2/.72

Next, using
a=GM/r^2
where G is the gravitational constant
6.672x10E-11 Nm^2/kg^2
and r=2550km (convert to meters)

then
M=((3.52)^2/.72)*r^2/G

j

Answer 3

i think of a few persons are lazy. and that i think of a few people would have asked stupid trivial questions (i like a number of those) and dont somewhat have a suitable answer possibly. and a few people ignore to grant proper solutions as they are... waiting 3 days or a million week or greater to get greater solutions to their questions. and a few people would possibly no longer get any proper solutions, they might all be equivalent as judged by potential of the question-asker!

Answer 4

As I said.