A satellite fired off a planet's surface

In summary, the conversation discusses the calculation of the farthest distance a particle fired tangentially from the surface of a nonrotating spherical planet with mass M and no atmosphere will reach. The formula for calculating the escape speed is used to determine the initial velocity and then the equation for conservation of energy is used to solve for the farthest distance. The correct solution is r = 32R/18.
  • #1
Joules6626
11
0

Homework Statement


A nonrotating spherical planet with mass M and no atmosphere has radius R. A particle is fired off the surface at 3/4 the escape speed. Calculate the farthest distance it reaches from the center of the planet if it's fired of tangentially.


Homework Equations


l = r x p
U = MmG/r
F = -MmG/r^2
dKE = Fdr

The Attempt at a Solution


E1 = E2
1/2mv^2 - GMm/r = 0
1/2mv^2 = GMm/r
V(escape) = sqrt(2GM/r)
v_o = 3/4sqrt(G2M/R)

So I solved the initial velocity, but I'm confused as to what to do next. I tried this:
d1/2m(3/4sqrt(G2M/R))^2 = -MmG/r^2dr
and solving for r
so
9/32(G2M/R) = 2GM/r^3
9/32(1/R) = 1/r^3
r = cubedroot(1/(9/32*1/R)

Am I right?
 
Physics news on Phys.org
  • #2
I'm sorry, the integral should be 18/(32R) = 1/r
r = 32R/18
 
  • #3
Can someone please help me with this?
 

What is a satellite?

A satellite is a man-made object that orbits around a planet, moon, or other celestial body in space.

Why would a satellite be fired off a planet's surface?

A satellite may be fired off a planet's surface for various reasons, such as to study the planet's atmosphere, to collect data on the planet's surface, or to gather information about the planet's orbit and rotation.

How is a satellite fired off a planet's surface?

A satellite is typically launched using a rocket or spacecraft, which provides the necessary propulsion and speed to reach orbit around the planet.

What are the benefits of launching a satellite off a planet's surface?

Launching a satellite off a planet's surface allows scientists to gather valuable data and information about the planet and its surrounding environment, which can aid in further research and exploration.

What precautions are taken when launching a satellite off a planet's surface?

Before launching a satellite, scientists and engineers carefully plan and test the launch to ensure the safety and success of the mission. This may include testing the satellite's components and systems, as well as monitoring weather conditions and potential hazards in the launch area.

Similar threads

  • Introductory Physics Homework Help
Replies
7
Views
995
  • Introductory Physics Homework Help
Replies
1
Views
784
  • Introductory Physics Homework Help
Replies
5
Views
1K
  • Introductory Physics Homework Help
2
Replies
39
Views
3K
  • Introductory Physics Homework Help
Replies
14
Views
2K
  • Introductory Physics Homework Help
Replies
5
Views
1K
  • Introductory Physics Homework Help
Replies
10
Views
2K
  • Introductory Physics Homework Help
Replies
3
Views
1K
  • Introductory Physics Homework Help
Replies
5
Views
1K
  • Introductory Physics Homework Help
Replies
4
Views
2K
Back
Top