Question

A synchronous satellite, which always remains above the same point on a planet's equator, is put in orbit around Jupiter to study that planet's famous red spot. Jupiter rotates once every 9.84 h. Use the following data to find the altitude of the satellite above the surface of the planet. Jupiter has a mass of 1.90 1027 kg, and a mean radius of 6.99 107 m.

km=?

Answer 1

Answer:

89212744.01088 m

Explanation:

G = Gravitational constant = 6.67 × 10⁻¹¹ m³/kgs²

R = Radius of Jupiter

h = Altitude

M = Mass of Jupiter

T = Time taken by the satellite to complete one rotation around Jupiter

$r=\left(\frac{GMT^2}{4\pi^2}\right)^{\frac{1}{3}}\\\Rightarrow r=\left(\frac{6.67\times 10^{-11}1.9\times 10^{27}\times (9.84\times 3600)^2}{4\pi^2}\right)^{\frac{1}{3}}\\\Rightarrow r=159112744.01088\ m$

Now, r = R+h

$\\\Rightarrow h=r-R\\\Rightarrow h=159112744.01088-6.99\times 10^7\\\Rightarrow h=89212744.01088\ m$

The satellite is at an altitude of 89212744.01088 m above Jupiter's surface

Answer 2

The altitude of the satellite above the surface of the planet is; 89212744.01 m

What is the altitude above the surface?

The formula to find the radius of the planet is;

r = ∛(GMT²/(4π²))

Where;

G is Gravitational constant = 6.67 × 10⁻¹¹ m³/kgs²

r is Radius of Jupiter

M is Mass of Jupiter = 1.9 * 10²⁷ kg

T is Time taken by the satellite to complete one rotation around Jupiter = 9.84 * 3600 seconds

Thus;

r = ∛(6.67 × 10⁻¹¹ × 1.9 * 10²⁷ × (9.84 * 3600)²/(4π²))

r = 159112744.01

The altitude will be gotten from;

h = r - R

where R is mean radius given = 6.99 * 10⁷ m

Thus;

h = 159112744.01 - (6.99 * 10⁷)

h = 89212744.01 m

Read more about Planet Altitude at; https://brainly.com/question/24496270