Question

A spacecraft is in orbit around a planet. The radius of the orbit is 2.9 times the radius of the planet (which is R = 71451 km). The gravitational field at the surface of the planet is 21 N/kg. What is the period of the spacecraft's orbit?

Answer #1

Kepler's third law tells us that

MP^2 = (4 pi^2/G) d^3

M is the mass of the planet (in kg)

P the period (in secs)

G is the newtonian grav cst = 6.67 x10^-11 in MKS units

d = orbital radius in m

we can find M knowing that the

surface gravity g = 21N/kg from

g = GM/R^2

M = g R^2/G = 21N/kg x (71451*1000m)^{2} /
6.67x10^{-11} = 1.60735x10^{27} kg

we know that d = 2.9R =207207900 m

so that

P^2 = (4 pi^2/G)(207207900 m)^3/1.60735x10^{27}kg

P^2 = 3.275 x 10^{9}s

**P = 57236.3 s**

An artificial satellite is in a circular orbit around a planet
of radius r = 2.25 × 103 km at a distance d = 380.0 km
from the planet\'s surface. The period of revolution of the
satellite around the planet is T = 1.15 hours. What is the average
density of the planet?

A spacecraft of mass 2 · 10^3 kg is in a circular orbit of
radius R = 10^4 km around a planet. The speed of the spacecraft on
the orbit is 20km/s. Determine the mass of the planet and the
energy of the spacecraft. Submit your answer in the following
form:
• Give your numerical answer for the mass of the planet.
• Give your numerical answer for the energy of the
spacecraft.

In order to measure the mass of an alien planet, imagine you put
a spacecraft moving in a circular orbit of radius 400000 km around
this planet. You happen to be located in the plane of the
spacecraft's orbit. You find that the spacecraft's radio signal
varies periodically in wavelength between 4.99979 mm and 5.00021 mm
.
Assuming that the radio is broadcasting normally, at a constant
wavelength, what is the mass of the planet?

A Titan IV rocket has put your spacecraft in a circular orbit
around Earth at an altitude of 260 km. Calculate the force due to
gravitational attraction between the Earth and the spacecraft in N
if the mass of the spacecraft is 2150 kg.

An Apollo spacecraft describes a circular orbit with a 2414 km
radius around
the moon with a velocity of 5133 km/h. In order to transfer it to a
smaller
circular orbit with a 1930 km radius, the spacecraft is first
placed on an
elliptical path AB by reducing its velocity to 4827 km/h as it
passes through A.
Determine (a) the velocity of the spacecraft as it approaches B on
the elliptic
path, (b) the value to which its velocity...

1).
a). An asteroid is discovered in a nearly circular orbit around
the Sun, with an orbital radius that is 2.83 times Earth's. What is
the asteroid's orbital period ?, its "year," in terms of Earth
years?
b). An artificial satellite is in a circular orbit ?=390.0 km
above the surface of a planet of radius ?=3.65×103 km.
The period of revolution of the satellite around the planet is
?=3.15 hours. What is the average density of the planet?

A satellite is in circular orbit around an unknown planet. A
second, different, satellite also travels in a circular orbit
around this same planet, but with an orbital radius four times
larger than the first satellite. Sue-Bob, the bad physics student,
says: "The gravitational force of the planet depends inversely on
the orbital radius squared. Since the second satellite's orbitai
radius is four times that of the first satellite, the second
satellite experiences on-sixteenth the gravitational force that is
exerted...

A spacecraft lands on a new planet of mass 2.5 x 1024
kg and radius 5100 km. If an object is dropped 3.22 meters above
the surface of the planet how long will it take reach the
surface?

(a) What is the period of the spacecraft's orbit about the
Earth?
Given: A spacecraft of 130 kg mass is in a circular orbit about
the Earth at a height h = 3RE.

A satellite of 400 Kg was originally placed into an orbit of
radius 30,000 km and a period of 31 hours around planet Barigou. a)
Deduce the expression of the mass of this planet in terms of the
Universal constant G, the radius R and the period T. b) Calculate
the value of new time period if the satellite was then put into its
final orbit of radius 10,000 km. c) Estimate the change in the
kinetic energy of the...

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 6 minutes ago

asked 52 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 2 hours ago

asked 2 hours ago